1 / 43

A Hybrid Method to Categorical Clustering

A method is proposed to cluster categorical data by defining a measure of similarity between groups and using a gravitation model to optimize the clustering result.

savoy
Download Presentation

A Hybrid Method to Categorical Clustering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. A Hybrid Method to Categorical Clustering 學生：吳宗和 Advisor : Prof. J. Hsiang Date : 7/4/2006

  2. Outlines • Introduction • Motivation • Related Work • Research Goal / Notation • Our Method • Experiments • Conclusion • Future Work

  3. Introduction • Data clustering is to partition a set of data elements into groups such that elements in the same groups are similar, while elements in different groups are dissimilar. [1] • The similarity must be well-defined by developer. • Data elements can be • Recorded as Numerical values. (Degree: 0o~360o ) • Recorded as Categorical values. (Sex : { Male, Female})  Find the latent structure in the dataset. • Clustering Methods purposed for numerical data can’t fit for categorical data, because lack of a proper measure of similarity[21].

  4. Example: • An instance of the movie database.

  5. Outlines • Introduction • Motivation • Related Work • Research Goal / Notation • Our Method • Experiments • Conclusion • Future Work

  6. Motivation • Needs, • For database, much of the data in databases are categorical (described by people). • For web navigation, web documents can be categorical data after feature selection. • For knowledge discovery, find latent structure in data. • The difficulties to solve clustering categorical data, • data elements with categorical values they can take are not ordered.  no intuitive measure of distance.[21] • methods specified for clustering categorical data are not easy to use.

  7. Motivation (cont’) • Problems in Related work • Hard to understand or use. • Parameters are data sensitive. • Most of them CANNOT decide the number of groups when clustering.[3,13,17,18] • Our gauss/assumption. • Need All new method? • Reuse the methods proposed for numerical data. ( measure of distance can’t fit the categorical data ) • Or only NEED a good measure of similarity / distance between two groups. • REUSE the framework for clustering numerical data. ( intuitive approach, fewer parameters, and less sensitive for data ) • Get better clustering result.

  8. Related Work • Partition Based • K-modes [Z. Huang. (1998)] • Monte-Carlo algorithm [Tao Li, et. al 2003] • COOLCAT [Barbara, D., Couto, J., & Li, Y. (2002)] • Agglomerative Based • ROCK [Guha, S., Rastogi, R.,& Shim, K. (2000)] • CACTUS [ Ganti, V., Genhrke, J., & Ramarkrishnan, R. (1999)] • Best-K ( ACE )[Keke Chen, Ling Liu (2005)]

  9. Summarization of relate work

  10. Outlines • Introduction • Motivation • Related Work • Research Goal / Notation • Our Method • Experiments • Conclusion • Future Work

  11. Research Goal • Propose a method • A measure of similarity between two groups. • Reuse the gravitation concept.( for intuition, fewer parameters ) • Decide the proper number of groups by machine. • Strength the clustering result.( for better result )

  12. Notation • D：data set of N elements p1,p2,p3,…,pn ,|D| = n. • Element pi is a multidimensional vector of d categorical attributes, i.i.e. pi = <ai1,ai2,…,aid> , where aij Aj, Aj is the set of all possible values aij can take, and Ajis a finite set. • For related work, K : an integer given by user, then divide elements into K groups G1,G2,…,GKsuch that ∪Gi=D and i,j , ij, Gi∩Gj =ψ.

  13. Outlines • Introduction • Motivation • Related Work • Research Goal • Our Method • A measure of similarity • Step 1: Gravitation Model • Step 2: Strength the result. • Experiments • Conclusion • Future Work

  14. Our method • One similarity function, two steps. • Define a measure of similarity between two groups. • Use the similarity to be the measure of distance. • Two steps. • Step 1. • Use the concept of gravitation model. • Find the most suitable group k. • Step 2. • Conquer the local optimal. Optimize the result.

  15. Similarity(Gi,Gj) The Intuition of similarity • Based on the structure of the group. • Each group has its own probability distribution of each attribute and can be represented as its group structure. • Groups are similar if their have very similar probability distribution of each attribute.

  16. The Similarity function • A group Gi = <A1,A2,A3,…,Ad>, Aris a random variable for all r = 1…d, p(Ar=v | Gi) is the probability, when Ar=v. • Entropy of Arin group Gi : entropy(Ar) = • Entropy of GiE(Gi) = Sim(Gi,Gj)=

  17. To geometric analogy • Use Sim(Gi,Gj) to be our geometric analogy, because • Sim(Gi,Gj) ≧ 0, i,j. • Sim(Gi,Gi) = 0, i. • Sim(Gi,Gi) = Sim(Gj,Gi), i,j.

  18. Step 1. • Use the concept of gravitation model. • Mass, Radius, and Time. • Mass of a group = the # of elements. • Radius of two groups Gi,Gj = similarity(Gi,Gj) • Time = ∆T, a constant. • Merging groups Get a clustering tree.

