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Ђ9Z0g)!F%9VMy)E]mZۥmhsssޯgCt``N~a:s6٬%׍p8P898 -s66`ΰ|3,CY gCP/>؈b3V bgwfl<1rgcC llh -RB=k7=3\٧?)q$ g8m %gO- \8miUkP04isBFz>Wೱ>ZgcC \ey4Y/-Y VH` ygH!y乘dAAܫI+hRhHwq@AEb>ﴒ[UJV\ zqYt);=h\ 4ЂFshD--Tdu˾Z2[ )?[PQ>~Dw>Ƶ++u*L+<>iSgTBx e*7%Y[ 31PU70qϝI&G/_Vz:Y_V?t`Ђ9#`,΅K@!ǜV ̹l}?p(XO9999k-v0gc$=sFAv=b3CA ,#I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!z%drs/downrev.xmlDN@EM͘&[6PY1ݡm߳Aɹ9yoZq  qiuÕ[ˤD)yMMDQABK˚ c`UR;I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!drs/downrev.xmlDN@EM͘bd VBF#iwhuwnx;wrnd֛VƲ A\Zp`zYcklz}5\ 9*Cr)}YA?qv 1Jj7%Xl8.sM~s0 >Ӈte~Qz)2gKno@}eD۹p^.h-ANPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!drs/downrev.xmlPK d m~v0___PPT106___PPT9  Confidence0 (  c "   G  < c $ "PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!92drs/downrev.xmlDAN0EH$vԡ(U u+@EZzII)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!.drs/downrev.xmlDN0EHk*APx$ml{hS X޹suf޴H>4*% ȖN7RaɮJD 9*\Pd0\G6v; r)M+$K 5vPSyX]n?uZfɛR~ytW^P/ZA4= &Dh r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!.drs/downrev.xmlPK  ~v0___PPT106___PPT9  Antecedent 1.   c "   K  < c $0 "PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!˚drs/downrev.xmlDN1M|fL1V 1FOaۮOoÅ^9{ۊ=xf i\`t=;Rp nE5W"A\,PARF]8m})JfHZl\Znm,~C^>DR_"'ԋQL24f).4YPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!˚drs/downrev.xmlPK  ~v0___PPT106___PPT9  Antecedent 2.   c "   @  < c $p"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! @drs/downrev.xmlDN@EM͘&[1%XY!ݡmݭ#w>޹ss&޴H>*x$ N׶T~{Vc,)8Sfv'K!6db2)CQ0p71Rj7&Hm\EEE5 >ӧtc~!f\Z~ej嵼>hrx?[ LrPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! @drs/downrev.xmlPK Pd.~v0___PPT106___PPT9 y6.2.( c "  B  < c $"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!&drs/downrev.xmlD]K1EC7eK]Efn57A\|9NȇY D`;gI,s̴;56\!C sIʆ Ʈr k=#tr$Siq*#+]owe:+u}5<܃`<^hR 5&Dh r PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!&drs/downrev.xmlPK dm.~v0___PPT106___PPT9 z92.3.( c "  C < c $"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!>drs/downrev.xmlDAO@&͐x,Q&ަݡmʿwAo{f޴@>4*% ȖN7R}ϯ :K N`1\0htp%"Ć ]&e(k2F#9F_Iᦕ$H 5vPS&}3ŘWvr[RSϟ_mgԳVMvO7zɟ/4ZPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!>drs/downrev.xmlPK m .~v0___PPT106___PPT9 zcell.( c "  B < c $`"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!zdrs/downrev.xmlDN@EM͘&[ %XY!0mCwP xNYӉ:`AFs\(jy{Liϵ2T0j`l}-sNNd& 6.4Ӧ1 >irŸeq|{]aiqȋI)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!>Ldrs/downrev.xmlDN@M|͘x'[kJb$#~`BwP zyLo2M+N|cY A\Zp`Y<@L .a6`WtZJD!tɠ؎8v; ]%sVI2 5vRSyX_S4" ߯1.S~ "PFd+]+&KB]/4ZPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!>Ldrs/downrev.xmlPK . 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D ^??eg`SMO&{ 3p  * "    / D ^J??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # D bD??opGrS`SMO&{ 5  *( "     D  r050e0eRectangle 2=p   USummary "0 8 D  r0G0e0eRectangle 3p  rAssociation rule mining is a fundamental tool in data mining Several algorithms Apriori: Use a provable mathematical property to improve performance FP-Growth: Stop candidate generation, use effective data structure ARCS CBA MOUCLAS algorithm2P  P""*    D f:??Rectangle 4  W Applications and Evaluation     3333"=     H (  H! H ^PH??eg`SMO&{ 3p  * "    / H ^8??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # H bP??opGrS`SMO&{ 5  *( "    : H  ~8gֳgֳRectangle 1026p   h References,  "0&0   H  ~4gֳgֳRectangle 1027`$  8___PPT10N___PPT90( VJiawei Han and Micheline Kamber. Data Mining: Concepts and Techniques. Morgan Kaufmann Publishers R. Agrawal, T. Imielinski, and A. Swami. Mining association rules between sets of items in large databases. SIGMOD'93, 207-216, Washington, D.C. Rakesh Agrawal and Ramakrishnan Srikant, Fast Algorithms for Mining Association Rules in Large Databases, Proceedings of the Twentieth International Conference on Very Large Databases, pp. 487-499, Santiago, Chile, 1994. J. Han, J. Pei, and Y. Yin:  Mining frequent patterns without candidate generation . In Proc. ACM-SIGMOD 2000, pp. 1-12, Dallas, TX, May 2000. B. Lent,A. Swami,J. Widom: Clustering Association Rules. ICDE '97, 1996| n"j"M"%"T""""  3333"   a Y 0 LA (  L! L ^S??eg`SMO&{ 3p  * "    / L ^H??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # L b0??opGrS`SMO&{ 5  *( "     L  r`20e0eRectangle 2=   X References   "0  X L  r00e0eRectangle 3p @___PPT10 f___PPT9H@ \S. Brin, R. Motwani, and C. Silverstein. Beyond market basket: Generalizing association rules to correlations. SIGMOD'97, 265-276, Tucson, Arizona. J. Han, L. V. S. Lakshmanan, and R. T. Ng, "Constraint-Based, Multidimensional Data Mining", COMPUTER (special issues on Data Mining), 32(8): 46-50, 1999. Craig A. Struble. Association Rule Mining. Slides, Marquette University Yalei Hao . Markus Stumptner . Gerald Quirchmayr. Qing He . Data Mining by MOUCLAS Algorithm for Petroleum Reservoir Characterization from Well Logging Data. AIAI2004. Chew-Hung Lee, Christopher Khoo, Jin-Cheon Na. Automatic Identification of Treatment Relations for Medical Ontology Learning: An Exploratory Study. Knowledge Organization & Discovery Research Group, Division of Information Studies, School of Communication & Information, Nanyang Technological University, Singapore  x ; P x" "*"*&"*"*""   "b         3333"  @ P(  P! 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'   ̙3380___PPT10. c[0C(  C   ~PCcc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r=cc Rectangle 3 >   R    ̙3380___PPT10.$Kv@G P(  C   ~@cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2   p   rEcc Rectangle 3 >   \There are 2^m itemsets, the number of subsets of a set (or the cardinality of the power set)]] ]   ̙3380___PPT10.( c[pC(  C   ~9cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r`-cc Rectangle 3 >   R    ̙3380___PPT10.$Ky@ c[C(  C   ~pDcc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r%cc Rectangle 3 >   R    ̙3380___PPT10.$Ky@g (  C   ~P(cc??Rectangle 7P o  * (c   >   0e0e  ?Rectangle 2   N   (cc  ?Rectangle 3 >   R    ̙3380___PPT10.$K/N@ c[C(  C   ~p)cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rP:cc Rectangle 3 >   R    ̙3380___PPT10.$Ky@ c[C(  C   ~`Hcc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rp;cc Rectangle 3 >   R    ̙3380___PPT10.$K{@ c[C(  C   ~Jcc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rNcc Rectangle 3 >   R    ̙3380___PPT10.$K{@ c[0C(  C   ~飥cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r꣥cc Rectangle 3 >   R    ̙3380___PPT10.$K}@  c[PC(  C   ~p$cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rcc Rectangle 3 >   R    ̙3380___PPT10.$K;@ c[pC(  C   ~cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rpcc Rectangle 3 >   R    ̙3380___PPT10.$K@ c[C(  C   ~Pcc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rcc Rectangle 3 >   R    ̙3380___PPT10.$K@ c[C(  C   ~cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rcc Rectangle 3 >   R    ̙3380___PPT10.$K@  c[C(  C   ~ cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r0cc Rectangle 3 >   R    ̙3380___PPT10.$Kp@  c[C(  C   ~ cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r@cc Rectangle 3 >   R    ̙3380___PPT10.$Kpg@  c[C(  C   ~ )cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r)cc Rectangle 3 >   R    ̙3380___PPT10.$Kpg@ c[4C(  4C 4  ~W(cc??Rectangle 7P o  * (c   > 4  l0e0e Rectangle 2     4  r>(cc Rectangle 3 >   R    ̙3380___PPT10.$Kp؉@g <(  <C <  ~K(cc??Rectangle 7P o  * (c   > <  0e0e  ?Rectangle 2   N <  7(cc  ?Rectangle 3 >   R    ̙3380___PPT10.$K/N@ c[DC(  DC D  ~?(cc??Rectangle 7P o  * (c   > D  l0e0e Rectangle 2     D  rPT(cc Rectangle 3 >   R    ̙3380___PPT10.$Kp؉@ c[0LC(  LC L  ~B(cc??Rectangle 7P o  * (c   > L  l0e0e Rectangle 2     L  rE(cc Rectangle 3 >   R    ̙3380___PPT10.$K`"@ c[PTC(  TC T  ~p:(cc??Rectangle 7P o  * (c   > T  l0e0e Rectangle 2     T  r0J(cc Rectangle 3 >   R    ̙3380___PPT10.$K`"@ c[p\C(  \C \  ~I(cc??Rectangle 7P o  * (c   > \  l0e0e Rectangle 2     \  r <(cc Rectangle 3 >   R    ̙3380___PPT10.$K`"@ c[dC(  dC d  ~(cc??Rectangle 7P o  * (c   > d  l0e0e Rectangle 2     d  rp(cc Rectangle 3 >   R    ̙3380___PPT10.$KPN@ c[lC(  lC l  ~(cc??Rectangle 7P o  * (c   > l  l0e0e Rectangle 2     l  r)cc Rectangle 3 >   R    ̙3380___PPT10.$KP@C t(  tC t  ~䨁cc??Rectangle 7P o  * (c   > t  l0e0e Rectangle 2   l t  rP䨁cc Rectangle 3 >   XHeader table has item, current count, and links to first node of a particular item type.YY Y   ̙3380___PPT10.p |p(  |C |  ~䨁cc??Rectangle 7P o  * (c   > |  l0e0e Rectangle 2   9 |  r䨁cc Rectangle 3 >   %Exercise: Build the rest of the tree.&& &   ̙3380___PPT10. |(  C   ~a威cc??Rectangle 7P o  * (c   >   r0e0e Rectangle 1026   ?   x@]威cc Rectangle 1027 >   %Exercise: Build the rest of the tree.&& &   ̙3380___PPT10.  c[0C(  C   ~i威cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rv威cc Rectangle 3 >   R    ̙3380___PPT10.$K@z@ c[PC(  C   ~o威cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       rpZ威cc Rectangle 3 >   R    ̙3380___PPT10.$K@z@ c[pC(  C   ~r威cc??Rectangle 7P o  * (c   >   l0e0e Rectangle 2       r`U威cc Rectangle 3 >   R    ̙3380___PPT10.$K@@ RJ2(  C   ~`威cc??Rectangle 7P o  * (c   >   0e0e  ?Rectangle 2      p威cc ?Rectangle 3 >   cExercise: What other frequent patterns come from the CP tree? 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ApplicationsApplications Applications History of Association RulesHistory of Association Rules Outlines The Market-Basket Model AssociationsMarket Basket Analysis TransactionAssociation Rules Association Rules MiningMeasuring Interesting RulesMeasuring Interesting RulesMeasuring Interesting RulesMarket Basket AnalysisFrequent ItemsetsStrong Association RulesAssociation Rule Mining Outlines *Apriori Algorithm: A Candidate GenerationGenerating Frequent Itemsets2Apriori: A Candidate Generation-and-test Approach"The Apriori AlgorithmAn ExampleThe Apriori AlgorithmThe Apriori AlgorithmThe Apriori AlgorithmThe Apriori AlgorithmImportant Details of AprioriHow to Generate Candidates?%How to Count Supports of Candidates?Illustrating Apriori PrincipleGenerate Hash Tree&Association Rule Discovery: Hash tree&Association Rule Discovery: Hash tree&Association Rule Discovery: Hash treeSubset Operation!Subset Operation Using Hash Tree!Subset Operation Using Hash Tree!Subset Operation Using Hash TreeFactors Affecting Complexity&Challenges of Frequent Pattern Mining Outlines &Bottleneck of Frequent-pattern Mining6Mining Frequent Patterns Without Candidate GenerationFP Growth (Han, Pei, Yin 2000)'Mining Frequent Patterns With FP-treesFrequent 1-itemsetsFP-Tree ConstructingFP-Tree ConstructingFP-Tree ConstructingFP-Tree ConstructingFP-Tree Constructing FP-Tree Constructing Mining the FP-treeMining the FP-TreeMining the FP-Tree Mining FP-tree.Construct FP-tree from a Transaction Database!Partition Patterns and Databases3Find Patterns Having P From P-conditional Database+Recursion: Mining Each Conditional FP-tree.A Special Case: Single Prefix Path in FP-tree#Scaling FP-growth by DB ProjectionPartition-based Projection Improvements"Benefits of the FP-tree Structure.Mining Various Kinds of Rules or Regularities!Multiple-level Association Rules5ML/MD Associations with Flexible Support ConstraintsMulti-dimensional Association.Multi-level Association: Redundancy Filtering*Multi-Level Mining: Progressive Deepening&Techniques for Mining MD Associations Outlines #Association Rule Clustering System#Association Rule Clustering System#Association Rule Clustering System$Association Rules Clustering SystemPowerPoint ʾĸ Outlines $Classification based on AssociationWhy & How to IntegrateCBA: Three Steps Set of CARRule Generator: Basic ConceptsRG: Basic Concepts (Cont.)RG: An ExampleRG: The AlgorithmRG: The Algorithm(cont.)