SlideServe
Télécharger Obtenir Pro
Menu
Accueil Pro
Préférences
ApparenceLight Aide et commentaires
© SlideServe · v2026

Efficient Algorithms for Mining Share-Frequent Itemsets

ping avatar
ping
24 diapositives · 383 Views · Aug 29, 2014

This presentation by Yu-Chiang Li discusses innovative algorithms for discovering share-frequent itemsets, essential for analyzing customer buying patterns. The Enhanced Fast Share Measure (EFSM), Support-Counted Fast Share Measure (SuFSM), and Share-Counted Fast Share Measure (ShFSM) algorithms are introduced as enhancements over the existing Fast Share Measure algorithm. The performance and efficiency of these algorithms are evaluated through experimental results, highlighting their advantages in mining data from larger datasets.

Efficient Algorithms for Mining Share-Frequent Itemsets - slide 1
01 / 24Efficient Algorithms for Mining Share-Frequent Itemsets
1 / 17

Télécharger la présentation

Efficient Algorithms for Mining Share-Frequent Itemsets
Une image / un lien ci-dessous est fourni (tel quel) pour télécharger la présentation

Politique de téléchargement : le contenu du site vous est fourni TEL QUEL pour votre information et votre usage personnel ; il ne peut être vendu, concédé sous licence ni partagé sur d’autres sites sans l’accord de son auteur.Le contenu vous est fourni TEL QUEL, pour votre information et votre usage personnel uniquement. Téléchargez la présentation en cliquant sur ce lien. Lors du téléchargement, si vous ne parvenez pas à télécharger une présentation, l’éditeur a peut-être supprimé le fichier de son serveur.Pendant le téléchargement, si vous ne parvenez pas à obtenir une présentation, le fichier a peut-être été supprimé par l’éditeur.

F I N

Plus de contenu associé

Transcription de la présentation

  1. Efficient Algorithms for Mining Share-Frequent Itemsets Authors: Y. C. Li, J. S. Yeh and C. C. Chang Speaker: Yu-Chiang Li Date :July 28, 2005

  2. Outline • Introduction • Related Work • Enhanced Fast Share Measure (EFSM) Algorithm • Support-Counted Fast Share Measure (SuFSM) Algorithm • Share-Counted Fast Share Measure (ShFSM) Algorithm • Experimental Results • Conclusions

  3. Introduction (1/2) • Goal: discovering the buying patterns of customers • Itemset: a group of items (products) bought together in a transaction • Support: the ratio of transactions containing the itemset to the total transaction number (limited in informative feedback) • Share: the ratio of the total count of items in the itemset to the total count of items in the database

  4. Introduction (2/2) • Share-confidence framework: providing useful information about numerical values associated with transaction items ( Carter et al., 1997) • Share-frequent (SH-frequent) itemset: usually includes some infrequent subsets • Fast Share Measure (FSM) algorithm discovers share-frequent itemsets on small dataset efficiently • This study proposes Enhanced FSM, SuFSM and ShFSM to discover share-frequent itemsets more efficiently than that of FSM

  5. Related Work • Support-Confidence Framework (Agrawal et al., 1993) • Each item is a binary variable denoting whether an item was purchased • Apriori (Agrawal & Swami, 1994) & Apriori-like algorithms • Pattern-growth algorithms (Han et al., 2000; Han et al, 2004) • Share-Confidence Framework (Carter et al., 1997) • Support-confidence framework does not analyze the exact number of products purchased • The support count method does not measure the profit or cost of an itemset • Exhaustive search algorithm (Carter et al., 2000) • FSM algorithm (Li et al., 2005)

  6. Related Work Apriori algorithm (Agrawal and Srikant, 1994): minSup = 40%

  7. Share-Confidence Framework • Measure value: mv(ip, Tq) • mv({D}, T01) = 1 • mv({C}, T03) = 3 • Transaction measure value: tmv(Tq) = • tmv(T02) = 9 • Total measure value: Tmv(DB)= • Tmv(DB)=44 • Itemset measure value: imv(X, Tq)= • imv({A, E}, T02)=4 • Local measure value: lmv(X)= • lmv({BC})=2+4+5=11

  8. Itemset share: SH(X)= • SH({BC})=11/44=25% • SH-frequent: if SH(X) >= minShare, X is a share-frequent (SH-frequent) itemset minShare=30%

