Association (Part II)

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Sybil Watson
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1 Association (Part II) Outlin Improving Apriori (FP Growth, ECLAT) Qustioning confidnc masur Qustioning support masur 2 1

2 FP growth Algorithm Us a comprssd rprsntation of th dtb databas using an FP tr Onc an FP tr has bn constructd, it uss a rcursiv divid and conqur approach to min th frqunt itmsts FP tr construction minsup = 2 Aftr rading TID=1: TID Itms 1 {A,B} 2 {B,C,D} 3 {A,C,D,E} 4 {A,D,E} 5 {A,B,C} 6 {A,B,C,D} 7 {B,C} 8 {A,B,C} 9 {A,B,D} 10 {B,C,E} A:1 B:1 Aftr rading TID=2: A:1 B:1 B:1 C:1 2

3 FP tr construction TID Itms 1 {A,B} 2 {B,C,D} 3 {A,C,D,E} 4 {A,D,E} 5 {A,B,C} 6 {A,B,C,D} 7 {B,C} 8 {A,B,C} 9 {A,B,D} 10 {B,C,E} FP Tr Construction TID Itms 1 {A,B} 2 {B,C,D} 3 {A,C,D,E} 4 {A,D,E} 5 {A,B,C} 6 {A,B,C,D} 7 {B,C} 8 {A,B,C} 9 {A,B,D} 10 {B,C,E} Transaction Databas B:5 A:7 C:1 B:3 C:3 Hadr tabl Itm Pointr A B C D E C:3 D1 E:1 E1 E:1 Pointrs ar usd to assist frqunt itmst gnration E:1 3

4 FP growth E is frqunt Prhaps also frqunt AE, ABE, tc. A:7 B:3 Conditional pattrn bas and fptr for E: B:5 C:1 C:3 C:3 E:1 E:1 D1 E:1 FP growth Conditional bas and tr for E: A:2 Conditional Pattrn bas for E: P = {(A:1,C:1,), (A:1,), C:1 (B:1,C:1)} Prun B C:1 Build conditional FP-tr Rcursivly apply FPgrowth 4

5 FP growth Conditional bas and tr for D within conditional tr for E: A:2 Conditional pattrn bas for D within conditional bas for E: P = {(A:1,C:1), (A:1)} Prun C Build conditional FP-tr ADE and all its substs ar frqunt FP growth Conditional tr for A within D within E: A:2 Count for A is 2: {A,D,E} is frqunt itmst Nxt stp: Construct conditional tr C within conditional tr E Continu until xploring conditional tr for A (which has only nod A) 5

6 Rsult 11 Bnfits of th FP tr Structur Prformanc study shows FP growth is an ordr of magnitud fastr than Apriori, and is also fastr than tr projction Rasoning No candidat gnration, no candidat tst Us compact data structur Eliminat rpatd databas scan Basic opration is counting and FP tr building Run tim(sc.) D1 FP-grow th runtim D1 Apriori runtim Support thrshold(%) 6

7 ECLAT For ach itm, stor a list of transaction ids (tids) Horizontal Data Layout TID Itms 1 A,B,E 2 B,C,D 3 C,E 4 A,C,D 5 A,B,C,D 6 A,E 7 A,B 8 A,B,C 9 A,C,D 10 B Vrtical Data Layout A B C D E TID-list ECLAT Dtrmin support of any k itmst by intrscting tid lists of two of its (k 1) substs. A B AB travrsal approachs: top down, bottom up and hybrid Advantag: vry fast support counting Disadvantag: intrmdiat tid lists may bcom too larg for mmory

8 Pattrn Evaluation Association rul algorithms tnd to produc too many ruls many of thm ar unintrsting or rdundant Rdundant if {A,B,C} {D} and {A,B} {D} hav sam support & confidnc Intrstingnss masurs can b usd to prun/rank th drivd pattrns In th original formulation of association ruls, support & confidnc ar th only masurs usd Intrstingnss Masur Intrstingnss Masurs Pattrns Knowldg Postprocssing Prprocssd Data Slctd Data Fatur Fatur Fatur Fatur Fatur Fatur Fatur Fatur Fatur Fatur Prod uct Mining Data Prprocssing Slction 8