!Class Builder M1: Basic ConceptsM1: Three StepsM1: Algorithm M1: Two conditions it satisfies Outlines  MOUCLAS AlgorithmMOUCLASThe MOUCLAS algorithm The MOUCLAS algorithmThe MOUCLAS algorithmThe MOUCLAS algorithmThe MOUCLAS algorithmThe MOUCLAS algorithmThe MOUCLAS algorithmThe MOUCLAS algorithmAutomatic Ontology Learning4UMLS Semantic Network (from UMLS Knowledge Source) !Application of Apriori Algorithm*Top Ten Rules Using Normalized Chi SquareEvaluation of PatternsSummary References Referenceswww.lianyimf.com/en/shizz/  õǶ OLE   õƬu< 8@ _PID_HLINKSA !http://www.intsci.ac.cn/en/shizz!http://www.intsci.ac.cn/en/shizz_<  !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./012356789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~      !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~                           ! 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Frequent pattern: pattern (set of items, sequence, etc.) that occurs frequently in a database Motivation: finding regularities in datavH PH P_ )   $O ) `  3333" kc(K(  (! ( ^w??eg`SMO&{ 3p  * "    / ( ^r??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # ( bP??opGrS`SMO&{ 5  *( "     (  r0e0eRectangle 2=p   T Applications    f (  r}0e0eRectangle 3PP H$  tReal market baskets: chain stores keep terabytes of information about what customers buy together. Tells how typical customers navigate stores, lets them position tempting items. Suggests tie-in  tricks, e.g., run sale on diapers and raise the price of beer.<c  $33P    3333""  ,(  ,! , ^??eg`SMO&{ 3p  * "    / , ^ ??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # , bz??opGrS`SMO&{ 5  *( "     ,  rq0e0eRectangle 2=p   U Applications     ,  r0e0eRectangle 3 H$  . Baskets = documents;  items = words in those documents. Lets us find words that appear together unusually frequently, i.e., linked concepts.  Baskets = sentences,  items = documents containing those sentences. Items that appear together too often could represent plagiarism.\; U G A ; U G A    3333"  0(  0! 0 ^??eg`SMO&{ 3p  * "    / 0 ^@??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 0 b@x??opGrS`SMO&{ 5  *( "     0  r0e0eRectangle 2=p   U Applications     0  r{0e0eRectangle 3 H$   Baskets = Web pages;  items = linked pages. Pairs of pages with many common references may be about the same topic.  Baskets = Web pages p ;  items = pages that link to p . Pages with many of the same links may be mirrors or about the same topic./ H ; J / H       J    3333"( ((''4j((  4! 4 ^??eg`SMO&{ 3p  * "    / 4 ^pu??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 4 b0??opGrS`SMO&{ 5  *( "    * 4  rx0e0eRectangle 2=p   dHistory of Association Rules   !z    4C ,Group 324"    4C ,Group 322" % -  4C ,Group 303"- &4 dP??Rectangle 292+~v0___PPT106___PPT9 uTransaction ID  (c   '4 j??Rectangle 302- R    -  4C ,Group 305"- $4 d{??Rectangle 293X~v0___PPT106___PPT9 lItems  (c   %4 j??Rectangle 304- R    -   4C ,Group 307"-  "4 dv??Rectangle 294+ ~v0___PPT106___PPT9 iT1  (c   #4 j w??Rectangle 306-  R   ( -   4C ,Group 309"-   4 dPt??Rectangle 295X ~v0___PPT106___PPT9 xBread, Butter, Eggs  c   !4 jt??Rectangle 308-  R     - 4C ,Group 311" - 4 dy??Rectangle 296+ ~v0___PPT106___PPT9 iT2  (c   4 js??Rectangle 310 - R   ' -  4C ,Group 313"-  4 d??Rectangle 297X ~v0___PPT106___PPT9 wButter, Eggs, Milk  c   4 jv??Rectangle 312-  R    - 4C ,Group 315"- 4 d??Rectangle 298+~v0___PPT106___PPT9 iT3  (c   4 j??Rectangle 314- R    - 4C ,Group 317"- 4 dr??Rectangle 299X~v0___PPT106___PPT9 kButter  c   4 j0s??Rectangle 316- R    -  4C ,Group 319"-  4 d@??Rectangle 300+ ~v0___PPT106___PPT9 iT4  (c   4 j0??Rectangle 318-  R   " -  4C ,Group 321"-  4 dp??Rectangle 301X ~v0___PPT106___PPT9 rBread, Butter  c   4 j??Rectangle 320-  R     4 j`??Rectangle 323   R    4 d??Rectangle 325p 4___PPT10 B___PPT9$ :1993 Agrawal: Mining of association rules from a database 2; c.c;   3333" | {{ww8{(  8! 8 ^𝤥??eg`SMO&{ 3p  * "    / 8 ^p??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 8 bࡤ??opGrS`SMO&{ 5  *( "    0 8  x0e0eRectangle 1026=p   dHistory of Association Rules    8 HA c ?Object 1027P c  8 HA d ?Object 1028v* d  8 HA e ?Object 1029& e ]s| 8  8C .Group 1030"0``q 6  8C .Group 1031"68 f 8C .Group 1032"f v8 fǤ??Rectangle 1033+;~v0___PPT106___PPT9  Algorithm 2 ( cc    w8 l??Rectangle 1034f R   3 f 8C .Group 1035"f t8 fpƤ??Rectangle 1036~v0___PPT106___PPT9 }Year 2(cc   u8 l@ɤ??Rectangle 1037f R   3 R 8C .Group 1038"R r8 f??Rectangle 1039'~v0___PPT106___PPT9 }Scan 2(cc   s8 lˤ??Rectangle 1040R R   = R  8C .Group 1041"R  p8 f@ۤ??Rectangle 1042} ~v0___PPT106___PPT9 Data structure 2(cc   q8 lҤ??Rectangle 1043R  R   7  6 8C .Group 1044" 6 n8 fp??Rectangle 1045 ~v0___PPT106___PPT9  Comments 2 (cc    o8 l@??Rectangle 1046 6 R   $ f  8C .Group 1047"f  l8 fŤ??Rectangle 1048+; ~v0___PPT106___PPT9 nApriori  ( c    m8 lǤ??Rectangle 1049f  R   ! f  8C .Group 1050"f  j8 fp??Rectangle 1051 ~v0___PPT106___PPT9 k1994  (c   k8 l??Rectangle 1052f  R     R  8C .Group 1053"R  h8 fP??Rectangle 1054' ~v0___PPT106___PPT9 jm+1  (c   i8 l??Rectangle 1055R  R    R  8C .Group 1056"R  f8 f??Rectangle 1057} ~v0___PPT106___PPT9  Lk-1 : Hash table Ck: Hash tree d!(ckck c!   g8 l??Rectangle 1058R  R   M  6  8C .Group 1059" 6  d8 f0??Rectangle 1060   ~v0___PPT106___PPT9 1Transaction database with moderate cardinality;  2(2c2   e8 l𔤥??Rectangle 1061 6  R   (  fk 8C .Group 1062" fk b8 f??Rectangle 1063+ ;k~v0___PPT106___PPT9 r Apriori-TID  ( c    c8 l`??Rectangle 1064 fk R   ! f k 8C .Group 1065"f k `8 f??Rectangle 1066 k~v0___PPT106___PPT9 k1994  (c   a8 l ??Rectangle 1067f k R      Rk 8C .Group 1068" Rk ^8 fp??Rectangle 1069 'k~v0___PPT106___PPT9 jm+1  (c   _8 l??Rectangle 1070 Rk R    R  k 8C .Group 1071"R  k? \8 f??Rectangle 1072}  k~v0___PPT106___PPT9 QLk-1 : Hash table Ck: array indexed by TID Sequential structure ID: bitmap R(ck cckc'cR   ]8 l೤??Rectangle 1073R  k R   t  6k 8C .Group 1074" 6k Z8 fМ??Rectangle 1075  k~v0___PPT106___PPT9 XVery slow with larger number of ; Outperforms Apriori with smaller number of ;  Y(YcY   [8 l`??Rectangle 1076 6k R     kfq  8C .Group 1077"kfq  X8 f??Rectangle 1078+k;q ~v0___PPT106___PPT9 jPDM  (c   Y8 l0??Rectangle 1079kfq  R   ! fkq  8C .Group 1080"fkq  V8 fЮ??Rectangle 1081kq ~v0___PPT106___PPT9 k1995  (c   W8 l??Rectangle 1082fkq  R     kRq   8C .Group 1083"kRq  T8 f??Rectangle 1084k'q ~v0___PPT106___PPT9 jm+1  (c   U8 l??Rectangle 1085kRq  R   0 Rk q  !8C .Group 1086"Rk q  R8 f ??Rectangle 1087}k q ~v0___PPT106___PPT9 zHash table and tree  (c   S8 l??Rectangle 1088Rk q  R   K  k6q  "8C .Group 1089" k6q  P8 f??Rectangle 1090 k q ~v0___PPT106___PPT9 /Data Parallelism; with early candidate pruning  0(0c0   Q8 l??Rectangle 1091 k6q  R   & q fw  #8C .Group 1092"q fw  N8 fз??Rectangle 1093+q ;w ~v0___PPT106___PPT9 p Partition  ( c    O8 l`??Rectangle 1094q fw  R   ! fq w  $8C .Group 1095"fq w  L8 f ??Rectangle 1096q w ~v0___PPT106___PPT9 k1995  (c   M8 l犕??Rectangle 1097fq w  R    q Rw  %8C .Group 1098"q Rw  J8 f@??Rectangle 1099q 'w ~v0___PPT106___PPT9 h2  (c   K8 l??Rectangle 1100q Rw  R   ' Rq w  &8C .Group 1101"Rq w  H8 f??Rectangle 1102}q w ~v0___PPT106___PPT9 q Hash Table  ( c    I8 l??Rectangle 1103Rq w  R   Q  q 6w  '8C .Group 1104" q 6w  F8 f??Rectangle 1105 q w ~v0___PPT106___PPT9 5Suitable for large DB with high cardinality of data;  6(6c6   G8 lХ??Rectangle 1106 q 6w  R   ! w f}  (8C .Group 1107"w f}  D8 f??Rectangle 1108+w ;} ~v0___PPT106___PPT9 kARCS  (c   E8 l ??Rectangle 1109w f}  R   ! fw }  )8C .Group 1110"fw }  B8 f??Rectangle 1111w } ~v0___PPT106___PPT9 k1996  (c   C8 l??Rectangle 1112fw }  R    w R}  *8C .Group 1113"w R}  @8 f`??Rectangle 1114w '} ~v0___PPT106___PPT9 g  (c   A8 l@??Rectangle 1115w R}  R    Rw }  +8C .Group 1116"Rw }  >8 fP??Rectangle 1117}w } ~v0___PPT106___PPT9 g  (c   ?8 l@??Rectangle 1118Rw }  R   S  w 6}  ,8C .Group 1119" w 6}  <8 f??Rectangle 1120 w } ~v0___PPT106___PPT9 7Applicable where the users expect to segment the data  8(8c8   =8 l??Rectangle 1121 w 6}  R   $ } f -8C .Group 1122"} f :8 f0??Rectangle 1123+} ;~v0___PPT106___PPT9 nFP Tree  ( c    ;8 lP??Rectangle 1124} f R   ! f}  .8C .Group 1125"f}  88 f??Rectangle 1126} ~v0___PPT106___PPT9 k2000  (c   98 l0??Rectangle 1127f}  R    } R /8C .Group 1128"} R 68 f??Rectangle 1129} '~v0___PPT106___PPT9 h2  (c   78 l??Rectangle 1130} R R    R}  08C .Group 1131"R}  48 fત??Rectangle 1132}} ~v0___PPT106___PPT9 h  (c   58 l𦤥??Rectangle 1133R}  R   4  } 6 18C .Group 1134" } 6 28 f??Rectangle 1135 } ~v0___PPT106___PPT9 ~Applicable in large DB  (c   38 lp??Rectangle 1136 } 6 R    8 l??Rectangle 11378 R     8 HA f ?Object 1138@( f   8 HA g ?Object 1139p* g   8 HA h ?Object 1140vJ h  3333"  tl<T(  <! < ^P??eg`SMO&{ 3p  * "    / < ^ ??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # < bpϤ??opGrS`SMO&{ 5  *( "    - <  xägֳgֳRectangle 2   a Outlines &  "6"   \ <  xΤgֳgֳRectangle 3`P0H$   dIntroduction Basic concepts Apriori Algorithms Frequent-pattern tree Association Rules Clustering System (ARCS) Classification based on Association MOUCLAS algorithm Summary  &&*"+"$"c c"  3333" +#D (  D! D ^Ĥ??eg`SMO&{ 3p  * "    / D ^٤??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # D bȤ??opGrS`SMO&{ 5  *( "    % D  rФ0e0eRectangle 2=p   _The Market-Basket Model    D  rۤ0e0eRectangle 3PPp H$  )A large set of items, e.g., things sold in a supermarket. A large set of baskets, each of which is a small set of the items, e.g., the things one customer buys on one day.L x $f5 $f\   3333"  OG H/(  H! H ^`Ӥ??eg`SMO&{ 3p  * "    / H ^ ڤ??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # H bФ??opGrS`SMO&{ 5  *( "    J H  rɤ0e0eRectangle 3 00  Rules expressing relationships between items Example cereal, milk fruit  People who bought cereal and milk also bought fruit. Stores might want to offer specials on milk and cereal to get people to buy more fruit.5   8 X n5" ""8 " X "   H  r0e0eRectangle 2=p   T Associations     3333"#k  jj@Pj(  P! 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D- collection of transactions (i.e., our data) Transaction identifier TID Each transaction is associated with an identifier, called TIDV0 P0 P2H0 P2"""   3333" C  h(  h! h ^??eg`SMO&{ 3p  * "    / h ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # h bp ??opGrS`SMO&{ 5  *( "    3 h  r0e0eRectangle 2@   m Association Rules Mining"  "0  h  rp0e0eRectangle 3`x H$   Finding frequent patterns, associations, correlations, or causal structures among sets of items or objects in transaction databases, relational databases, and other information repositories. 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This is taken to be the conditional probability, P(B|A) confidence(A B )=P(B|A) The conditional probability, P(B|A) , means that the probability of B happen under A happened.  ZI Z""""pV   3333"   TL4(  !  ^??eg`SMO&{ 3p  * "    /  ^0??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b ??opGrS`SMO&{ 5  *( "    )   r0e0eRectangle 2=p   cMeasuring Interesting Rules   @   r0e0eRectangle 3  zRules are included/excluded based on two metrics minimum support level - how frequently all of the items in a rule appear in transactions minimum confidence level - how frequently the left hand side of a rule implies the right hand side\1  1" " D" " K"   3333"k   LkDk ,k(  !  ^0'??eg`SMO&{ 3p  * "    /  ^'??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b>??opGrS`SMO&{ 5  *( "    $   rF0e0eRectangle 2=p   ^Market Basket Analysis      r`?0e0eRectangle 3`   ] What is I? What is T for transaction ID B? What is s(Chips=>Salsa)? 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 ^@??eg`SMO&{ 3p  * "    /  ^@5??