  9. Existing algorithms • ZP(Zero Pruning)、ZSP(Zero Subset Pruning) • Variants of exhaustive search • Prune the candidate itemsets whose local measure values are exactly zero • FSM(Fast Share Measure)(Li et al., 2005) • Fast on a small dataset • Generate too many candidates • Existing algorithms are inefficient on a large datasets

  10. ZP Algorithm

  11. ZSP Algorithm

  12. FSM: Fast Share Measure Algorithm • ML: Maximum transaction length in DB • MV: Maximum measure valuein DB • Let min_lmv=minShare×Tmv • Let CF(X)FSM= lmv(X)+(lmv(X)/k)×MV ×(ML-k) • If CF(X)FSM< min_lmv, all supersets of X are infrequent

  13. FSM: Fast Share Measure Algorithm • minShare=30%, ML=6, MV=3, TMV=44 • min_lmv=14 • Prune X if CF(X)FSM <min_lmv • Let X={A B C} • CF(X)FSM =3+(3/3)×3×(6-3)=12<14=min_lmv

  14. Enhanced FSM (EFSM) Algorithm • EFSM: instead of joining arbitrary two itemsets in RCk-1, EFSM joins arbitrary itemset of RCk-1 with a single item in RC1 to generate Ck efficiently • Reduce time complexity from O(n2k-2) to O(nk)

  15. SuFSM (Support-counted FSM) • Xk+1:arbitrary superset of X with length k+1 in DB • S(Xk+1): the set which contains all Xk+1 in DB • dbS(Xk+1): the set of transactions of which each transaction contains at least one Xk+1 • SuFSM and ShFSM from EFSM which prune the candidates more efficiently than FSM • SuFSM (Support-counted FSM): • Theorem 1. If lmv(X)+Sup(S(Xk+1))×MV×(ML – k)< min_lmv, all supersets of X are infrequent

  16. lmv(X)/k Sup(X) Sup(S(Xk+1)) EX. lmv({BCD})/k=15/3=5, Sup({BCD})=3, Sup(S({BCD}k+1))=2 If there is no superset of X is an SH-frequent itemset, then the following three equations hold lmv(X)+(lmv(X)/k)×MV×(ML - k) < min_lmv lmv(X)+Sup(X) ×MV×(ML - k) < min_lmv lmv(X)+Sup(S(Xk+1)) ×MV×(ML - k) < min_lmv SuFSM (Support-counted FSM)

  17. ShFSM (Share-counted FSM) • dbS(Xk+1): the set of transactions of which each transaction contains at least one Xk+1 • ShFSM (Share-counted FSM): • Theorem 2. If Tmv(dbS(Xk+1)) < min_lmv, all supersets of X are infrequent • FSM:lmv(X)+(lmv(X)/k)×MV×(ML - k) < min_lmv • SuFSM:lmv(X)+Sup(S(Xk+1)) ×MV×(ML - k) < min_lmv • ShFSM: Tmv(dbS(Xk+1)) < min_lmv • CF(X)FSM>=CF(X)SuFSM>=CF(X)ShFSM

  18. FSM:lmv(X)+(lmv(X)/k)×MV×(ML - k) < min_lmv • SuFSM:lmv(X)+Sup(S(Xk+1)) ×MV×(ML - k) < min_lmv • ShFSM: Tmv(dbS(Xk+1)) < min_lmv • Ex. X = {BCD} • CF(X)FSM = 9+(9/3)×3×(6-3)=36 • CF(X)SuFSM = 9+2×3×(6-3)=18 • CF(X)ShFSM = 6+8=14

  19. ShFSM (Share-counted FSM) • Ex. X={AB} • Tmv(dbS(Xk+1)) = tmv(T01)+tmv(T05) =6+6=12 <14 = min_lmv

  20. Experimental Results (1/3) • PC: Pentium IV 1.5 GHZ, 1.5GB SDRAM, running Windows XP professional • All algorithms were coded in VC++ 6.0 Figure 1 Figure 2

  21. Experimental Results (2/3) minShare=0.1% Figure 3 Figure 4

  22. T6.I4.D100k.N200.S10 minShare = 0.1% ML=20 , MV=10 Tmv=2,302,443 ExperimentalResults (3/3)

  23. Conclusions • This study proposes the Enhanced FSM (EFSM) algorithm to efficiently reduce the time complexity of the join step • We have also developed SuFSM and ShFSM from EFSM • SuFSM and ShFSM can efficiently prune the candidates, and significantly improve the performance • The experimental results have indicated that ShFSM has the best performance • In the future, we plan to develop even more advanced algorithms to accelerate the process of identifying all share-frequent itemsets

  24. Thank You