A matrix density based algorithm to hierarchically co-cluster documents and words

1. A matrix density based algorithm to hierarchically co-cluster documents and words Advisor ： Dr. Hsu Graduate：Keng-Wei Chang Author ：Bhushan Mandhani Sachindra Joshi Krishna Kummamuru

2. outline • Motivation • Objective • Introduction • background • Rowset Partitioning and Submatrix Agglomeration(RPSA) • Experimental results • Conclusions • Personal Opinion

3. Motivation • With this explosion of unstructured information, it has become increasingly important to organize the information in a comprehensible and navigable manner.

4. Objective • A hierarchical arrangement of documents is very useful in browsing a document collection, as the popularity of the Yahoo、Google. • This paper proposes an algorithm to hierarchically cluster documents for solving problems.

5. Introduction • 90s -> 100 thousand pages； • 2002 -> 2 billion pages; • it has become increasingly important to organize the information • Manually is accurate, but not always feasible • Need tools to automatically arrange documents to labeled hierarchies • Propose RPSA -> two step partitional-agglomerative

6. background • Vector Model for Documents • Evaluation of Clustering Quality • Evaluation of Hierarchical Clustering

7. Vector Model for Documents Unitized-TF IDF We have d documents Document i is represented by is the number of occurrences of word j in document i Term Frequency，TF Inverse Document Frequency，IDF

8. Evaluation of Clustering Quality • 1. Purity： • 2. Entropy：

9. Evaluation of Hierarchical Clustering

10. Rowset Partitioning and Submatrix Agglomeration(RPSA) • tow-step partitional-agglomerative algorithm • 1th step：The Partitioning Step • 2th step：The Agglomerative Step

11. The Partitioning Step • Define the density of submatices a row r，a column c a set R of rows，a set C of columns

12. The Partitioning Step • Generating a Leaf Cluster

13. The Partitioning Step • Choice of Leader Documents • The sum of TFIDF vector representing that document • Documents with relatively large lengths were observed to be better leader documents for the algorithm above

14. The Partitioning Step • The Complete Partitioning Algorithm

15. The Partitioning Step • Complexity Analysis • The time complexity is O(mz) • The space complexity is O(z)

16. The Agglomerative Step • Reduce the number of clusters • The similarity measure between two clusters for merging • Flat Clustering • Hierarchical Clustering

17. The Agglomerative Step • Complexity Analysis • The time complexity is O( ) • The space complexity is O( )

18. Experimental results-Flat Clustering • Data Sets

19. Experimental results-Flat Clustering • Results

20. Experimental results-Flat Clustering

21. Experimental results-Hierarchical Clustering • Data Sets

22. Experimental results-Hierarchical Clustering • Data Sets

23. Experimental results-Hierarchical Clustering • Results

24. Conclusions • It is comparable with or better than the best k-means run • It’s performance does not degrade on small data sets • It’s acceptable on purity in hierarchy

25. Personal Opinion