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b+??opGrS`SMO&{ 5  *( "    %   x@G0e0eRectangle 1026=p   YFrequent Itemsets   0   xG0e0eRectangle 1027P  ditemset  any set of items k-itemset  an itemset containing k items frequent (or large) itemset  an itemset that satisfies a minimum support level If I contains m items, how many different itemsets are there? =" " A" " " " " " ." 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Z ZS Z:  ?     ,      3333"  WO7(  !  ^<??eg`SMO&{ 3p  * "    /  ^B??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b@,??opGrS`SMO&{ 5  *( "    +   x00e0eRectangle 1026=p   _Association Rule Mining   A   xC0e0eRectangle 1027`  uTwo basic steps Find all frequent itemsets Satisfying minimum support Find all strong association rules Generate association rules from frequent itemsets Keep rules satisfying minimum confidence   " [ " " " "" [ "    3333"  tlT(  !  ^.??eg`SMO&{ 3p  * "    /  ^E??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b F??opGrS`SMO&{ 5  *( "    -   x&gֳgֳRectangle 2   a Outlines &  "6"   \   x&gֳgֳRectangle 3`P0H$   dIntroduction Basic concepts Apriori Algorithms Frequent-pattern tree Association Rules Clustering System (ARCS) Classification based on Association MOUCLAS algorithm Summary &&"+"$"c c"  3333"W   (  !  ^5??eg`SMO&{ 3p  * "    /  ^`6??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b*??opGrS`SMO&{ 5  *( "    K   r80e0eRectangle 2 p   )Apriori Algorithm: A Candidate Generation* *"*  S   r*0e0eRectangle 3 PH$  WApriori is an influential algorithm for mining frequent itemsets for Boolean association rules. The name is based on the fact that the algorithm uses prior knowledge of frequent itemset properties. Idea: Apriori employs an iterative approach knows as a level-wise search, where k-itemsets are used to explore (k+1)-itemsets. First, the set of frequent 1-itemsets is found. This set is denoted L1. L1 is used to find L2, the set of frequent 2-itemsets, which is used to find L3, and so on, until no more frequent k-itemsets can be found. The finding of each Lk requires one full scan of the database..X ZaeX  3333"s  (  !  ^P1??eg`SMO&{ 3p  * "    /  ^ =??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bA??opGrS`SMO&{ 5  *( "    *   r +0e0eRectangle 2=p   dGenerating Frequent Itemsets      r:0e0eRectangle 3    8Central idea: Build candidate k-itemsets from frequent (k-1)-itemsets Approach Find all frequent 1-itemsets Extend (k-1)-itemsets to candidate k-itemsets Prune candidate itemsets that do not meet the minimum support..O  O    3333"  F>&(  !  ^<??eg`SMO&{ 3p  * "    /  ^L??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bpM??opGrS`SMO&{ 5  *( "    Y   xN0e0eRectangle 1026 p   1Apriori: A Candidate Generation-and-test Approach2 2"2  S   xI0e0eRectangle 1027 PH$  &Apriori pruning principle: If there is any itemset which is infrequent, its superset should not be generated/tested! 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idrs/downrev.xmlDAO1&fHIW$,b FO& ۰vӵ-mǙy޶L> Giõn "DdcRpfv^ӹH&rTR!a:t;8o1R{$sq=JSB=7TU-V}ڕۯI9uiV^{oC$Ip PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! idrs/downrev.xmlPK9FB  0o#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! idrs/downrev.xmlDAO1&fHIW$,b FO& ۰vӵ-mǙy޶L> Giõn "DdcRpfv^ӹH&rTR!a:t;8o1R{$sq=JSB=7TU-V}ڕۯI9uiV^{oC$Ip PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! idrs/downrev.xmlPK@ FB  0o#"@PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK! idrs/downrev.xmlDAO1&fHIW$,b FO& ۰vӵ-mǙy޶L> Giõn "DdcRpfv^ӹH&rTR!a:t;8o1R{$sq=JSB=7TU-V}ڕۯI9uiV^{oC$Ip PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-! idrs/downrev.xmlPK@ 99 3333"  NF@.(  !  ^0죥??eg`SMO&{ 3p  * "    /  ^@񣥇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b죥??opGrS`SMO&{ 5  *( "    #   r𣥁0e0eRectangle 2    ]The Apriori Algorithm   @    r0e0eRectangle 3 P  zDAlgorithm: Apriori Input: Database, D, of transactions; minimum support threshold,min_sup. Output: L, freuqent itemsets in D. Procedure: Ck: Candidate itemset of size k Lk : frequent itemset of size k L1 = find_frequent_1_itemsets(D); for (k = 2; Lk+1 !=; k++) do begin{ Ck = apriori_gen(Lk-1 ,min_sup); for each transaction t in database D do{//scan D for counts Ct =subset(Ck ,t);// get the subsets of t that are candidates For each candidate c Ct c.count++; } Lk = candidates in Ck with min_support }end return L=k Lk; Z@0 Z0 Z0 Zj0 ZB0 Z"v""*""*"""* """"""*"""" """*" &""*"" ""&"" (   (F  ( ""*""*"""""*""*"#  3333"     `| (  !  ^!??eg`SMO&{ 3p  * "    /  ^'??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b@ ??opGrS`SMO&{ 5  *( "    #   rp0e0eRectangle 2    ]The Apriori Algorithm      r` 0e0eRectangle 3 P  Procedure apriori_gen(Lk-1: frequent (k-1)-itemsets; min_sup:minimum support threshold ) for each itemset l1 Lk-1 for each itemset l2Lk-1 if(l1[1]=l2[1]) (l1[2]=l2[2]) & (l1[k-1]=l2[k-1]) Then{ c=join(l1,l2)//join step: generate candidates if has_infrequent_subset(c, Lk-1 ) then delete c;//prune step: remove unfruitful candidate else add c to Ck } return Ckz  "*<" ""*"*"   "*"*""""*"*""*"*""*"*""  $,$,$) $$,$T  ( "   (   3333"X   (  !  ^??eg`SMO&{ 3p  * "    /  ^&??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b??opGrS`SMO&{ 5  *( "    #   rP0e0eRectangle 2    ]The Apriori Algorithm      r0e0eRectangle 3 P  Join is generate candidates set of itemsets Ck from 2 itemsets in Lk-1 Procedure join(p,q) insert into Ck select p.item1, p.item2,..., p.itemk-1, q.itemk-1 from Lk-1 p, Lk-1 q where p.item1=q.item1, ..., p.itemk-2=q.itemk-2, p.itemk-1 = q.itemk-1  - ( (  $   ( ( ( ( (  (  ( ( ( ( ( ( (   3333"   v(  !  ^??eg`SMO&{ 3p  * "    /  ^ ??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b??opGrS`SMO&{ 5  *( "    #   r0"0e0eRectangle 2    ]The Apriori Algorithm      r0eRectangle 3    Procedure has_infrequent_subset(c:candidate k-itemset;Lk-1: frequent (k-1)-itemsets;)//use prior knowledge for each (k-1)-subset s of c if s Lk-1 then return TRUE; return FALSE.  7"*" " ""  "*""      3333"Y      (  !  ^%??eg`SMO&{ 3p  * "    /  ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b0??opGrS`SMO&{ 5  *( "    0   x 0e0eRectangle 1026=p   dImportant Details of Apriori      x0e0eRectangle 10270  "How to generate candidates? Step 1: self-joining Lk Step 2: pruning How to count supports of candidates? Example of Candidate-generation L3={abc, abd, acd, ace, bcd} Self-joining: L3*L3 abcd from abc and abd acde from acd and ace Pruning: acde is removed because ade is not in L3 C4={abcd}  n( nE n1 n, n  n) n  n n"""*"E""*"""""*"*"""""""""" "  "  "  "  "  "  * "*""""#  3333"     x (  !  ^"??eg`SMO&{ 3p  * "    /  ^P??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b??opGrS`SMO&{ 5  *( "    )   r 0e0eRectangle 2P@m   cHow to Generate Candidates?      rp 0e0eRectangle 3H$  Suppose the items in Lk-1 are listed in an order Step 1: self-joining Lk-1 insert into Ck select p.item1, p.item2, & , p.itemk-1, q.itemk-1 from Lk-1 p, Lk-1 q where p.item1=q.item1, & , p.itemk-2=q.itemk-2, p.itemk-1 < q.itemk-1 Step 2: pruning forall itemsets c in Ck do forall (k-1)-subsets s of c do if (s is not in Lk-1) then delete c from CkL n n n n n, n""*-""*" """*""*"* "*"*"""*"*"""*"* "*"*"*"*"""*"" "  "  " ""*" """"*"[  3333",   (  !  ^@)??eg`SMO&{ 3p  * "    /  ^P#)??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b%)??opGrS`SMO&{ 5  *( "    :   x)0e0eRectangle 1026p   n$How to Count Supports of Candidates?% %" %    x@')0e0eRectangle 1027 ``H$  gWhy counting supports of candidates a problem? The total number of candidates can be very huge One transaction may contain many candidates Method: Candidate itemsets are stored in a hash-tree Leaf node of hash-tree contains a list of itemsets and counts Interior node contains a hash table Subset function: finds all the candidates contained in a transaction/ n] n n n/"]""#"&&4" &&"&5""h  3333"o g_  G(  !  ^()??eg`SMO&{ 1p  * "    /  ^)??u`SMO&{ 2@`   Association rules Zhongzhi Shi( "    #  b)??opGrS`SMO&{ 3  *( "    v K C (Group 2"KB   \1??Line 3`@0   d")1??Text Box 4@  Found to be Infrequent8 2g m m     `A o ?1?Object 5pK o "   r`)0e0eRectangle 6=p   hIllustrating Apriori Principle "  \v pK C (Group 7#"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK![ðdrs/downrev.xmlDOMk@ zM*1]E-Dې`v6dInԢUēqnuŅxydeRp'h=Sw!2TPzdR$nb]mkR؇pS(IږߎFWftu{yRofNi:MrPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-![ðdrs/downrev.xmlPKpK,$D  `A n ?1?Object 8pK n *   d*)1??Text Box 9 ` ` Pruned supersets8 2g   3333___PPT10x+-|D\' = @B D' = @BA?%,( < +O%,( < +DN' = @B%(D' = @B%(D' =4@BBBB%(D' =1:Bvisible*o3>+B#style.visibility<*%(+"! #  0%%  (   !   ^.)??eg`SMO&{ 1p  * "    /   ^)??u`SMO&{ 2@`   Association rules Zhongzhi Shi( "    #   b &)??opGrS`SMO&{ 3  *( "        r)0e0eRectangle 2`0   ZGenerate Hash Tree   %v `   C (Group 3" ` B  B \??Line 4 ` PB   \??Line 5`  B   \??Line 6` `     d*)??Text Box 7 q  o 2 3 4 5 6 7  c   B  B \??Line 8}O o   d0+)??Text Box 9o  i1 4 5 c  B   ^??Line 10 O 0 B   ^??Line 11 O    f )??Text Box 126   i1 3 6 c  B  B ^??Line 13 0     f)??Text Box 14`P 1F  o 1 2 4 4 5 7  c   B   ^??Line 15 0     f+)??Text Box 16  o 1 2 5 4 5 8  c   B   ^??Line 17 0    fP,)??Text Box 18  i1 5 9 c  B  B ^??Line 19 p !  f)??Text Box 20 y  i3 4 5 c  B "  ^??Line 21 p #  f,)??Text Box 22p@  u3 5 6 3 5 7 6 8 9 c  B $  ^??Line 23 p  %  fp-)??Text Box 24I?  o 3 6 7 3 6 8  c   fx 0  C *Group 25"m P B  B R??Line 26`B   R??Line 27``   f)??Text Box 28 i1,4,7 c     f')??Text Box 29J i2,5,8 c  B   R??Line 30`   fp)??Text Box 31YS i3,6,9 c     f)??Text Box 32PI u Hash function" g     n)??Rectangle 330 R      f&)1??Text Box 34  YSuppose you have 15 candidate itemsets of length 3: {1 4 5}, {1 2 4}, {4 5 7}, {1 2 5}, {4 5 8}, {1 5 9}, {1 3 6}, {2 3 4}, {5 6 7}, {3 4 5}, {3 5 6}, {3 5 7}, {6 8 9}, {3 6 7}, {3 6 8} You need: Hash function Max leaf size: max number of itemsets stored in a leaf node (if number of candidate itemsets exceeds max leaf size, split the node)T 2 " 2cccZ   3333___PPT10i./J+D=' = @B +"tT SS@iikS(  !  ^)??eg`SMO&{ 2p  * "    /  ^.)??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    #  b /)??opGrS`SMO&{ 4  *( "    3   r/)0e0eRectangle 2=p   m%Association Rule Discovery: Hash tree& & &   d@0)??Text Box 3vf Z a  Y@v  0z C (Group 4"FB~ p@  C (Group 5"p@PB gB \??Line 6p@ PB h \??Line 7 @ B i \??Line 8 @ PH~ p  C (Group 9"@P B dB ^??Line 10pp B e ^??Line 11ppp B f ^??Line 12pp J  p@  C *Group 13" @@P B aB ^??Line 14 p B b ^??Line 15 p B c ^??Line 16 p@ J 0@  C *Group 17"0 B ^B ^??Line 180@ p B _ ^??Line 19p@ p B ` ^??Line 20p@  Pp C *Group 21" @ [ n`U)??Rectangle 22Pp R   B \ ^??Line 23B ] ^??Line 24 0 P p C *Group 25" @@ X n`g)??Rectangle 260 P p R   B Y ^??Line 270  B Z ^??Line 280    @  C *Group 29"   U n@])??Rectangle 30 @  R   B V ^??Line 31  B W ^??Line 32   P J C *Group 33" ` Z  S nW)??Rectangle 34P @ R    T fg)??Text Box 35P dJ }1 5 92 gc   P J C *Group 36"   Q n0=)??Rectangle 37P @ R   ? R f_)??Text Box 38P dJ 1 4 5V gcgc   P J  C *Group 39" p  O n@9)??Rectangle 40P @ R    P f:)??Text Box 41P dJ }1 3 62 gc   P J !C *Group 42" P J  M np6)??Rectangle 43P @ R   + N f8)??Text Box 44P dJ 3 4 5B cgc     "C *Group 45"PP 0:  P J GC *Group 46"   K nI)??Rectangle 47P @ R    L fI)??Text Box 48P dJ i3 6 7 c   P J HC *Group 49"  I nE)??Rectangle 50P @ R    J f1)??Text Box 51P dJ i3 6 8 c    j #C *Group 52"P *    =C *Group 53" z P J AC *Group 54"   E n`1)??Rectangle 55P @ R    F f<)??Text Box 56P dJ i3 5 6 c   P J BC *Group 57"  C n0)??Rectangle 58P @ R    D f@K)??Text Box 59P dJ i3 5 7 c   P J >C *Group 60"pj ? n@T)??Rectangle 61P @ R    @ fE)??Text Box 62P dJ i6 8 9 c     $C *Group 63" P :  P J 7C *Group 64"   ; nD)??Rectangle 65P @ R    < fP5)??Text Box 66P dJ i2 3 4 c   P J 8C *Group 67"  9 npQ)??Rectangle 68P @ R    : fJ)??Text Box 69P dJ i5 6 7 c     %C *Group 70"@` J P J 1C *Group 71"   5 np?)