A Survey of Recent Clustering Methods for Data Mining (part 2)

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1 A Survey of Recent Clustering Methods for Data Mining part 2) Challenges to Conquer Giga Data Sets and The Curse of Dimensionality Toshihiro Kamishima National Institue of Advanced Industrial Science and Technology AIST) mail@kamishima.net, keywords: Clustering, Unsupvervised Learning, Survey, Data Mining ON 2 ) k-means ONk) ON) 1 CLARANS Ng CLARANS Clustering Large Applications based on RANdomized Search) [Ng 94] CLARANS PAM CLARA PAM Partition Around Medoids k-means medoid medoid medoid medoid 1 x i : object N : X={x 1,...,x N } : d : x i=x i1,...,x id ) : x i D 1,...,D d : k : C 1,...,C k : n i : C i c i : C i Dx i,x j ) : x i x j k-means k medoid medoid medoid PAM ON 2 k) CLARA Clustering LARge Applications) N k PAM medoid medoid CLARA Ok 3 + Nk) CLARANS CLARA medoid medoid kn k)/ CLARANS CLARA 2 BIRCH Zhang BIRCH Balanced Iterative Reducing and Clustering using Hierarchies) [Zhang 96, Zhang 97] ON) Clustering Feature Tree CF-tree CF-tree CF-tree N ON) CF-tree Clustering Feature CF

2 2 171 Phase1: Phase2option): Density Phase3: Phase4option): a) =ξ b) ξ 2 DENCLUE [Hinneburg 98] 1 BIRCH [Zhang 97] B L T B CF L CF B L T CF C xi,xj C,xi xj x i x j ) x i x j ) nn 1) CF-tree T N CF 2 CF=n, x i, x i x i ) x i C x i C CF C i C j CF C i C j CF Zhang CF D0 D4 D2C i,c j ) = x i C i x j C j x i x j ) x i x j ) n i n j CF BIRCH CF-tree 1 Phase Phase1 BIRCH CF-tree B+-tree CF-tree D0 D4 CF T CF CF CF L B CF-tree T T CF-tree Phase2 CF-tree Phase CF CF Phase3 D0 D4 D2 D4 Phase4 Phase3 2 JOIN I/O 3 L L d L L L d N ON) Hinneburg DENCLUE DENsity-based CLUstEring) [Hinneburg 98] 2a)

3 ξ 2b) 2σ G p ξ/2d G sp 4σ g G sp G p G r G sp G p N x g g 1 G r x 4σ g 1 nearx) x x nearx 1) exp Dx,x1 ) ) ) 2 2σ 2 BIRCH ξ σ Xu DBCLASD Distribution Based Clustering of LArge Spatial Databases [Xu 98] C x C min xi C,x x i Dx,x i ) seed Wavelet Sheikholeslami WaveCluster [Sheikholeslami 98] Wang STINGSTatistical INformation Grid-based method) [Wang 97] 4 VFKM CF-tree CLARANS Domingos VFKM [Domingos 01] CLARANS k-means k-means C c i N C N c N i Yi Yj H 3 x a x b [Faloutsos 95] xi G xi' F xb E xa xj xj' 4 x a x b H [Faloutsos 95] LC N,C )= k Dc N i,c i ) i ϵ δ Pr[LC N,C ) ϵ] δ k-means N k- means k-means FastMap 4 ON 2 ) N

4 ξ τ i A i 4 A 1 <8) 2 A 2 <5)) 2 A 1 <6) 4 A 2 <8)) 5 CLIQUE [Agrawal 98] Faloutsos FastMap 1 [Faloutsos 95] ON) x a x b x a x b x i x i Y i 3 x i x a x b E x a E Y i = Dxa,x i ) ) 2 + Dxa,x b ) ) 2 Dxb,x i ) ) 2 2Dx a,x b ) x i x a x b d 1 H H x a x b N 1 d 1 H H x i x j H D x i,x j ) x i x j G D x i,x j ) ) 2 = Dxi,x j ) ) 2 Y i Y j) 2 FastMap HyperMap [ 02] Fisher [ 02] 2 CLIQUE Apriori [Agrawal 94] Agrawal Apriori CLIQUE CLustering In QUEst [Agrawal 98] CLIQUE A 2 A 1 C D CLIQUE Apriori d d 1 1 d K OK d + N d) d d 3 ORCLUS Aggarwal ORCLUS arbitrarily ORiented projected CLUSter generation [Aggarwal 00] ORCLUS d β α 8 BIRCH CF k 0 Ok k 0 Nd + k 2 0d 3 ) k k-means 6