9 Computing Intrstingnss Masur Givn a rul X Y, information ndd to comput rul intrstingnss can b obtaind from a contingncy tabl Contingncy tabl for X Y Y Y X f 11 f 10 f 1+ X f 01 f 00 f o+ f +1 f +0 T f 11 : support of X and Y f 10 : support of X and Y f 01 : support of X and Y f 00 : support of X and Y Usd to dfin various masurs support, confidnc, lift, Gini, J-masur, tc. Drawback of Confidnc Coff Coff Ta Ta Association Rul: Ta Coff Confidnc= P(Coff Ta) = but P(Coff) = 0.9 Although confidnc is high, rul is mislading P(Coff Ta) =

10 Statistical Indpndnc Population of 1000 studnts 600 studnts know how to swim (S) 700 studnts know how to bik (B) 420 studnts know how to swim and bik (S,B) P(S B) = 420/1000 = 0.42 P(S) P(B) = = 0.42 P(S B) = P(S) P(B) => Statistical indpndnc P(S B) > P(S) P(B) => Positivly corrlatd P(S B) < P(S) P(B) => Ngativly corrlatd Statistical basd Masurs Masurs that tak into account statistical dpndnc P( Y X ) Lift = P( Y ) P( X, Y ) Intrst = P( X ) P( Y ) PS = P ( X, Y ) P ( X ) P ( Y ) P( X, Y ) P( X ) P( Y ) φ cofficint = P( X )[1 P( X )] P( Y )[1 P( Y )] 10

11 Exampl: Lift/Intrst Coff Coff Ta Ta Association Rul: Ta Coff Confidnc= P(Coff Ta) = but P(Coff) = 0.9 Lift = 0.75/0.9= (< 1, thrfor is ngativly associatd) Drawback of Lift & Intrst Y Y X X Y Y X X Lift = = Lift = = (0.1)(0.1) ) (0.9)(0.9) ) Statistical indpndnc: If P(X,Y)=P(X)P(Y) => Lift = 1 11

12 Thr ar lots of masurs proposd in th litratur Som masurs ar good for crtain applications, but not for othrs What critria should w us to dtrmin whthr a masur is good or bad? Compact Rprsntation of Frqunt Itmsts Som itmsts ar rdundant bcaus thy hav idntical support as thir suprsts TID A1 A2 A3 A4 A5 A6 A7 A8 A9 A10 B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 C1 C2 C3 C4 C5 C6 C7 C8 C9 C Numbr of frqunt itmsts Nd a compact rprsntation = 10 = 3 10 k 1 k 12

13 Maximal Frqunt Itmst An itmst is maximal frqunt if non of its immdiat suprsts is frqunt Maximal Itmsts Infrqunt Itmsts Bordr Closd Itmst An itmst is closd if non of its immdiat suprsts has th sam support as th itmst TID Itms 1 {A,B} 2 {B,C,D} 3 {A,B,C,D} 4 {A,B,D} 5 {A,B,C,D} Itmst Support {A} 4 {B} 5 {C} 3 {D} 4 {A,B} 4 {A,C} 2 {A,D} 3 {B,C} 3 {B,D} 4 {C,D} 3 Itmst Support {A,B,C} 2 {A,B,D} 3 {A,C,D} 2 {B,C,D} 3 {A,B,C,D} 2 13

14 Maximal vs Closd Itmsts TID Itms 1 ABC 2 ABCD 3 BCE 4 ACDE 5 DE Transaction Ids A B C D E AB AC AD AE BC BD BE CD CE DE ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE 2 4 ABCD ABCE ABDE ACDE BCDE Not supportd by any transactions ABCDE Maximal vs Closd Minimum support = A B C D E Closd but not maximal AB AC AD AE BC BD BE CD CE DE Closd and maximal ABC ABD ABE ACD ACE ADE BCD BCE BDE CDE 2 4 ABCD ABCE ABDE ACDE BCDE ABCDE # Closd = 9 # Maximal = 4 14

15 Maximal vs Closd Itmsts 15

CS 584 Data Mining. Association Rule Mining 2

CS 584 Data Mining. Association Rule Mining 2 CS 584 Data Mining Association Rule Mining 2 Recall from last time: Frequent Itemset Generation Strategies Reduce the number of candidates (M) Complete search: M=2 d Use pruning techniques to reduce M