  19. A Merging Pass • M(Gi)= # elements in Gi. • R(Gi,Gj)=Sim(Gi,Gj). • G is 1.0. • fg(Gi,Gj) is the gravitation force. • Δt is the time period. Δt = 1.0. • Rnew(Gi,Gj) = R(Gi,Gj) －1/2(accgi+accgj)Δt2 • If Rnew(Gi,Gj) < 0, Merge Gi and Gj. • Getting closer {Radius = 0}  merge.  Build a clustering tree

  20. A clustering tree.

  21. Suitable K. • In the sequence of merging passes, find  Suitable number of groups in the partition. • Suppose step1 merges to 1 group, after T iterations. • S1, S2, S3,…, ST-1, ST. Si : i-th iteration • Stablei= ΔTime(Si , Si+1) x Radius(Si), Radius(Si) = Min{ Sim( Gα,Gβ) ,  Gα,Gβ in Si and αβ }  • In the following slides, we use K to denote the proper number of clusters in the partition.

  22. Step 2. • Still has Local minimal problem? • Yes. Conquer it by randomized algorithm. • Randomized step. • If Exchange two elements from two groups[11]  Time consumption. • Goal : Enlarge distance/radius of two groups. • For Efficiency • Tree-structured data structure  digital search tree. • Enlarge the distance/radius of each two groups in the result obtained from Step 1.

  23. Step 2(con’t) • Why digital search tree (D.S.T)? • Locality. • Storing elements • storing strings from elements. • Deeper nodes are looked like their siblings and children.

  24. Operations in D.S.T • D.S.T is tree-structured, storing binary strings, and degree of each node ≦ 2. • Operations cost less ( O(d) ) • Search • Insert • Delete • Search operation. ( O(d) ) • Ex:

  25. Operations in D.S.T (cont’) • Insertion (O(d)), Ex: Insert C010 into the tree.  • Deletion (O(d)), Ex: delete G110 

  26. Randomizing • Transform the result from step 1 into a forest with K digital search trees. • Nodes in Tree i ≡ elements in Gi ,  i. • Randomly select 2 trees i,j, and select an internal node αfrom tree i. • Let gα = { node n | α is the ancestor of node n } ∪{α} • To calculate,

  27. Randomizing (cont’) • For example, K = 2. • α= ‘0101’ Good Exchange !!!

  28. Outlines • Introduction • Motivation • Related Work • Research Goal / Notation • Our Method • Experiments • Datasets • Compared methods and Criterion • Conclusion • Future Work

  29. Experiments • Datasets • Real datasets[7]. • Congressional Voting Record. • Mushroom. • Document datasets[8,9]. • Reuters 21578. • 20 Newsgroups.

  30. Compared methods & Criterion • Compared methods • K-modes ( randomly partition elements into K groups ) • Coolcat ( select some elements to be seeds and place seeds into K groups, then place the remaining) • Criterion (10 times average) • Category Utility = • Expected Entropy = • Purity =

  31. Real datasets • Do classify like human. • Mushroom dataset • 2 classes( edible, poisonous ) • 22 attributes. • 8124 records.

  32. Real datasets • Voting Record dataset • 2 classes (democrat, republican), 435 records, 16 attributes (all boolean valued). • Some records (10%) have missed value.

  33. Document Datasets • For applying. • 20 Newsgroups • 20 subjects.Each subject contains 1000 articles. • 20000 documents (too many). • Select documents from 3 subjects to be the dataset (3000 articles). • Use BOW package[4] to do feature selection. 100 features.

  34. Document Datasets • Reuters 21578 • 135 subjects. 21578 articles, each subject contains different # of articles. • Select first 10 most articles subjects. • Use BOW package[4] to do feature selection. 100 features.

  35. Conclusion • In this work, we purposed a measure of similarity such that • Can reuse the framework used on numerical data clustering. • With FEWER parameters and easy to use. • Try to avoid trapping into local minima. • Still can obtain same or better clustering result than methods proposed for categorical data.

  36. Future Work • For our method itself, • Still take a long time to calculate, because we need to fix and satisfy “triangle-inequality law” for our similarity function. • For application. • To build a framework to cluster documents without other packages’ help. • Use our method to solve “Binding sets” problem in Bioinformatics.

  37. Reference • [1] A.K. Jain M.N Murty, and P.J. Flynn, Data Clustering: A Review, ACM Computing Surveys. Vol.31, 1999. • [2] Yen-Jen Oyang, Chien-Yu Chen, Shien-Ching Huang, and Cheng-Fang Lin. Characteristics of a Hierarchical Data Clustering Algorithm Based on Gravity Theory. Technical Report of NTUCSIE 02-01. • [3] S. Guha, R. Rastogi, and K. Shim. ROCK: A robust clustering algorithm for categorical attributes. Proc. of IEEE Intl. Conf. on Data Eng. (ICDE), 1999. • [4] McClallum, A. K. Bow: A tookit for statistical language modeling, text retrieval, classification and clustering. http://www.cs.cmu.edu/mccallum/bow. • [5] DIGITAL LIBRARIES: Metadata Resources. http://www.ifla.org/II/metadata.htm • [6] W.E. Wright. A formulization of cluster analysis and gravitational clustering. Doctoral Dissertation. Washington University, 1972. • [7] Newman, D.J. & Hettich, S. & Blake, C.L. & Merz, C.J. (1998). UCI Repository of machine learning databases. [http://www.ics.uci.edu/~mlearn/MLRepository.html]. Irvine, CA: University of California, Department of Information and Computer Science. • [8] David D. Lewis. Reuters-21578 text categorization test collection. AT&T Labs – Research. 1997. • [9] Ken Lang. 20 Newsgroups. Http://people.csail.mit.edu/jrennie/20Newsgroups/ • [10] T. Cover and J. Thomas. Elements of Information Theory. Wiley, 1991.