5 [Ester 96] xq xp xo 7 DBSCAN[Ester 96] DBSCAN Ester DBSCAN [Ester 96] Web /Forschung/KDD/Clustering/ DBSCAN Eps MinPts 7 directly densityreachable DDR) x p x q DDR xr 1) x q N Eps x p ) 2) N Eps x p ) MinPts N Eps x p ) = {x q X Dx p,x q ) Eps} 7 x q x p DDR 2 DDR x o x r x o x q x p DDR seed DDR DDR seed 6 MinPts R -tree ON log N) DBSCAN GDBSCAN [Sander 98] Eps OPTICS [Ankerst 00] 2 CURE Guha CURE [Guha 98] k-means α k DBSCAN CURE ON 2 log N) 2 ON 2 ) 3 Zahn [Zahn 71] minimum spanning tree Gabriel relative neighborhood Urquhart [Urquhart 82] k Mizoguchi [Mizoguchi 80] Karypis [Karypis 99] Harel [Harel 01] [Barbará 00] Learning from Cluster Examples; LCE) [Kamishima 03a, 03b] LCE 8

6 2 175 O1,FO1)) π * 1 O2,FO2)) π * 2 O#EX,FO#EX)) π * #EX 8 OU,FOU)) π^ U WWW /home/wkiri/cop-kmeans/ 3 [Bensaid 96, Nigam 98, Goldman 00, 01] LCE LCE LCE-MAP LCE-Maximum A Posteriori 3 Ax i ): N Ap ij ): x i x j p ij NN 1)/2 Aπ): Pr[π=π,Aπ),{Ax)},{Ap)}] π=π π π Pr[Aπ) π=π ] Pr[π=π {Ax)},{Ap)}] 2 COP-KMEANS Wagstaff COBWEB [Wagstaff 00] k-means COP-KMEANS [Wagstaff 01] k-means COP- KMEANS [Barbará 02] [Ramoni 02, Keogh 98, 02] [Taskar 01] [Ding 01] 11 [Cohn 00] [Aggarwal 00] Aggarwal, C. C. and Yu, P. S.: Finding Generalized Projected Clusters in High Dimensional Spaces, in Proc of the ACM SIGMOD Int l Conf. on Management of Data, pp ) [Agrawal 94] Agrawal, R. and Srikant, R.: Fast Algorithms for Mining Association Rules, in Proc. of the 20th Very Large Database Conf., pp )