??Rectangle 72P @ R   / 6 f4)??Text Box 73P dJ 1 2 4F gcg   P J 2C *Group 74"  3 nC)??Rectangle 75P @ R   / 4 fpH)??Text Box 76P dJ 4 5 7F gcg     &C *Group 77" ` z P J +C *Group 78"   / nPP)??Rectangle 79P @ R    0 fP)??Text Box 80P dJ }1 2 52 gc   P J ,C *Group 81"  - n A)??Rectangle 82P @ R    . fN)??Text Box 83P dJ }4 5 82 gc   Pp 'C *Group 84"0  @ ( nM)??Rectangle 85Pp R   B ) ^??Line 86B * ^??Line 87x Pp C *Group 88"F  nG)??Rectangle 89Pp R   B  ^??Line 90B  ^??Line 91B  @ ^??Line 92|aB   ^??Line 93\\FB   ^??Line 94a    f04)??Text Box 95L 1,4,78 gg     f`L)??Text Box 96 `v {2,5,80 cc    fK)??Text Box 97L k3,6,9  c    f`C)??Text Box 98V*  Hash Function, ca    f=)??Text Box 99V` = Candidate Hash Tree. ca  '  hR)1??Text Box 100   Hash on 1, 4 or 78 2g m m     | 8)1??Rectangle 101`   R      |PG)1??Rectangle 102 ` 0  R    3333y___PPT10Y+D=' = @B +"U UTPjjT(  !  ^a)??eg`SMO&{ 2p  * "    /  ^p)??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    #  bh)??opGrS`SMO&{ 4  *( "    3   r`p)0e0eRectangle 2P@   m%Association Rule Discovery: Hash tree& & &   dq)??Text Box 3vf Z a  @v  0z C (Group 4"FB~ p@  C (Group 5"p@PB hB \??Line 6p@ PB i \??Line 7 @ B j \??Line 8 @ PH~ p  C (Group 9"@P B eB ^??Line 10pp B f ^??Line 11ppp B g ^??Line 12pp J  p@  C *Group 13" @@P B bB ^??Line 14 p B c ^??Line 15 p B d ^??Line 16 p@ J 0@  C *Group 17"0 B _B ^??Line 180@ p B ` ^??Line 19p@ p B a ^??Line 20p@  Pp C *Group 21" @ \ n'??Rectangle 22Pp R   B ] ^??Line 23B ^ ^??Line 24 0 P p C *Group 25" @@ Y n '??Rectangle 260 P p R   B Z ^??Line 270  B [ ^??Line 280    @  C *Group 29"   V n'??Rectangle 30 @  R   B W ^??Line 31  B X ^??Line 32   P J C *Group 33" ` Z  T n'??Rectangle 34P @ R   + U f@'??Text Box 35P dJ 1 5 9B cgc   P J  C *Group 36"   R n '??Rectangle 37P @ R    S fp'??Text Box 38P dJ i1 4 5 c   P J !C *Group 39" p  P n'??Rectangle 40P @ R    Q fp'??Text Box 41P dJ i1 3 6 c   P J "C *Group 42" P J  N n)??Rectangle 43P @ R    O f|)??Text Box 44P dJ i3 4 5 c     #C *Group 45"PP 0:  P J HC *Group 46"   L nz)??Rectangle 47P @ R    M f{)??Text Box 48P dJ i3 6 7 c   P J IC *Group 49"  J n`y)??Rectangle 50P @ R    K fy)??Text Box 51P dJ i3 6 8 c  a   j $C *Group 52"P *    >C *Group 53" z P J BC *Group 54"   F nr)??Rectangle 55P @ R   + G f0|)??Text Box 56P dJ 3 5 6B cgc   P J CC *Group 57"  D ni)??Rectangle 58P @ R   + E f@o)??Text Box 59P dJ 3 5 7B cgc   P J ?C *Group 60"pj @ nj)??Rectangle 61P @ R   + A f@f)??Text Box 62P dJ 6 8 9B cgc     %C *Group 63" P :  P J 8C *Group 64"   < ne)??Rectangle 65P @ R    = fi)??Text Box 66P dJ }2 3 42 gc   P J 9C *Group 67"  : n e)??Rectangle 68P @ R    ; fn)??Text Box 69P dJ }5 6 72 gc     &C *Group 70"@` J P J 2C *Group 71"   6 nb)??Rectangle 72P @ R   + 7 fd)??Text Box 73P dJ 1 2 4B cgc   P J 3C *Group 74"  4 n0a)??Rectangle 75P @ R   + 5 f`^)??Text Box 76P dJ 4 5 7B cgc  6   'C *Group 77" ` z P J ,C *Group 78"   0 n n)??Rectangle 79P @ R   ? 1 fpZ)??Text Box 80P dJ 1 2 5V cgcg   P J -C *Group 81"  . nm)??Rectangle 82P @ R   ? / fY)??Text Box 83P dJ 4 5 8V cgcg   Pp (C *Group 84"0  @ ) n@x)??Rectangle 85Pp R   B * ^??Line 86B + ^??Line 87x Pp C *Group 88"F  nPY)??Rectangle 89Pp R   B  ^??Line 90B  ^??Line 91B  @ ^??Line 92|aB   ^??Line 93\\FB   ^??Line 94a    fW)??Text Box 95L {1,4,70 cc     f[)??Text Box 96 `v 2,5,88 gg    f w)??Text Box 97L k3,6,9  c    fk)??Text Box 98V*  Hash Function, ca    fX)??Text Box 99V` = Candidate Hash Tree. ca     |r)1??Rectangle 1000   R      |pu)1??Rectangle 101   R   '  h0j)1??Text Box 102   Hash on 2, 5 or 88 2g m m     |w)1??Rectangle 103 0  R    3333y___PPT10Y+D=' = @B +"bU yTqT`jjYT(  !  ^'??eg`SMO&{ 2p  * "    /  ^@'??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    #  b'??opGrS`SMO&{ 4  *( "    3   rЀ'0e0eRectangle 2P@   m%Association Rule Discovery: Hash tree& & &   d'??Text Box 3vf Z a  E@v  0z C (Group 4"FB~ p@  C (Group 5"p@PB hB \??Line 6p@ PB i \??Line 7 @ B j \??Line 8 @ PH~ p  C (Group 9"@P B eB ^??Line 10pp B f ^??Line 11ppp B g ^??Line 12pp J  p@  C *Group 13" @@P B bB ^??Line 14 p B c ^??Line 15 p B d ^??Line 16 p@ J 0@  C *Group 17"0 B _B ^??Line 180@ p B ` ^??Line 19p@ p B a ^??Line 20p@  Pp C *Group 21" @ \ n'??Rectangle 22Pp R   B ] ^??Line 23B ^ ^??Line 24 0 P p C *Group 25" @@ Y nP'??Rectangle 260 P p R   B Z ^??Line 270  B [ ^??Line 280    @  C *Group 29"   V n`'??Rectangle 30 @  R   B W ^??Line 31  B X ^??Line 32   P J C *Group 33" ` Z  T n '??Rectangle 34P @ R    U f'??Text Box 35P dJ }1 5 92 cg   P J  C *Group 36"   R nЛ'??Rectangle 37P @ R    S f'??Text Box 38P dJ i1 4 5 c   P J !C *Group 39" p  P n'??Rectangle 40P @ R    Q f'??Text Box 41P dJ }1 3 62 cg   P J "C *Group 42" P J  N n'??Rectangle 43P @ R    O fp'??Text Box 44P dJ }3 4 52 gc  6   #C *Group 45"PP 0:  P J HC *Group 46"   L n'??Rectangle 47P @ R   ? M fP'??Text Box 48P dJ 3 6 7V gcgc   P J IC *Group 49"  J n@'??Rectangle 50P @ R   ? K f'??Text Box 51P dJ 3 6 8V gcgc  1   j $C *Group 52"P *    >C *Group 53" z P J BC *Group 54"   F n'??Rectangle 55P @ R    G f'??Text Box 56P dJ }3 5 62 gc   P J CC *Group 57"  D n'??Rectangle 58P @ R    E fЉ'??Text Box 59P dJ }3 5 72 gc   P J ?C *Group 60"pj @ n'??Rectangle 61P @ R    A f@'??Text Box 62P dJ }6 8 92 gc     %C *Group 63" P :  P J 8C *Group 64"   < n'??Rectangle 65P @ R    = f'??Text Box 66P dJ i2 3 4 c   P J 9C *Group 67"  : nP'??Rectangle 68P @ R    ; f'??Text Box 69P dJ i5 6 7 c     &C *Group 70"@` J P J 2C *Group 71"   6 n`'??Rectangle 72P @ R    7 f'??Text Box 73P dJ i1 2 4 c   P J 3C *Group 74"  4 n '??Rectangle 75P @ R    5 f0'??Text Box 76P dJ i4 5 7 c     'C *Group 77" ` z P J ,C *Group 78"   0 n`'??Rectangle 79P @ R    1 fP'??Text Box 80P dJ i1 2 5 c   P J -C *Group 81"  . n0'??Rectangle 82P @ R    / f'??Text Box 83P dJ i4 5 8 c   Pp (C *Group 84"0  @ ) n'??Rectangle 85Pp R   B * ^??Line 86B + ^??Line 87x Pp C *Group 88"F  n'??Rectangle 89Pp R   B  ^??Line 90B  ^??Line 91B  @ ^??Line 92|aB   ^??Line 93\\FB   ^??Line 94a    f`'??Text Box 95L {1,4,70 cc     f'??Text Box 96 `v {2,5,80 cc    fВ'??Text Box 97L o3,6,9$ g    f'??Text Box 98V*  Hash Function, ca    f0'??Text Box 99V` = Candidate Hash Tree. ca     |'1??Rectangle 1000 `  R      |p'1??Rectangle 101   R   '  h0'1??Text Box 102   Hash on 3, 6 or 98 2g m m     |'1??Rectangle 103` p  R    3333y___PPT10Y+D=' = @B +" p(  !  ^'??eg`SMO&{ 2p  * "    /  ^'??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    #  b'??opGrS`SMO&{ 4  *( "       r'0e0eRectangle 2=p   XSubset Operation   j 0  A  p ?18c8c    ?Object 3"&u p 7  d@'1??Text Box 4 ?Given a transaction t, what are the possible subsets of size 3?@ 2@c@   3333y___PPT10Y+D=' = @B +"` ._&_tt _(   !   ^P'??eg`SMO&{ 2p  * "    /   ^'??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    #   b'??opGrS`SMO&{ 4  *( "    .    r@'0e0eRectangle 2=p   h Subset Operation Using Hash Tree! ! ! ;7v p  C (Group 3"@B 2 B \??Line 4@x tB 3  \??Line 5x x B 4  \??Line 6x tB 5 B \??Line 7 5 B 6  \??Line 85 5 B 7  \??Line 95 B 8 B ^??Line 10  B 9  ^??Line 11  B :  ^??Line 12  B ; B ^??Line 130 @ B <  ^??Line 14@0 @ B =  ^??Line 15@0 P  >  n'??Rectangle 16p  R   B ?  ^??Line 17B @  ^??Line 180 0  A  n'??Rectangle 19Pp  R   B B  ^??Line 20PB C  ^??Line 21P0 0  D  n'??Rectangle 22 0  R   B E  ^??Line 23  B F  ^??Line 24p p  G  n@'??Rectangle 25  R    H  f'??Text Box 26  y1 5 9. cc      I C *Group 27"   s  n'??Rectangle 28   R    t  f'??Text Box 29   y1 4 5. cc   J  n`'??Rectangle 30` @  R    K  f'??Text Box 31` F  y1 3 6. cc   L  n'??Rectangle 32   R    M  fP'??Text Box 33   y3 4 5. cc   P g N C *Group 34"    q  nP'??Rectangle 35P @ R    r  f'??Text Box 36a g y3 6 7. cc   P h O C *Group 37"    o  n '??Rectangle 38P @ R    p  fp'??Text Box 39a h y3 6 8. cc     P C *Group 40"   P g i C *Group 41"  m  n`'??Rectangle 42P @ R    n  f'??Text Box 43a g y3 5 6. cc   P g j C *Group 44"  k  n'??Rectangle 45P @ R    l  f '??Text Box 46a g y3 5 7. cc   P g Q C *Group 47"  g  n'??Rectangle 48P @ R    h  fp'??Text Box 49a g y6 8 9. cc   P g R C *Group 50"   e  n'??Rectangle 51P @ R    f  f'??Text Box 52a g i2 3 4 c   P h S C *Group 53"  c  n0'??Rectangle 54P @ R    d  f'??Text Box 55b h y5 6 7. cc   P g T C *Group 56"  a  n'??Rectangle 57P @ R    b  f0'??Text Box 58a g y1 2 4. cc   P i U C *Group 59" _  n'??Rectangle 60P @ R    `  f`'??Text Box 61b i y4 5 7. cc   P h V C *Group 62"P 6  ]  n'??Rectangle 63P @ R    ^  fp'??Text Box 64a h y1 2 5. cc   P f W C *Group 65"P6  [  n'??Rectangle 66P @ R    \  f'??Text Box 67` f y4 5 8. cc   X  n'??Rectangle 68 p  R   B Y  ^??Line 69  B Z  ^??Line 70 0 0x @  C *Group 71"`  Z 0  nP'??Rectangle 72@u ^ (a    1  f`'??Text Box 73@ m 1 2 3 5 6  c   B   jo??Line 74PpppB   jo??Line 750B  @ jo??Line 76` @B  @ jo??Line 77 x @  C *Group 78"0  P * C *Group 79"@ .  n'??Rectangle 80Pm ^ (a   /  f'??Text Box 81P g1 + c   ` + C *Group 82"` ,  n'??Rectangle 83` ^ (a    -  f'??Text Box 84Q k2 3 5 6 c  x @ `Z  C *Group 85"p j @ $ C *Group 86"` `Z (  n '??Rectangle 87@u ^ (a   )  f'??Text Box 88@ i3 5 6 c   P9 % C *Group 89"@ ` Z &  n'??Rectangle 90Pm ^ (a   '  f'??Text Box 91P9 g2 + c  x ,   C *Group 92" | @!  C *Group 93",  "  np'??Rectangle 94@u ^ (a   #  f0'??Text Box 95@! g5 6 c   P9  C *Group 96"    n'??Rectangle 97Pm ^ (a   !  fp'??Text Box 98P9 g3 + c   x `I  C *Group 99"*   h0'??Text Box 100` {1,4,70 cc  u  I  C ,Group 101"I   h`'??Text Box 102qI Z a   Pp  C ,Group 103"p   pж'??Rectangle 104Pp R   B   `??Line 105B   `??Line 106B  B `??Line 107u@B   `??Line 108pppB   `??Line 109u @   h'??Text Box 110! {2,5,80 cc      h'??Text Box 111a k3,6,9  c     h0'??Text Box 112v_  Hash Function, ca     h '??Text Box 113` G o transaction  c    3333y___PPT10Y+D=' = @B +"q pp$p(  $! $ ^'??eg`SMO&{ 2p  * "    / $ ^`'??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    # $ b@'??opGrS`SMO&{ 4  *( "    . $  r'0e0eRectangle 2=p   h Subset Operation Using Hash Tree! ! ! B $@ \??Line 3O xB $ \??Line 4O O B $ \??Line 5O xB  $@ \??Line 6r  B  $ \??Line 7r  B  $ \??Line 8r \ B  $@ \??Line 9r R C B  $ ^??Line 10r C B $ ^??Line 11r C B $@ ^??Line 12  B $ ^??Line 13 ? B $ ^??Line 14   $ n'??Rectangle 15u}r  R   B $ ^??Line 16}B $ ^??Line 17 }  $ n'??Rectangle 18u !r  R   B $ ^??Line 19 !B $ ^??Line 20 !  $ n0'??Rectangle 21 }  R   B $ ^??Line 22n }n B $ ^??Line 23 }  $ n'??Rectangle 24   R    $ f'??Text Box 25#   y1 5 9. cc  x    $C *Group 26"   $ n '??Rectangle 27   R    $ f (??Text Box 28   y1 4 5. cc   $ n0'??Rectangle 29 K n  R    $ f'??Text Box 30 P  y1 3 6. cc    $ nP'??Rectangle 31C    R    !$ f'??Text Box 32R  9  y3 4 5. cc  x P g "$C *Group 33"C l9  $ n'??Rectangle 34P @ R    $ f (??Text Box 35a g y3 6 7. cc  x P h #$C *Group 36" l  $ n'??Rectangle 37P @ R    $ fp'??Text Box 38a h y3 6 8. cc  x   $$C *Group 39"C   P g $C *Group 40"  $ n'??Rectangle 41P @ R    $ f'??Text Box 42a g y3 5 6. cc   P g $C *Group 43"  $ n(??Rectangle 44P @ R    $ fP'??Text Box 45a g y3 5 7. cc  x P g %$C *Group 46"   ~$ np(??Rectangle 47P @ R    $ f(??Text Box 48a g y6 8 9. cc  x P g &$C *Group 49" /  |$ n (??Rectangle 50P @ R    }$ f0'??Text Box 51a g i2 3 4 c  x P h '$C *Group 52"r / i  z$ n0'??Rectangle 53P @ R    {$ f(??Text Box 54b h y5 6 7. cc  x P g ($C *Group 55" &  x$ n'??Rectangle 56P @ R    y$ f'??Text Box 57a g y1 2 4. cc  x P i )$C *Group 58" & v$ n(??Rectangle 59P @ R    w$ f (??Text Box 60b i y4 5 7. cc  x P h *$C *Group 61"? 5 t$ n@'??Rectangle 62P @ R    u$ fp (??Text Box 63a h y1 2 5. cc  x P f +$C *Group 64" r$ n (??Rectangle 65P @ R    s$ f'??Text Box 66` f y4 5 8. cc   ,$ n '??Rectangle 67  R   B -$ ^??Line 68% %B .