Advanced Multimedia

1. Advanced Multimedia Text Clustering Tamara Berg

2. Reminder - Classification • Given some labeled training documents • Determine the best label for a test (query) document

3. What if we don’t have labeled data? • We can’t do classification.

4. What if we don’t have labeled data? • We can’t do classification. • What can we do? • Clustering - the assignment of objects into groups (called clusters) so that objects from the same cluster are more similar to each other than objects from different clusters.

5. What if we don’t have labeled data? • We can’t do classification. • What can we do? • Clustering - the assignment of objects into groups (called clusters) so that objects from the same cluster are more similar to each other than objects from different clusters. • Often similarity is assessed according to a distance measure.

6. What if we don’t have labeled data? • We can’t do classification. • What can we do? • Clustering - the assignment of objects into groups (called clusters) so that objects from the same cluster are more similar to each other than objects from different clusters. • Often similarity is assessed according to a distance measure. • Clustering is a common technique for statistical data analysis, which is used in many fields, including machine learning, data mining, pattern recognition, image analysis and bioinformatics.

9. Any of the similarity metrics we talked about before (SSD, angle between vectors)

10. Document Clustering Clustering is the process of grouping a set of documents into clusters of similar documents. Documents within a cluster should be similar. Documents from different clusters should be dissimilar.

11. Source: Hinrich Schutze

12. Source: Hinrich Schutze

13. Source: Hinrich Schutze

14. Source: Hinrich Schutze

15. Source: Hinrich Schutze

16. Google news Flickr Clusters Source: Hinrich Schutze

17. Source: Hinrich Schutze

18. How to cluster Documents

19. Reminder - Vector Space Model • Documents are represented as vectors in term space • A vector distance/similarity measure between two documents is used to compare documents Slide from Mitch Marcus

20. Document Vectors:One location for each word. A B C D E F G H I nova galaxy heat h’wood film role diet fur 10 5 3 5 10 10 8 7 9 10 5 10 10 9 10 5 7 9 6 10 2 8 7 5 1 3 “Nova” occurs 10 times in text A “Galaxy” occurs 5 times in text A “Heat” occurs 3 times in text A (Blank means 0 occurrences.) Slide from Mitch Marcus

21. Document Vectors Document ids A B C D E F G H I nova galaxy heat h’wood film role diet fur 10 5 3 5 10 10 8 7 9 10 5 10 10 9 10 5 7 9 6 10 2 8 7 5 1 3 Slide from Mitch Marcus

22. TF x IDF Calculation A Slide from Mitch Marcus

23. Features Define whatever features you like: Length of longest string of CAP’s Number of $’s Useful words for the task … A

24. Similarity between documents A = [10 5 3 0 0 0 0 0]; G = [5 0 7 0 0 9 0 0]; E = [0 0 0 0 0 10 10 0]; Sum of Squared Distances (SSD) = SSD(A,G) = ? SSD(A,E) = ? SSD(G,E) = ? Which pair of documents are the most similar?

25. Source: Hinrich Schutze

26. source: Dan Klein

27. K-means clustering • Want to minimize sum of squared Euclidean distances between points xi and their nearest cluster centers mk source: Svetlana Lazebnik

28. K-means clustering • Want to minimize sum of squared Euclidean distances between points xi and their nearest cluster centers mk source: Svetlana Lazebnik

40. source: Dan Klein

41. source: Dan Klein

42. source: Dan Klein

43. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: Source: Hinrich Schutze

44. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: • The sum of squared distances (RSS) decreases during reassignment. Source: Hinrich Schutze

45. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: • The sum of squared distances (RSS) decreases during reassignment. • (because each vector is moved to a closer centroid) Source: Hinrich Schutze

46. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: • The sum of squared distances (RSS) decreases during reassignment. • (because each vector is moved to a closer centroid) • RSS decreases during recomputation. Source: Hinrich Schutze

47. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: • The sum of squared distances (RSS) decreases during reassignment. • (because each vector is moved to a closer centroid) • RSS decreases during recomputation. • Thus: We must reach a fixed point. Source: Hinrich Schutze

48. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: • The sum of squared distances (RSS) decreases during reassignment. • (because each vector is moved to a closer centroid) • RSS decreases during recomputation. • Thus: We must reach a fixed point. • But we don’t know how long convergence will take! Source: Hinrich Schutze

49. Convergence of K Means • K-means converges to a fixed point in a finite number of iterations. Proof: • The sum of squared distances (RSS) decreases during reassignment. • (because each vector is moved to a closer centroid) • RSS decreases during recomputation. • Thus: We must reach a fixed point. • But we don’t know how long convergence will take! • If we don’t care about a few docs switching back and forth, then convergence is usually fast (< 10-20 iterations). Source: Hinrich Schutze

50. source: Dan Klein