  38. Reference • [11] T. Li, S. Ma, and M. Ogihara. Entropy-based criterion in categorical clustering. Proc. of Intl. Conf. on Machine Learning (ICML), 2004. • [12] Bock, H.-H. Probabilistic aspects in cluster analysis. In O. Opitz(Ed.), Conceptual and numerical analysis of data, 12-44. Berlin: Springer-verlag. 1989. • [13] Z. Huang. A fast clustering algorithm to cluster very large categorical data sets in data mining. Workshop on Research Issues on Data Mining and Knowledge Discovery, 1997. • [14] MacQueen, J. B. (1967) Some Methods for Classification and Analysis of Multivariate Observations, In Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability, pp. 281-297. • [15] Richard O. Duda and Peter E. Hard. Pattern Classification and Secen Analysis. A Wiley-Interscience Publication, New York, 1973. • [16] P Andritsos, P Tsaparas, RJ Miller, KC Sevcik. LIMBO: Scalable Clustering of Categorical Data. Hellenic Database Symposium, 2003. • [17] V. Ganti, J. Gehrke, and R. Ramakrishnan. CACTUS-clustering categorical data using summaries. Proc. of ACM SIGKEE Conference, 1999. • [18] D. Barbara, Y. Li, and J. Couto. Coolcat: an entropy-based algorithm for categorical clustering. Proc. of ACM Conf. on Information and Knowledge Mgt. (CIKM), 2002. • [19] R. C.Dubes. How many clusters are best? – an experiment. Pattern Recognition, vol. 20, no 6, pp.645-663, 1987. • [20] Keke Chen and Ling Liu: "The ‘Best K’ for Entropy-based Categorical Clustering ", Proc of Scientific and Statistical Database Management (SSDBM05). Santa Barbara, CA June 2005. • [21] 林正芳，歐陽彥正，”以重力為基礎的二階段階層式資料分群演算法特性之研究”，國立臺灣大學資訊工程學系，碩士論文。民91。 • [24] I.H. Witten, E. Frank. Data Mining: Practical Machine Learning Tools and Techniques with Java Implementations, Morgan Kaufmann Publishers, San Francisco, 2000.

  39. Appendix 1 • K-modes • Extend the k-means algorithm for clustering large data sets with categorical values. • Use “Mode” to represent a group.

  40. Appendix 2 • ROCK • Using Jaccard coefficient: to measure the distance between points Xi,Xk in attribute j • Define Otherwise Neighbor(xi,xk) = false. • Define Link(p,Ci ) = the # of Neightbor(p,q) = 1, for every q belongs to cluster Ci. • Best clusters (Objective function): • For well defined data set , ψ is 0.5, f(ψ) = (1+ψ)/(1-ψ) • Threshold ψ affects the result is good or not, and hard to decide. • Relaxing the problem to many clusters.

  41. Appendix 3 • CACTUS is an agglomerative algorithm. • Use attribute values to group data. • Define: • Support : • Strong connection: S_conn(sij,sjt)=true, , if Pair(sij,sjt) > threshold ψ. • From pairs to sets of attributes. • A cluster is defined as a region of attributes that are pairwise strongly connected. • From the attributes view. • Find k regions of attributes. • Setting threshold ψ decides the result is good or not.

  42. Appendix 4 • COOLCAT [2002] • Use entropy to measure the uncertainty of the attribute j. • Si = { Si1, Si2, Si3,…,Sit }, • Entropy(Si) = • When Si is much clear, Entropy(Si)  0. uncertainty is small. • For a cluster k, the entropy of k is • 在Ci中，各屬性Si的亂度的總和。 • For a partition P = {C1,C2,…Ck} • The expected Entropy of P is

  43. Appendix 4 (cont’) • For a given partition P, P is best clusters, P satisfies unique value in each attribute for each cluster Ci. • COOLCAT’s objective function is . • Since • Coolcat picks k points from data set S, such that k are most unlike for each other, when beginning. And assign these points to k clusters. • For each point p in S-{ assigned points }, assign p into cluster i with the minimal increasing entropy. • Very easy to implement, but performance is strongly connected to the initial selection. • Sequence sensitive. • Trapped in local minima easily, expected entropy is not the minimal.

More Related