$ ^??Line 69y y x `I /$C *Group 70"0Z e$ f'??Text Box 71` {1,4,70 cc  ]  I f$C *Group 72"I g$ fP (??Text Box 73qI Z a   Pp h$C *Group 74"p o$ n '??Rectangle 75Pp R   B p$ ^??Line 76B q$ ^??Line 77B i$B ^??Line 78u@B j$ ^??Line 79pppB k$ ^??Line 80u @ l$ f (??Text Box 81! {2,5,80 cc    m$ f(??Text Box 82a k3,6,9  c   n$ f'??Text Box 83v_  Hash Function, ca  x @ 0$C *Group 84"  c$ n@(??Rectangle 85@u ^ (a    d$ f(??Text Box 86@ m 1 2 3 5 6  c   B 1$ jo??Line 87. . B 2$ jo??Line 88`@B 3$@ jo??Line 89^ pB 4$@ jo??Line 90 @x d 5$C *Group 91"0* d ]$C *Group 92"d a$ n'??Rectangle 93` ^ (a   b$ f`'??Text Box 94d i3 5 6 c   P ^$C *Group 95" _$ nP(??Rectangle 96Pm ^ (a   `$ f(??Text Box 97P i1 2 + c  x pj  6$C *Group 98" @ W$C *Group 99"pj  [$ p(??Rectangle 100@u ^ (a   \$ h'??Text Box 101@ g5 6 c   P X$C ,Group 102"pj  Y$ p`'??Rectangle 103Pm ^ (a    Z$ h@(??Text Box 104P i1 3 + c  z  p  7$C ,Group 105"0 *    Q$C ,Group 106" p  U$ p'??Rectangle 107@u ^ (a   V$ h(??Text Box 108  e6 c   P R$C ,Group 109"   S$ p`'??Rectangle 110Pm ^ (a    T$ h(??Text Box 111P i1 5 + c  B 8$ lfԔ??Line 112 B 9$ lfԔ??Line 113 0 B :$ lfԔ??Line 114p z @ `Z ;$C ,Group 115"  @ K$C ,Group 116"` `Z O$ p'??Rectangle 117@u ^ (a    P$ h'??Text Box 118@ i3 5 6 c   P9 L$C ,Group 119"@ ` Z M$ p@'??Rectangle 120Pm ^ (a   N$ h'??Text Box 121P9 g2 + c  z ,  <$C ,Group 122": @! E$C ,Group 123",  I$ p'??Rectangle 124@u ^ (a   J$ h'??Text Box 125@! g5 6 c   P9 F$C ,Group 126"  G$ p'??Rectangle 127Pm ^ (a   H$ h'??Text Box 128P9 g3 + c  z @ =$C ,Group 129"@N: P ?$C ,Group 130"@ C$ p'??Rectangle 131Pm ^ (a   D$ h'??Text Box 132P g1 + c   ` @$C ,Group 133"` A$ p'??Rectangle 134` ^ (a    B$ h'??Text Box 135Q k2 3 5 6 c   >$ h'??Text Box 136~ jw o transaction  c    3333y___PPT10Y+D=' = @B +"v{ zz(mz(  (! ( ^(??eg`SMO&{ 2p  * "    / ( ^'??u`SMO&{ 3@`   Association rules Zhongzhi Shi( "    # ( b(??opGrS`SMO&{ 4  *( "    . (  r0 (0e0eRectangle 2=p   h Subset Operation Using Hash Tree! ! ! B (@ \??Line 3O xB ( \??Line 4O O B ( \??Line 5O xB  (@ \??Line 6r  B  ( \??Line 7r  B  ( \??Line 8r \ B  (@ \??Line 9r R C B  ( ^??Line 10r C B ( ^??Line 11r @ B (@ ^??Line 12  B ( ^??Line 13 ? B ( ^??Line 14   ( n@'??Rectangle 15u}r  R   B ( ^??Line 16}B ( ^??Line 17 }  ( n (??Rectangle 18u !r  R   B ( ^??Line 19 !B ( ^??Line 20 !  ( n'??Rectangle 21 }  R   B ( ^??Line 22n }n B ( ^??Line 23 }  ( n'??Rectangle 24   R    ( f0(??Text Box 25#   y1 5 9. cc  x    (C *Group 26"   ( n'(??Rectangle 27   R    ( f)(??Text Box 28   y1 4 5. cc   ( n(??Rectangle 29 K n  R    ( f`(??Text Box 30 P  y1 3 6. cc    ( n'??Rectangle 31C    R    !( f'??Text Box 32R  9  y3 4 5. cc  x P g "(C *Group 33"C l9  ( np(??Rectangle 34P @ R    ( f-(??Text Box 35a g y3 6 7. cc  x P h #(C *Group 36" l  ( n@(??Rectangle 37P @ R    ( f(??Text Box 38a h y3 6 8. cc  x   $(C *Group 39"C   P g (C *Group 40"  ( n0(??Rectangle 41P @ R    ( f(??Text Box 42a g y3 5 6. cc   P g (C *Group 43"  ( nP(??Rectangle 44P @ R    ( f%(??Text Box 45a g y3 5 7. cc  x P g %(C *Group 46"   ( n(??Rectangle 47P @ R    ( f@+(??Text Box 48a g y6 8 9. cc  x P g &(C *Group 49" /  ( n(??Rectangle 50P @ R    ( f(??Text Box 51a g i2 3 4 c  x P h '(C *Group 52"r / i  ( n(??Rectangle 53P @ R    ( f%(??Text Box 54b h y5 6 7. cc  x P g ((C *Group 55" &  ( n(??Rectangle 56P @ R    ( f0(??Text Box 57a g y1 2 4. cc  x P i )(C *Group 58" & ( n`(??Rectangle 59P @ R    ( f(??Text Box 60b i y4 5 7. cc  x P h *(C *Group 61"? 5 ( n!(??Rectangle 62P @ R    ( f*(??Text Box 63a h y1 2 5. cc  x P f +(C *Group 64" }( nP'(??Rectangle 65P @ R    ~( fP(??Text Box 66` f y4 5 8. cc   ,( n'??Rectangle 67  R   B -( ^??Line 68% %B .( ^??Line 69y y x `I /(C *Group 70"0Z p( f@4(??Text Box 71` {1,4,70 cc  ]  I q(C *Group 72"I r( f)(??Text Box 73qI Z a   Pp s(C *Group 74"p z( n$(??Rectangle 75Pp R   B {( ^??Line 76B |( ^??Line 77B t(B ^??Line 78u@B u( ^??Line 79pppB v( ^??Line 80u @ w( f(??Text Box 81! {2,5,80 cc    x( f(??Text Box 82a k3,6,9  c   y( f(??Text Box 83v_  Hash Function, ca  x @ 0(C *Group 84"  n( np((??Rectangle 85@u ^ (a    o( f(??Text Box 86@ m 1 2 3 5 6  c   B 1( jo??Line 87. . B 2( jo??Line 88`@B 3(@ jo??Line 89^ pB 4(@ jo??Line 90 @x d 5(C *Group 91"0* d h(C *Group 92"d l( n#(??Rectangle 93` ^ (a   m( f&(??Text Box 94d i3 5 6 c   P i(C *Group 95" j( n@"(??Rectangle 96Pm ^ (a   k( f(??Text Box 97P i1 2 + c  x pj  6(C *Group 98" @ b(C *Group 99"pj  f( p0(??Rectangle 100@u ^ (a   g( hp(??Text Box 101@ g5 6 c   P c(C ,Group 102"pj  d( p2(??Rectangle 103Pm ^ (a    e( h3(??Text Box 104P i1 3 + c  z  p  7(C ,Group 105"0 *    \(C ,Group 106" p  `( pP0(??Rectangle 107@u ^ (a   a( h`#(??Text Box 108  e6 c   P ](C ,Group 109"   ^( p *(??Rectangle 110Pm ^ (a    _( h0/(??Text Box 111P i1 5 + c  B 8( lfԔ??Line 112 B 9( lfԔ??Line 113 0 B :( lfԔ??Line 114p z @ `Z ;(C ,Group 115"  @ V(C ,Group 116"` `Z Z( pp1(??Rectangle 117@u ^ (a    [( h"(??Text Box 118@ i3 5 6 c   P9 W(C ,Group 119"@ ` Z X( p(??Rectangle 120Pm ^ (a   Y( h2(??Text Box 121P9 g2 + c  z ,  <(C ,Group 122": @! P(C ,Group 123",  T( p(??Rectangle 124@u ^ (a   U( h !(??Text Box 125@! g5 6 c   P9 Q(C ,Group 126"  R( p(??Rectangle 127Pm ^ (a   S( h (??Text Box 128P9 g3 + c  z @ =(C ,Group 129"@N: P J(C ,Group 130"@ N( p0&(??Rectangle 131Pm ^ (a   O( h (??Text Box 132P g1 + c   ` K(C ,Group 133"` L( p(??Rectangle 134` ^ (a    M( h (??Text Box 135Q k2 3 5 6 c   >( h'??Text Box 136~ jw o transaction  c    ?( v'3Ԕ??Rectangle 137 0 R   B @(@ l3??Line 138  B A( l3??Line 139 p  B( v'3Ԕ??Rectangle 140  @ R    C( vP'3Ԕ??Rectangle 141p @  R    D( v'3Ԕ??Rectangle 142 `  R   B E( l3??Line 143  B F( l3??Line 144   G( vp'3Ԕ??Rectangle 145   R    H( v`,(3Ԕ??Rectangle 146   R   ' I( b 3(??Text Box 147  1Match transaction against 11 out of 15 candidates2 2c2   3333y___PPT10Y+D=' = @B +"N    , (  ,! , ^+(??eg`SMO&{ 3p  * "    / , ^,(??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # , b.(??opGrS`SMO&{ 5  *( "    * ,  r.(0e0eRectangle 2=p   dFactors Affecting Complexity    ,  r/(0e0eRectangle 3  Choice of minimum support threshold lowering support threshold results in more frequent itemsets this may increase number of candidates and max length of frequent itemsets Dimensionality (number of items) of the data set more space is needed to store support count of each item if number of frequent items also increases, both computation and I/O costs may also increase Size of database since Apriori makes multiple passes, run time of algorithm may increase with number of transactions Average transaction width transaction width increases with denser data sets This may increase max length of frequent itemsets and traversals of hash tree (number of subsets in a transaction increases with its width)$ P P1 P P Pe P P P$""1"""e" " "  333380___PPT10.9ne"  0p(  0! 0 ^V(??eg`SMO&{ 3p  * "    / 0 ^@F(??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 0 bA(??opGrS`SMO&{ 5  *( "    5 0  rF(0e0eRectangle 2=p   o%Challenges of Frequent Pattern Mining& &" & p 0  rpC(0e0eRectangle 3     Challenges Multiple scans of transaction database Huge number of candidates Tedious workload of support counting for candidates Improving Apriori: general ideas Reduce passes of transaction database scans Shrink number of candidates Facilitate support counting of candidatesf  nu n! nr n u !"r   3333"  h`8H(  8! 8 ^<(??eg`SMO&{ 3p  * "    / 8 ^9(??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 8 bPB(??opGrS`SMO&{ 5  *( "    - 8  xD(gֳgֳRectangle 2   a Outlines &  "6"   P 8  x@(gֳgֳRectangle 3`P0H$   XIntroduction Basic concepts Apriori Algorithms Frequent-pattern tree Association Rules Clustering System (ARCS) Classification based on Association MOUCLAS algorithm Summaryv /&&+"$"c c"  3333"     @x (  @! @ ^M(??eg`SMO&{ 3p  * "    / @ ^pL(??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # @ bD(??opGrS`SMO&{ 5  *( "    5 @  r@=(0e0eRectangle 2=p   o%Bottleneck of Frequent-pattern Mining& &" & x @  rS(0e0eRectangle 3P    zMultiple database scans are costly Mining long patterns needs many passes of scanning and generates lots of candidates To find frequent itemset i1i2& i100 # of scans: 100 # of Candidates: (1001) + (1002) + & + (110000) = 2100-1 = 1.27*1030 ! Bottleneck: candidate-generation-and-test Can we avoid candidate generation?w # W M  $S $  ( ( (   $ (( ((  (((((( ( $,$L  $ >  3333"  NF H.(  H! H ^PK(??eg`SMO&{ 3p  * "    / H ^T(??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # H b08(??opGrS`SMO&{ 5  *( "    e H  r E(0e0eRectangle 2p   5Mining Frequent Patterns Without Candidate Generation86  " & & 6  H  r@(0e0eRectangle 3H$  Grow long patterns from short ones using local frequent items  abc is a frequent pattern Get all transactions having  abc : DB|abc  d is a local frequent item in DB|abc abcd is a frequent patternL>  > m    3333"  @Pk(  P! P ^P(??eg`SMO&{ 3p  * "    / P ^G(??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # P bH(??opGrS`SMO&{ 5  *( "    : P  r`P(0e0eRectangle 2=p   tFP Growth (Han, Pei, Yin 2000)$  ","  f P  r N(0e0eRectangle 3P0`  One problematic aspect of the Apriori is the candidate generation Source of exponential growth Another approach is to use a divide and conquer strategy Idea: Compress the database into a frequent pattern tree representing frequent itemsB Z Z ZB" " 9" " " " "   3333"    ) ! `X (  X! 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(00`8(0 8PLh`@   0`0 `Freeform 36"p 0 , c @AB CDE(FQ&RUVX18c8c    ?? $,HX`xp P @   `P Freeform 37"0 P0 - c @ABCDE(FQ&RUVX18c8c    ?? p@`(@   `Freeform 38"p p0  `娿??Text Box 39} min_support = 340<2cc    b娿??Rectangle 40@ TID Items bought (ordered) frequent items 100 {f, a, c, d, g, i, m, p} {f, c, a, m, p} 200 {a, b, c, f, l, m, o} {f, c, a, b, m} 300 {b, f, h, j, o, w} {f, b} 400 {b, c, k, s, p} {c, b, p} 500 {a, f, c, e, l, p, m, n} {f, c, a, m, p}0(2-cccccc cccccc cccccccccccc cccccccccccc cc  @`   `娿??Text Box 41p PD<4___PPT9 Scan DB once, find frequent 1-itemset (single item pattern) Sort frequent items in frequency descending order, f-list Scan DB again, construct FP-tree0 P2"  @`   f娅??Text Box 42,5 F-list=f-c-a-b-m-p, & "  `           ! 3333"-  (  !  ^娇??eg`SMO&{ 3p  * "    /  ^娇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b娇??opGrS`SMO&{ 5  *( "    4   x威0e0eRectangle 1026=p   h Partition Patterns and Databases! ! !    x`威0e0eRectangle 1027`  ,Frequent patterns can be partitioned into subsets according to f-list F-list=f-c-a-b-m-p Patterns containing p Patterns having m but no p & Patterns having c but no a nor b, m, p Pattern f Completeness and non-redundencyBF w  F w    3333".9.  88 ++.7(  !  ^P樇??eg`SMO&{ 3p  * "    /  ^娇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b娇??opGrS`SMO&{ 5  *( "    D   r威0e0eRectangle 2     ~2Find Patterns Having P From P-conditional Database3 Z3"3 V   r`樁0e0eRectangle 30H$  dStarting at the frequent item header table in the FP-tree Traverse the FP-tree by following the link of each frequent item p Accumulate all of transformed prefix paths of item p to form p s conditional pattern base P{"""& """""   `娿??Rectangle 4 p  oConditional pattern bases item cond. pattern base c f:3 a fc:3 b fca:1, f:1, c:1 m fca:2, fcab:1 p fcam:2, cb:1f 2V0P2 ccc>cp  -v  ) C (Group 5") -    # 0娅1??Text Box 6 f{} c  #   # @娅1??Text Box 7  if:4  c  #   # 樅1??Text Box 8$  ic:1  c  #   # P娅1??Text Box 9 )  ib:1  c  %   # 樅1??Text Box 10 )  ip:1  c    t1??AutoShape 11    t1??AutoShape 12    t1??AutoShape 13G B t1??AutoShape 143G%  #  娅1??Text Box 15\   ib:1  c  %  # 樅1??Text Box 16 )  ic:3  c   B t1??AutoShape 17 3   t1??AutoShape 183  %  # 0樅1??Text Box 19 -  ia:3  c  %  # p樅1??Text Box 20  ib:1  c  %  # 娅1??Text Box 21"  im:2  c  %  # 樅1??Text Box 224 ip:2  c    t1??AutoShape 23   B t1??AutoShape 24    t1??AutoShape 25 u   t1??AutoShape 26%  # 娅1??Text Box 27/ im:1  c    t1??AutoShape 28uu   # 0娅1??Text Box 29   =Header Table Item frequency head f 4 c 4 a 3 b 3 m 3 p 3V>0Zcccc>   ! c @ABCDE(FQ&RUVX18c8c    ?? l hpP0H@    0Freeform 30"'%   " c @ABCDEF QRUVX18c8c    ??