7 [Agrawal 98] Agrawal, R., Gehrke, J., Gunopulos, D., and Raghavan, P.: Automatic Subspaace Clustering of High Dimensional Data for Data Mining Applicatiosn, in Proc. of the ACM SIGMOD Int l Conf. on Management of Data, pp ) [ 02],,,,, HyperMap:, 13 DEWS2002), C ) [Ankerst 00] Ankerst, M., Breunig, M. M., and Sander, H.-P. K. J.: OPTICS: Ordering Points To Identify the Clustering Structure, in Proc of the ACM SIGMOD Int l Conf. on Management of Data, pp ) [Barbará 00] Barbará, D. and Chen, P.: Using the Fractal Dimension to Cluster Datasets, in Proc. of The 6th Int l Conf. on Knowledge Discovery and Data Mining, pp ) [Barbará 02] Barbará, D.: Requirements for Clustering Data Streams, SIGKDD Explorations, Vol. 3, No. 2, pp ) [Bensaid 96] Bensaid, A. M., Hall, L. O., Bezdek, J. C., and Clarke, L. P.: Partially Supervised Clustering for Image Segmentation, Pattern Recognition, Vol. 29, No. 5, pp ) [Cohn 00] Cohn, D., Caruana, R., and McCallum, A.: Semisupervised Clustering with User Feedback, 2.cs.cmu.edu/ mccallum/papers/semiup-aaai2000s.ps.gz 2000) [Ding 01] Ding, C. H. Q., He, X., Zha, H., Gu, M., and Simon, H. D.: A Min-max Cut Algorithm for Graph Partitioning and Data Clustering, in Proc. of the IEEE Int l Conf. on Data Mining, pp ) [Domingos 01] Domingos, P. and Hulten, G.: A General Method for Scaling Up Machine Learning Algorithms and its Application to Clustering, in Proc. of the 18th Int l Conf. on Machine Learning, pp ) [Ester 96] Ester, M., Kriegel, H.-P., Sander, J., and Xu, X.: A Density-Based Algorithm for Discovering Clusters in Large Spatial Databases with Noise, in Proc. of The 2nd Int l Conf. on Knowledge Discovery and Data Mining, pp ) [Faloutsos 95] Faloutsos, C. and Lin, K.-I.: FastMap: A Fast Algorithm for Indexing, Data-Mining and Visualization of Traditional and Multimedia Datasets, in Proc. of the ACM SIGMOD Int l Conf. on Management of Data, pp ) [Goldman 00] Goldman, S. and Zhou, Y.: Enhancing Supervised learning with Unlabeled Data, in Proc. of the 17th Int l Conf. on Machine Learning, pp ) [Guha 98] Guha, S., Rastogi, R., and Shim, K.: CURE: An Efficient Clustering Algorithm for Large Databases, in Proc. of the ACM SIGMOD Int l Conf. on Management of Data, pp ) [Harel 01] Harel, D. and Koren, Y.: Clustering Spatial Data Using Random Walks, in Proc. of The 7th Int l Conf. on Knowledge Discovery and Data Mining, pp ) [Hinneburg 98] Hinneburg, A. and Keim, D. A.: An Efficient Approach to Clustering in Large Multimedia Databases with Noise, in Proc. of The 4th Int l Conf. on Knowledge Discovery and Data Mining, pp ) [Kamishima 03a] Kamishima, T. and Motoyoshi, F.: Learning from Cluster Examples, Machine Learning 2003), in press) [ 03b],,,, Vol. 18, No. 2, pp ) [Karypis 99] Karypis, G., E.-H.Han,, and Kumar, V.: Chameleon: Hierarchical Clustering Using Dynamic Modeling, IEEE Computer, Vol. 32, No. 8, pp ) [Keogh 98] Keogh, E. J. and Pazzani, M. J.: An Enhanced Representation of Time Series Which Allows Fast And Accurate Classification, Clustering and Relevance Feedback, in Proc. of The 4th Int l Conf. on Knowledge Discovery and Data Mining, pp ) [Mizoguchi 80] Mizoguchi, R. and Shimura, M.: A Nonparametric Algorithm for Detecting Clusters Using Hierarchical Structure, IEEE Trans. on Pattern Analysis and Machine Intelligence, Vol. 2, No. 4, pp ) [Ng 94] Ng, R. T. and Han, J.: Efficient and Effective Clustering Methods for Spatial Data Mining, in Proc. of the 20th Very Large Database Conf., pp ) [Nigam 98] Nigam, K., McCallum, A., Thrun, S., and Mitchell, T.: Learning to Classify Text from Labeled and Unlabeled Documents, in Proc. of the 15th National Conf. on Artificial Intelligence, pp ) [Ramoni 02] Ramoni, M., Sebastiani, P., and Cohen, P.: Bayesian Clustering by Dynamics, Machine Learning, Vol. 47, pp ) [Sander 98] Sander, J., Ester, M., Kriegel, H.-P., and Xu, X.: Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications, Journal of Data Mining and Knowledge Discovery, Vol. 2, pp ) [Sheikholeslami 98] Sheikholeslami, G., Chatterjee, S., and Zhang, A.: WaveCluster: A Multi-Resolution Clustering Approach for Very Large Spatial Databases, in Proc. of the 24th Very Large Database Conf., pp ) [ 02],,, D-II, Vol. J85-D-II, No. 5, pp ) [Taskar 01] Taskar, B., Segal, E., and Koller, D.: Probabilistic Classification and Clustering in Relational Data, in Proc. of the 17th Int l Joint Conf. on Artificial Intelligence, pp ) [ 01], 4, pp ) [Urquhart 82] Urquhart, R.: Graph Theoretical Clustering Based on Limited Neghbourhood Sets, Pattern Recognition, Vol. 15, No. 3, pp ) [Wagstaff 00] Wagstaff, K. and Cardie, C.: Clustering with Instance-level Constraints, in Proc. of the 17th Int l Conf. on Machine Learning, pp ) [Wagstaff 01] Wagstaff, K., Cardie, C., Rogers, S., and Schroedl, S.: Constrained K-means Clustering with Background Knowledge, in Proc. of the 18th Int l Conf. on Machine Learning, pp ) [Wang 97] Wang, W., Yang, J., and Muntz, R.: STING: A Statistical Information Grid Approach to Spatial Data Mining, in Proc. of the 23rd Very Large Database Conf., pp ) [Xu 98] Xu, X., Ester, M., Kriegel, H.-P., and Sander, J.: A Distribution-Based Clustering Algorithm for Mining in Large Spatial Databases, in Proc. of the 14th Int l Conf. on Data Engineering, pp ) [ 02],,, ), LG 3 [Zahn 71] Zahn, C. T.: Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters, IEEE Trans. on Computers, Vol. 20, No. 1, pp ) [Zhang 96] Zhang, T., Ramakrishnan, R., and Livny, M.: BIRCH: An Efficient Data Clustering Method for Very Large Databases, in Proc. of the ACM SIGMOD Int l Conf. on Management of Data, pp ) [Zhang 97] Zhang, T., Ramakrishnan, R., and Livny, M.: BIRCH: A New Data Clustering Algorithm and Its Applications, Journal of Data Mining and Knowledge Discovery, Vol. 1, pp )

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A Survey of Recent Clustering Methods for Data Mining (part 1)

59 1 A Survey of Recent Clustering Methods for Data Mining (part 1) Try Clustering! Toshihiro Kamishima National Institue of Advanced Industrial Science and Technology (AIST) mail@kamishima.net, http://www.kamishima.net/