@ Freeform 31"'   # c @ABCDE(FQ&RUVX18c8c    ?? 0PX `8(@   0P`Freeform 32"%   $ c @ABCDE(FQ&RUVX18c8c    ?? 0 `0Hx P@   0 Freeform 33"'p 0  % c @ABCDE(FQ&RUVX18c8c    ?? L0H` `Xl@   0 Freeform 34"0   & c @AB8CDEFQRUVX18c8c    ??`( 08@40@  00Freeform 35" ( B ' # |1??Line 36w   ( c @AB CDE(FQ&RUVX18c8c    ?? 8p0P @   0 Freeform 37"0 P  ) c @AB`CDE(FQ&RUVX18c8c    ?? (00`8(0 8PLh`@   0`0 `Freeform 38"p 0 * c @AB CDE(FQ&RUVX18c8c    ?? $,HX`xp P @   `P Freeform 39"0 P0 + c @ABCDE(FQ&RUVX18c8c    ?? p@`(@   `Freeform 40"p p0`              3333""/  H"@"@!!@!(  !  ^P樇??eg`SMO&{ 3p  * "    /  ^` 樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b'樇??opGrS`SMO&{ 5  *( "    :   r 樁0e0eRectangle 2   t*Recursion: Mining Each Conditional FP-tree+ +" +  v  h C (Group 3"P 1~  3  C (Group 4"    # 樅1??Text Box 5   f{} c  #  # +樅1??Text Box 6 !   if:3  c  #  # 樅1??Text Box 7_ / Y  ic:3  c  #  # %樅1??Text Box 8 3  ia:3  c    r1??AutoShape 9     t1??AutoShape 10  _  ! t1??AutoShape 11 Y [  #  樅1??Text Box 12 h m-conditional FP-treeD ccc  <  f*樅??Text Box 13`8 DCond. pattern base of  am : (fc:3)# #"#  x )x  C *Group 14"`"  # `樅1??Text Box 15 f{} c  %  #  "樅1??Text Box 16`'Z if:3  c  %  #  樅1??Text Box 175 ic:3  c    t1??AutoShape 18`  t1??AutoShape 19Z\  # *樅1??Text Box 20)x  am-conditional FP-treeD ccc  :   f樅??Text Box 21p3  BCond. pattern base of  cm : (f:3)" """     # @樅1??Text Box 22 f{} c     #  樅1??Text Box 23` Z  if:3  c     t1??AutoShape 24` T   # 0樅1??Text Box 25q X  cm-conditional FP-treeD ccc  <  f樅??Text Box 26 @ DCond. pattern base of  cam : (f:3)# #"#    # !樅1??Text Box 27   f{} c    #  +樅1??Text Box 28 z if:3  c    t1??AutoShape 29 ll U  # 樅1??Text Box 30 0x cam-conditional FP-treeD ccc      ! 3333""00  //`22.(  !  ^樇??eg`SMO&{ 3p  * "    /  ^樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b 樇??opGrS`SMO&{ 5  *( "    ?   r樁0e0eRectangle 2P@   y-A Special Case: Single Prefix Path in FP-tree. Z.".    r`$樁0e0eRectangle 3 P   :Suppose a (conditional) FP-tree T has a shared single prefix-path P Mining can be decomposed into two parts Reduction of the single prefix path into one node Concatenation of the mining results of the two parts6l xg xl"g"   f樅??Rectangle 4 9 j" 2  v  = C (Group 5"-y~  F  !C (Group 6"  _ + # P樅1??Text Box 7 F  a2:n2Z ckck  _ , # p樅1??Text Box 8 A  a3:n3Z ckck  _ - # 6樅1??Text Box 9A  a1:n1Z ckck    *  .C *Group 10"  " / # N樅1??Text Box 11 *  f{} c   0 t1??AutoShape 12   1 t1??AutoShape 13  _  2 t1??AutoShape 14 Y  0 = "C *Group 15"0 =B #B ^??Line 160 P B $ ^??Line 170 P 5 % f樅??Text Box 18` G b1:m1L "*"*  5 & f樅??Text Box 194 C C1:k1L "*"*  B 'B ^??Line 20@B ( ^??Line 21`@7 ) h樅??Rectangle 22 0 C2:k2L "*"*  7 * h樅??Rectangle 230= C3:k3L "*"*  | x  @ =G  C *Group 24"@ 0mG 0 = C *Group 25" ` =GB B ^??Line 260 P B  ^??Line 270 P 5  f(樅??Text Box 28` G b1:m1L "*"*  5  fp)樅??Text Box 294 C C1:k1L "*"*  B B ^??Line 30@B  ^??Line 31`@7  h樅??Rectangle 32 0 C2:k2L "*"*  7   h`樅??Rectangle 330= C3:k3L "*"*    f樅??Text Box 34P @ , '  vr1. "*     h樅??Rectangle 35 P h i+" 2$  4 x @p 6 S  C *Group 36"p @6 S  F   C *Group 37" p 6 Sa  # 0'樅1??Text Box 38 F  a2:n2Z ckck  a  # &樅1??Text Box 39 A  a3:n3Z ckck  a  # @樅1??Text Box 40A  a1:n1Z ckck    *  C *Group 41"  "  # P(樅1??Text Box 42 *  f{} c    t1??AutoShape 43    t1??AutoShape 44  _   t1??AutoShape 45 Y    f$樅??Text Box 46@P ' J vr1. "*    h&樅??Rectangle 470 P $  g=  2  o/-0-+1+,2 3333" 1  {(  !  ^5樇??eg`SMO&{ 3p  * "    /  ^8樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bN樇??opGrS`SMO&{ 5  *( "    @   r.樁gֳgֳRectangle 2k   z"Scaling FP-growth by DB Projection&# "" " # p   x3樁gֳgֳRectangle 3` H$   xFP-tree cannot fit in memory? DB projection First partition a database into a set of projected DBs Then construct and mine FP-tree for each projected DB Parallel projection vs. Partition projection techniques Parallel projection is space costly^ $  $ $ $   3333"f+2  **$$*(  !  ^p;樇??eg`SMO&{ 3p  * "    /  ^C樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bpD樇??opGrS`SMO&{ 5  *( "    *   r?樁gֳgֳRectangle 2 @   dPartition-based Projection "     xO樁gֳgֳRectangle 3P H$   LParallel projection needs a lot of disk space Partition projection saves itFM n&"& "M $v  C (Group 4".  d@>樅??Text Box 5 k  "Tran. DB fcamp fcabm fb cbp fcamp*#  ""#  #   d`H樅??Text Box 6F =:  p-proj DB fcam cb fcam*  " "  3   d,樅??Text Box 73F :  m-proj DB fcab fca fca:  ""&  J   d@樅??Text Box 8F  :  "b-proj DB f cb & F  ""&"  8   d/樅??Text Box 9 F 2  a-proj DB fc & :  "&"  8   fp2樅??Text Box 10XF |  c-proj DB f & :  "&"  &  f F樅??Text Box 11F   f-proj DB & *   ""     s @AB@CDEFQRUVXo8c8c    ??0L` @@  Freeform 12"FV `   s @AB`CDE(FQ&RUVXo8c8c    ?? d(P8xP H`@   f<iFreeform 13"? 2 !   s @ABChDEFQRUVXo8c8c    ??,X`hHL0@  0Freeform 14" V  B B d??Line 15se F B B d??Line 16e F B B d??Line 17E e F B  d??Line 18 e F B  d??Line 19 eF B  d??Line 20 ejF "  fF樅??Text Box 21(  am-proj DB fc fc fc*  " "    s @AB@C8DE(FQ&RUVXo8c8c    ?? <x(08p80(@@   --Freeform 22"F ` B  d??Line 23 (   s @ABCDE(FQ&RUVXo8c8c    ?? P<xX`@P0@   E?*xFreeform 24" 7  s @ABCDE(FQ&RUVXo8c8c    ?? P<xX`@P0@   E?*Freeform 25"   s @ABCDE(FQ&RUVXo8c8c    ?? P<xX`@P0@   FgMKFreeform 26"V   f`?樅??Text Box 27 (  cm-proj DB f f f*  ""  B  jo??Line 2879 7B   jo??Line 299 B ! jo??Line 30t9 tB " d??Line 31 (  # fA樅??Text Box 32x ? b&      $ s @AB@C8DE(FQ&RUVXo8c8c    ?? <x(08p80(@@   W8WFreeform 33"0 u  3333"3  (  !  ^G樇??eg`SMO&{ 3p  * "    /  ^P1樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b<樇??opGrS`SMO&{ 5  *( "       r =樁0e0eRectangle 2=p   T Improvements        rH樁0e0eRectangle 3  p  CUse hash table to store counts for candidate k-itemsets Remove transactions that do not contain frequent itemsets Sampling the data Partitioning the data If an itemset is frequent, it must be frequent in some partition.6 ZB Z" B"   3333"| 4     (  !  ^<樇??eg`SMO&{ 3p  * "    /  ^K樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bPL樇??opGrS`SMO&{ 5  *( "    1   r`Z樁0e0eRectangle 2 p   k!Benefits of the FP-tree Structure" "" "    xi樁0e0eRectangle 3H$  >Completeness Preserve complete information for frequent pattern mining Never break a long pattern of any transaction Compactness Reduce irrelevant info infrequent items are gone Items in frequency descending order: the more frequently occurring, the more likely to be shared Never be larger than the original database (not count node-links and the count field) For Connect-4 DB, compression ratio could be over 100 h   "h" """>"  3333"5  (  !  ^0T樇??eg`SMO&{ 3p  * "    /  ^g樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bQ樇??opGrS`SMO&{ 5  *( "    =   rX樁0e0eRectangle 2   w-Mining Various Kinds of Rules or Regularities. .".    re樁0e0eRectangle 3   !Multi-level, quantitative association rules, correlation and causality, ratio rules, sequential patterns, emerging patterns, temporal associations, partial periodicity Classification, clustering, iceberg cubes, etc.    3333"6  <4 (  !  ^T樇??eg`SMO&{ 3p  * "    /  ^l樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b]樇??opGrS`SMO&{ 5  *( "    0   rn樁0e0eRectangle 2=p   j Multiple-level Association Rules! !" !    ra樁0e0eRectangle 3 0   !Items often form hierarchy Flexible support settings: Items at the lower level are expected to have lower support. Transaction database can be encoded based on dimensions and levels explore shared multi-level mining "  v pYn  C (Group 4"   `e樿??Rectangle 5p uniform support. &&    R@k樿??Text Box 6@ W ~Milk [support = 10%]$8<2c     Ro樿??Text Box 7 g  2% Milk [support = 6%]$8<2c   /   ^\樿??Text Box 8 0g  Skim Milk [support = 4%]:8<2gc     dR樅??Text Box 9 ~Level 1 min_sup = 5%$ g     fpV樅??Text Box 10 n  ~Level 2 min_sup = 5%$ g    fd樅??Text Box 116 ~Level 1 min_sup = 5%$ g    fn樅??Text Box 12 F  ~Level 2 min_sup = 3%$ g    h`l樅??Rectangle 13 pY ureduced support  &   B b??AutoShape 14@W   b??AutoShape 15 W /@     3333"7    @ (  !  ^W樇??eg`SMO&{ 3p  * "    /  ^W樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bi樇??opGrS`SMO&{ 5  *( "    D   rPg樁0e0eRectangle 2@   ~4ML/MD Associations with Flexible Support Constraints5 5"5    rj樁0e0eRectangle 30PH$  Why flexible support constraints? Real life occurrence frequencies vary greatly Diamond, watch, pens in a shopping basket Uniform support may not be an interesting model A flexible model The lower-level, the more dimension combination, and the long pattern length, usually the smaller support General rules should be easy to specify and understand Special items and special group of items may be specified individually and have higher priority" n. n* n0 n n n".*0    `m樿??Rectangle 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!|"drs/downrev.xmlDAK@Fa؍{QL1;Mٰm=oxoM/|gY,A\[qz2)zuzL#t(C#} LJ_d@:!1M/I; -RUM9Oyd]ُGx"\?ryt.r baPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!|"drs/downrev.xmlPK  ,$D  \   3333UM___PPT10-.+V0D' = @B D' = @BA?%,( < +O%,( < +D' = @B%(DZ' = @B%(D' =K@BBBBPB0B%(/%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+8+0+ +"48  _W`?(  !  ^`c樇??eg`SMO&{ 3p  * "    /  ^ph樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b0o樇??opGrS`SMO&{ 5  *( "    -   rPp樁0e0eRectangle 2=   gMulti-dimensional Association "  6   rpq樁0e0eRectangle 3  H$  DSingle-dimensional rules: buys(X,  milk ) buys(X,  bread ) Multi-dimensional rules: 2 dimensions or predicates Inter-dimension assoc. rules (no repeated predicates) age(X, 19-25 ) occupation(X, student ) buys(X, coke ) hybrid-dimension assoc. rules (repeated predicates) age(X, 19-25 ) buys(X,  popcorn ) buys(X,  coke ) Categorical Attributes finite number of possible values, no ordering among values Quantitative Attributes numeric, implicit ordering among valuesH & 6 6 = 4 7  ;  ( "&" """"&&    &&";""'"    `c樿??Rectangle 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!0hdrs/downrev.xmlDN0 @HCe$.hK`ʲ (h wxmETI|=8z[m%Grz*!!nV^>ML FY09P'Q>EM}*2觶'loGW 3)`C==4T}`dodcV[.Ub$gW\?r#E?9@NAAPK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!0hdrs/downrev.xmlPK  ,$D  \   3333UM___PPT10-.+V0D' = @B D' = @BA?%,( < +O%,( < +D' = @B%(DZ' = @B%(D' =K@BBBBPB0B%(/%(D' =1:Bvisible*o3>+B#style.visibility<*%(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<*D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<*+8+0+ +"9   (   !   ^`樇??eg`SMO&{ 3p  * "    /   ^S樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #   b a樇??opGrS`SMO&{ 5  *( "    S    rU樁0e0eRectangle 2p   -Multi-level Association: Redundancy Filtering.. " " .     rY樁0e0eRectangle 3 iH$  Some rules may be redundant due to  ancestor relationships between items. Example milk wheat bread [support = 8%, confidence = 70%] 2% milk wheat bread [support = 2%, confidence = 72%] We say the first rule is an ancestor of the second rule. A rule is redundant if its support is close to the  expected value, based on the rule s ancestor.S xn x xS"& !9b"]    `Z樿??Rectangle 4"PK![Content_Types].xml|N0 HC+jS8 @:Q۸ ??\o<7p]V޷O(I'6E=, ){Ō4>I)q7UuDހǏ)}nL"Mᴸ&g0eSA)΄2';2 WYu7{ɯΒzŘqFrj9K*(]mOlPK!Z,[ _rels/.relslj0 ``t_Pƈ[>,dgzjǎ?I'f#®Pb-\/Ƿ0Z]nLnp__3.iJV KQBiDžrL,Vʌ/7р4`ANar+m;E/'3U Aںv83/PK!*drs/downrev.xmlDN0 @HCd$.hKbʲ (\6uM՚JXh=oL'NC묂4Ar}2IAVc,))jyyL-贋` *hb3)CՐ0u=Yf F}-3M'od. /4SCqeMM>楿Oߥ>;pwUo[fi[]`p!2PK-![Content_Types].xmlPK-!Z,[ _rels/.relsPK-!*drs/downrev.xmlPKP ,$D  V    3333UM___PPT10-.+V0D' = @B D' = @BA?%,( < +O%,( < +D' = @B%(DZ' = @B%(D' =K@BBBBPB0B%(/%(D' =1:Bvisible*o3>+B#style.visibility<* %(D' =+4 8?dCB0-#ppt_w/2BCB#ppt_xB*Y3>B ppt_x<* D' =+4 8?\CB#ppt_yBCB#ppt_yB*Y3>B ppt_y<* +8+0+  +" :    (j (  (! ( ^@t樇??eg`SMO&{ 3p  * "    / ( ^@b樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # ( b\樇??opGrS`SMO&{ 5  *( "    K (  x0]樁gֳgֳRectangle 20   )Multi-Level Mining: Progressive Deepening$* )""* T (  xP樁gֳgֳRectangle 3`^kH$   \A top-down, progressive deepening approach: First mine high-level frequent items: milk (15%), bread (10%) Then mine their lower-level  weaker frequent itemsets: 2% milk (5%), wheat bread (4%) Different min_support threshold across multi-levels lead to different algorithms: If adopting the same min_support across multi-levels then toss t if any of t s ancestors is infrequent. If adopting reduced min_support at lower levels then examine only those descendents whose ancestor s support is frequent/non-negligible., Z'0 Z80 Z90 Z?0 ZS Z5 Z3 Z0 ZY Z," &"8"9"?"S" "   "  "  "  "  "  "  " " ""Y"G  3333"b ;    0 (  0! 0 ^S樇??eg`SMO&{ 3p  * "    / 0 ^P^樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 0 b^樇??opGrS`SMO&{ 5  *( "    5 0  rp_樁0e0eRectangle 2`p   o%Techniques for Mining MD Associations& &" &  0  rb樁0e0eRectangle 3 H$D  PSearch for frequent k-predicate set: Example: {age, occupation, buys} is a 3-predicate set Techniques can be categorized by how age are treated 1. Using static discretization of quantitative attributes Quantitative attributes are statically discretized by using predefined concept hierarchies 2. Quantitative association rules Quantitative attributes are dynamically discretized into  bins based on the distribution of the data 3. Distance-based association rules This is a dynamic discretization process that considers the distance between data pointsV% Zk Z: Z[ Z" Ze Z$ ZY Z""" "&&&;"& ":"["""e"$ " Y")  3333"<  ld8L(  8! 8 ^樇??eg`SMO&{ 3p  * "    / 8 ^樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 8 b樇??opGrS`SMO&{ 5  *( "    - 8  x{樁gֳgֳRectangle 2   a Outlines &  "6"   T 8  x樁gֳgֳRectangle 3`P0H$   \Introduction Basic concepts Apriori Algorithms Frequent-pattern tree Association Rules Clustering System (ARCS) Classification based on Association MOUCLAS algorithm Summaryz F&+&#"&c c"  3333"=  0( @(  @! @ ^@}樇??eg`SMO&{ 3p  * "    / @ ^{樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # @ bw樇??opGrS`SMO&{ 5  *( "    2 @  r樁0e0eRectangle 2`@   l"Association Rule Clustering System# # #  @ ` 樿??Rectangle 5` ,$D  OARCS: Association Rule Clustering System which borrows ideas from image processing. Essentially, this approach maps pairs of quantitative attributes onto 2-D grid for tuples satisfying a given categorical attribute condition. The grid is then searched for clusters of points, from which the association rules are generated. ARCS steps: Binning Find frequent predicate sets Clustering the association rules h) Z! Z  ZI ZJ" "I&3f  3333"O >    H (  H! H ^樇??eg`SMO&{ 3p  * "    / H ^樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # H b樇??opGrS`SMO&{ 5  *( "    > H  r樁0e0eRectangle 2p   x"Association Rule Clustering System$# " "(#  H `@樿??Rectangle 3` ,$D  ^Binning: The partitioning process is referred to as binning, that is, where the intervals are considered bins. Three common binning strategies are: Equiwidth binning, where the intervalsize of each bin is the same Equidepth: where each bin has approximately the same number of tuples assigned to it Homogeneity-based binning, where bin size is determined so that the tuples in each bin are uniformly distributed.D Z Z""  3333"q ?    @ P (  P! P ^@樇??eg`SMO&{ 3p  * "    / P ^u樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # P b0樇??opGrS`SMO&{ 5  *( "    > P  rt樁0e0eRectangle 2lp   x"Association Rule Clustering System$# " "(# F P `p樿??Rectangle 4`<  Find frequent predicate sets: Once the 2-D array containing the count distribution for each category is set up, this can be scanned in order to find the frequent predicate sets that also satisfy minimum confidence. Clustering the association rules p0 Z20 Z20 Z20 Z2&3f"&&3f   P ZA q ??Object 58 q $D P `p樿??Rectangle 6@ `  (age(X, 34-35 ) income(X, 31K - 50K ) buys(X, high resolution TV )<M 2g>L    3333" @    ` X(  X! X ^v樇??eg`SMO&{ 3p  * "    / X ^樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # X b@樇??opGrS`SMO&{ 5  *( "    A X  rpz樁0e0eRectangle 2 p   {#Association Rules Clustering System$ $ #   X ZA r ??Object 3 r  X `0樿??Rectangle 4 ,$D  Z  $ X  x樁0e0eRectangle 5`i H$  ,JARCS 1. Binning 2. Frequent Items Set 3. Clustering 4. Optimization N C } " D p     '     3333"A   `(  `! ` ^0x樇??eg`SMO&{ 3p  * "    / ` ^樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # ` b~樇??opGrS`SMO&{ 5  *( "    . `  rP樁0e0eRectangle 2 @H$  <fARCS: The successful application of concepts of clustering in classification. BUT only limited to 2D-rules based classifiers of the format A B Classi Using  Binning to discretize the value of quantitative attributes and the accuracy of ACRS is strongly related to the degree of discretization used.  ZI ZMp Z22 Z"   ( 4   `  ~Py樁gֳgֳ??Rectangle 3"üPK![Content_Types].xmlJ0*miG]`Hm6 Xwt?. g#Wi3E).+7 >ON ޑ1ˋz "+R RhB.} /<^ITխ%rHK4uK~I0xM e`|X}đ I`߽N4aG2$RKIZ)4(M9`ctB{m:f@`3n|O,ܗr޾jxR0T ,0@}WBLǬ5vPK!sS=Rdrs/shapexml.xmlXݎ6w|[$' jfi+IHqvWeߣoзǞcȬԋJl||r>rmJ%~(2Sy)W ؛Pb,9JpC?zjjK3&[ +fWZsåeD? qb`Jn\c){5)s2$D ^ `'o{ lcZ8=prv07HTkivkr0pv(~~S9`eU0/6QEA OFVű3"`S$8#d!ߣ`Z3W"h(Mmg"'!p8K!.eMRK͜yB:&/5FqSx?{)oro_%xM#J & ͬ"]Cy9{I(8UFfs Sg'4,2m~N9/`μ&y{B2Gr .Aho^"$`/>7BULRR3 4\`0 4fGV6#8lDW6 ecxe)h]@ Z6F,Q `Z(i ~Yh{WX;mb$4>qz]Rtr:9qp|usd%C$x*2鳲6E9g.ׅ2]̅i̶ Dg.!=m}ꆔ|]t:gΰЍ!(ʼVHHi#'8'p],K(dS>snh`vTe(Qj"\>/)a\u{xs`sby:# MB% @b/ҕ(p18h;֙{R(_/WQ!Xj*Yǻ~^=+P ~hQ5:ߑT4z&@% cT\U^0!3z5CW;Ѷomf]U[oS.9 @9uX/l՟*LKxrlo?xF)ܡ+^OzIۯPK!H&drs/downrev.xmlDOK@GaXhbE-9(&i kӻ [Ӊ#9ZVp?I@WV\+|@L FZ^_-0:Q>GM}.2''loOWK妓$K-Dž{zn:?Fz풏z-xCQ9Ufx|h]?xQ2,K @NA,\PK-![Content_Types].xmlPK-!1_a ._rels/.relsPK-!sS=R)drs/shapexml.xmlPK-!H&drs/downrev.xmlPK`0 { ARCS Features(( g6   33334,___PPT10 ."B  xp hX(  h! h ^y樇??eg`SMO&{ 3p  * "    / h ^}樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # h bІ樇??opGrS`SMO&{ 5  *( "    3 h  ~`樁gֳgֳRectangle 1026   a Outlines &  "6"   Z h  ~P樁gֳgֳRectangle 1027`P0H$   \Introduction Basic concepts Apriori Algorithms Frequent-pattern tree Association Rules Clustering System (ARCS) Classification based on Association MOUCLAS algorithm Summaryz q&$&&( &(&&(  3333"|C   p(  p! p ^ 樇??eg`SMO&{ 3p  * "    / p ^`~樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # p b樇??opGrS`SMO&{ 5  *( "    1 p  r樁0e0eRectangle 2`0t   k#Classification based on Association$ $ $  p  r樁0e0eRectangle 3P`  ":Classification rule mining versus Association rule mining Aim A small set of rules as classifier All rules according to minsup and minconf Syntax X y X Y :  M     :  M        3333"D  ZR x:(  x! x ^P樇??eg`SMO&{ 3p  * "    / x ^Џ樇??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # x b`樇??opGrS`SMO&{ 5  *( "    $ x  rp樁0e0eRectangle 2@`   ^Why & How to Integrate   K x  r@0e0eRectangle 3@  !Both classification rule mining and association rule mining are indispensable to practical applications. The integration is done by focusing on a special subset of association rules whose right-hand-side are restricted to the classification class attribute. CARs: class association rules2 Z Z  "  3333"E   (  !  ^@F??eg`SMO&{ 3p  * "    /  ^I??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bM??opGrS`SMO&{ 5  *( "       rJ0e0eRectangle 2=    XCBA: Three Steps      rD0e0eRectangle 3`   Discretize continuous attributes, if any Generate all class association rules (CARs) Building a classifier based on the generated CARs. "   3333"MF   (  !  ^6??eg`SMO&{ 3p  * "    /  ^K??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bpL??opGrS`SMO&{ 5  *( "    ,   rT0e0eRectangle 2`0t   f Set of CAR        r`50e0eRectangle 3p   To generate the complete set of CARs that satisfy the user-specified minimum support (minsup) and minimum confidence (minconf) constraints. To build a classifier from the CARs.    3333"G @ r(  !  ^08??eg`SMO&{ 3p  * "    /  ^4??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b9??opGrS`SMO&{ 5  *( "    2   xPB0e0eRectangle 1026`D   fRule Generator: Basic Concepts   u   xM0e0eRectangle 1027P  _Ruleitem :condset is a set of items, y is a class label Each ruleitem represents a rule: condset->y condsupCount The number of cases in D that contain condset rulesupCount The number of cases in D that contain the condset and are labeled with class y Support=(rulesupCount/|D|)*100% Confidence=(rulesupCount/condsupCount)*100%  Zt Z  Z. Z  ZO ZL Z "@"","  ."  O""" "!""`  3333" H 2 * `  (  !  ^pC??eg`SMO&{ 3p  * "    /  ^N??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bD??opGrS`SMO&{ 5  *( "    .   x@=0e0eRectangle 2050=    bRG: Basic Concepts (Cont.)      xO0e0eRectangle 2051   MFrequent ruleitems A ruleitem is frequent if its support is above minsup Accurate rule A rule is accurate if its confidence is above minconf Possible rule For all ruleitems that have the same condset, the ruleitem with the highest confidence is the possible rule of this set of ruleitems. The set of class association rules (CARs) consists of all the possible rules (PRs) that are both frequent and accurate. Z6 Z Z7 Z Z Zx Z"""""" """""^" "">"""""""  3333"\I   (  !  ^0A??eg`SMO&{ 3p  * "    /  ^ W??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b3??opGrS`SMO&{ 5  *( "       r`P0e0eRectangle 2=!   VRG: An Example      rQ0e0eRectangle 3  A ruleitem:<{(A,1),(B,1)},(class,1)> assume that the support count of the condset (condsupCount) is 3, the support of this ruleitem (rulesupCount) is 2, and |D|=10 then (A,1),(B,1) -> (class,1) [supt=20% (rulesupCount/|D|)*100% confd=66.7% (rulesupCount/condsupCount)*100%] & Z  Zv Z  ZR Z&"  !  %    "  R   3333"NJ   (  !  ^@??eg`SMO&{ 3p  * "    /  ^7??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b`>??opGrS`SMO&{ 5  *( "       r;0e0eRectangle 2@`t   YRG: The Algorithm       r <0e0eRectangle 3`Pp2 P___PPT100(___PPT9   1 F 1 = {large 1-ruleitems}; 2 CAR 1 = genRules (F 1 ); 3 prCAR 1 = pruneRules (CAR 1 ); //count the item and class occurrences to determine the frequent 1-ruleitems and prune it 4 for (k = 2; F k-1 ; k++) do C k = candidateGen (F k-1 ); //generate the candidate ruleitems Ck using the frequent ruleitems Fk-1 6 for each data case d D do //scan the database C d = ruleSubset (C k , d); //find all the ruleitems in Ck whose condsets are supported by d 8 for each candidate c C d do 9 c.condsupCount++; 10 if d.class = c.class then c.rulesupCount++; //update various support counts of the candidates in Ck 11 end 12 end ZD nZ^ nZ7 ZK nZK nZ Z""*""* ""*""*""*}" """"""**" " """"*"""*("*Z"*""""""""*""*"#"*"""I "  "  "  "  "  "    "  *  " * "  "  "  " H "  *  "  "  "  "  "  [  3333" K  ] U = (  !  ^5??eg`SMO&{ 3p  * "    /  ^ E??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bE??opGrS`SMO&{ 5  *( "    &   rk0e0eRectangle 2=p   `RG: The Algorithm(cont.)   L   rz0e0eRectangle 3`  8___PPT10N___PPT90( 13 F k = {c C k | c.rulesupCount minsup}; //select those new frequent ruleitems to form Fk 14 CAR k = genRules(F k ); //select the ruleitems both accurate and frequent 15 prCAR k = pruneRules(CAR k ); 16 end 17 CARs = k CAR k ; 18 prCARs = k prCAR k ; 1  nb ""*"""*""""a"*""* ""*"=""*" ""*""""""  "*"*""""  "*"*""@   3333" L  I A ) (  !  ^`k??eg`SMO&{ 3p  * "    /  ^P]??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bp^??opGrS`SMO&{ 5  *( "    0   r]0e0eRectangle 2@`   j Class Builder M1: Basic Concepts! !" ! .   rl0e0eRectangle 3 D___PPT10$r___PPT9TL Given two rules ri and rj, define: ri f rj if The confidence of ri is greater than that of rj, or Their confidences are the same, but the support of ri is greater than that of rj, or Both the confidences and supports are the same, but ri is generated earlier than rj. Our classifier is of the following format: <r1, r2, & , rn, default_class>, where ri R, ra f rb if b>a|. Z Z+ Z! Z Z"*"* "*"  "*" ( (9 ( (: ( ( +""*"*"*" "  * "*"   w  3333" M  Z R : (  !  ^@X??eg`SMO&{ 3p  * "    /  ^W??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b `??opGrS`SMO&{ 5  *( "       r i0e0eRectangle 2D   WM1: Three Steps   R   rb0e0eRectangle 3P    The basic idea is to choose a set of high precedence rules in R to cover D. Sort the set of generated rules R Select rules for the classifier from R following the sorted sequence and put in C. Each selected rule has to correctly classify at least one additional case. Also select default class and compute errors. Discard those rules in C that don t improve the accuracy of the classifier. Locate the rule with the lowest error rate and discard the rest rules in the sequence.O Zv Zy ZL ZW ZO"v"y"L"W "    3333"N d\ D(  !  ^`??eg`SMO&{ 3p  * "    /  ^_??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b_??opGrS`SMO&{ 5  *( "       rm0e0eRectangle 2!=#   U M1: Algorithm   ^    r@j0e0eRectangle 3  @___PPT10 f___PPT9H@  1 R = sort(R); //Step1:sort R according to the relation  f 2 for each rule r R in sequence do 3 temp = ; 4 for each case d D do //go through D to find those cases covered by each rule r 5 if d satisfies the conditions of r then 6 store d.id in temp and mark r if it correctly classifies d; 7 if r is marked then 8 insert r at the end of C; //r will be a potential rule because it can correctly classify at least one case d 9 delete all the cases with the ids in temp from D; 10 selecting a default class for the current C; //the majority class in the remaining data 11 compute the total number of errors of C; 12 end 13 end // Step 2 14 Find the first rule p in C with the lowest total number of errors and drop all the rules after p in C; 15 Add the default class associated with p to end of C, and return C (our classifier). //Step 3z Z""4"c  "" ""  "c" """"" c  "" ""  c""D"""""""" ""'""" """"""""""!""""D""/"""""   3333"mO  @ (  !  ^@a??eg`SMO&{ 3p  * "    /  ^x??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  be??opGrS`SMO&{ 5  *( "    /   r0n0e0eRectangle 2!=#   iM1: Two conditions it satisfies  "      rc0e0eRectangle 3  Each training case is covered by the rule with the highest precedence among the rules that can cover the case. Every rule in C correctly classifies at least one remaining training case when it is chosen. "   3333"P  H@` ((  !  ^py??eg`SMO&{ 3p  * "    /  ^z??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bn??opGrS`SMO&{ 5  *( "    -   xogֳgֳRectangle 2   a Outlines &  "6"   0   xPogֳgֳRectangle 3`P0H$   8Introduction Basic concepts Apriori Algorithms Frequent-pattern tree Association Rules Clustering System (ARCS) Classification based on Association MOUCLAS algorithm SummaryV && &&(  3333" Q v n V (  !  ^pp??eg`SMO&{ 3p  * "    /  ^v??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bv??opGrS`SMO&{ 5  *( "    E   r0e0e0eRectangle 2=p    MOUCLAS Algorithm0  cc0 F   r\0e0eRectangle 3H$  T:Assumption: MOUCLAS algorithm assumes that the initial association rules can be agglomerated into clustering regions The implication of the form of the Mouclas Pattern (so called MP) : Cluster(D)t y where Cluster(D)t is a cluster of D, t = 1 to m, and y is a class label.   m( D( <8 PO0 P                  (         (% (  """T     O   3333"a R    (  !  ^q??eg`SMO&{ 3p  * "    /  ^q??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bpg??opGrS`SMO&{ 5  *( "       r r0e0eRectangle 2   YMOUCLAS  c6    rPf0e0eRectangle 3`H$  Definitions: Frequency of Mouclas Patterns Accuracy of Mouclas Patterns Reliability of Mouclas Patterns Task of Mouclas: To discover MPs that have support and confidence greater than the user-specified minimum support threshold (called minsup), and minimum confidence threshold (called minconf) and minimum reliability threshold (called minR) respectively, and to construct a classifier based upon MPs.  8 Zg8 Z<8 Z<8 Z<8 Z " """ " """ """" "" "" ""d"","",""9""""bO         3333"S   (  !  ^ {??eg`SMO&{ 3p  * "    /  ^Y??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bZ??opGrS`SMO&{ 5  *( "    c   r[0e0eRectangle 2p   The MOUCLAS algorithm T c6c6 c6c     rr0e0eRectangle 3 pH$  Two steps: Step 1. Discovery of the frequent and accurate and reliable MPs. Step 2. Construction of a classifier, called De-MP, based on MPs. x Z<x Z< " " " " " " " " " 0" " " " " *;   H  33334,___PPT10 ."# T    (  !  ^t??eg`SMO&{ 3p  * "    /  ^u??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  bw??opGrS`SMO&{ 5  *( "    P   rPx0e0eRectangle 2p   The MOUCLAS algorithmB c6c6 c6    r@0e0eRectangle 3)H$   The core of the first step in the Mouclas algorithm is to find all cluster_rules that satisfy minsup and minconf and minR. Let C denote the dataset D after dimensionality reduction processing. A cluster_rule represents a MP, namely a rule: cluset y, where cluset is a set of itemsets from a cluster Cluster(C)t, y is a class label, y Y.   ( ] ""                .            %    (         B        |     Z  3333" U q i Q (  !  ^??eg`SMO&{ 3p  * "    /  ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b0??opGrS`SMO&{ 5  *( "    P   r0e0eRectangle 2p   The MOUCLAS algorithmB c6c6 c6 6   r0e0eRectangle 3` H$  DNAlgorithm of the first step: Mouclas Mining frequent and accurate and reliable Mouclas patterns (MPs) Input: A training transaction database, D; minimum support threshold (minsup); minimum confidence threshold (minconf) ; minimum reliability threshold (minR) Output: A set of frequent and accurate and reliable Mouclas patterns (MPs)pf8 Z<8 Z<%             "    !  #             bB          33334,___PPT10 ." V W O 7 (  !  ^P??eg`SMO&{ 3p  * "    /  ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b0??opGrS`SMO&{ 5  *( "    P   r 0e0eRectangle 2    The MOUCLAS algorithmB c6c6 c6    rЎ0e0eRectangle 3)H$  *Methods: (1)Reduce the dimensionality of transactions d, which efficiently reduces the data size by removing irrelevant or redundant attributes (or dimensions) from the training data, and (2)Identify the clusters of database C for all transactions d after dimensionality reduction on attributes Aj in database C, based on the Mountain function, which is a fuzzy set membership function, and specially capable of transforming quantitative values of attributes in transactions into linguistic terms, and (3)Generate a set of MPs that are both frequent and accurate, namely, which satisfy the user-specified minimum support (called minsup) and minimum confidence (called minconf) and minimum reliability (called minR) constraints. | 8 Z<8 Z<":"""""".""*" """"""""C""!""""""~           P 33334,___PPT10 ."qW  @ (  !  ^@??eg`SMO&{ 3p  * "    /  ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #  b??opGrS`SMO&{ 5  *( "    P   r0e0eRectangle 2p   The MOUCLAS algorithmB c6c6 c6    r0e0eRectangle 3$ ^___PPT10___PPT9| ~1 X = reduceDim (I); // reduce the dimensionality on the set of all items I of in D 2 Cluster(C)t = genCluster (C); // identify the complete clusters of C 3 for each Cluster(C)t do E = genClusterrules(cluset, class); // generate a set of candidate cluster_rules 4 for each transaction d C do 5 Ed = genSubClusterrules (E, d); // find all the cluster_rules in E whose cluset are supported by d 6 for each e Ed do 7 e. clusupCount++; // accumulate the clusupCount of the cluset of cluster_rule e 8 if d.class = e.class then e.cisupCount++ // accumulate the cisupCount of cluster_rule e supported by d 9 end 10 end 11 F = {e E | e.cisupCount minsupi }; // construct the set of frequent cluster_rules 12 MP = genRules (F); //generate MP using the genRules function by minconf and minR 13 end 14 MPs = *" MP; // discover the final set of MPs rC Z Z""""8""""c """"*""(""" c  """"""*"c """ """ ""c  "  "  "  "   "  "  "  "  " $c$  ("((*(("(("(("( ("(("(("(("(("(d("(("(,c,  0"00"00"00"00"0000"00"00*00"00"04c4 8"88"88"8 8"88"88"88"8 8"88"88"8, where MPi R, i = 1 to n, MPa {"MPb if n b > a 1 and a, b i, C *" cluset of MPi38 Z8 Z%8 Z[0 Z("2"9"""" ""h""""" "" ")"" *"N""""*""*""*"" * ""*""""""*"""*"""""""""" """" "*"T   .   4  3333"B Y     (   !   ^??eg`SMO&{ 3p  * "    /   ^p??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    #   b@??opGrS`SMO&{ 5  *( "    P    r@|0e0eRectangle 2p   The MOUCLAS algorithmB c6c6 c6 k    r0e0eRectangle 3H$  yAlgorithm: Mouclas constructing De-MP Classifier Input: A training database after dimensionality reduction, C; The set of frequent and accurate and reliable Mouclas patterns (MPs) Output: De-MP Classifier Methods: (1)Identify the order of all discovered MPs based on the definition of precedence and sequence them according to decreasing precedence order. (2)Determine possible MPs for De-MP classifier from R following the descending sequence of MPs. (3)Discard the MPs which cannot contribute to the improvement of the accuracy of the De-MP classifier and keep the final set of MPs to construct the De-MP classifier. 1H H H   """ "" """5"" """"" """""" " "  " 1 "  "  "  "  "  "  "  " % "  "  "  " C "  " & "  "  "  "  " F0      33334,___PPT10 ."Z  ((  (! ( ^ ??eg`SMO&{ 3p  * "    / ( ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # ( b??opGrS`SMO&{ 5  *( "    V (  xЗ0e0eRectangle 1026@   The MOUCLAS algorithmB c6c6 c6 x  (  x0e0eRectangle 1027 H$  1 R = sort(R); // sort MPs based on their precedence 2 for each MP R in sequence do 3 temp = ; 4 for each transaction d C do 5 if d satisfies the cluset of MP then 6 store d.ID in temp; 7 if MP correctly classifies d then 8 insert MP at the end of L; 9 delete the transaction who has ID in temp from C; 10 selecting a default class for the current L; // determine the default class based on majority class of remaining transactions in C 11 end 12 compute the total number of errors of L; // compute the total number of errors that are made by the current L and the default class 13 end 14 Find the first MP in L with the lowest total number of errors and discard all the MPs after the MP in L; 15 Add the default class associated with the above mentioned first MP to end of L; 16 De-MP classifier = L Hvx Z"""",""""" """"" """"""" """"""""""" """"""""""""3""""" "*""V""""-""E"""""""";"" """"R"""""""*]    3333"   0(  0! 0 ^}??eg`SMO&{ 3p  * "    / 0 ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 0 b??opGrS`SMO&{ 5  *( "    ) 0  r00e0eRectangle 2=p   cAutomatic Ontology Learning    0  r0e0eRectangle 3  6Proposed work is to develop automatic method to build an ontology from document collection uses a small seed ontology (i.e., UMLS metathesaurus and semantic network) and enriches it with semantic relations identified after analyzing domain texts -From Chew-Hung Lee, Christopher Khoo, Jin-Cheon Na   *      !  *   7  3333___PPT10i.::e+D=' = @B +"  |t 4\(  4! 4 ^{??eg`SMO&{ 3p  * "    / 4 ^??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 4 b|??opGrS`SMO&{ 5  *( "    C 4  r`}0e0eRectangle 2=p   }3UMLS Semantic Network (from UMLS Knowledge Source) 4 4" 4 N 4 S A?5%8c8c    ?Picture 3"   3333___PPT10i.`Pd+D=' = @B +"H   7/ 8(  8! 8 ^~??eg`SMO&{ 3p  * "    / 8 ^`??u`SMO&{ 4@`   Association rules Zhongzhi Shi( "    # 8 b ??opGrS`SMO&{ 5  *( "    . 8  r0e0eRectangle 2=p   h Application of Apriori Algorithm! ! !  8  r00e0eRectangle 3  XfEach drug+disease sentence divided into individual word tokens Punctuation marks, prepositions, determiners, conjunctions, disjunctions, pronoun and numbers were removed. Apriori algorithm (i.e., association rule mining) applied to dataset using Clementine data mining software Parameters Minimum support 2% Minimum confidence 80% Results 281 rules generated? 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