Nonnegative matrix factorization for interactive topic modeling and document clustering

Partitional Clustering Algorithms

Volumn , Issue , 2015, Pages 215-243

  da Kuang, D ^a   Choo, Jaegul ^a   Park, Haesun ^a  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Block coordinate descent; Document clustering; Interactive visual analytics; Nonnegative matrix factorization; Topic modeling

Indexed keywords

CLUSTER ANALYSIS; FACTORIZATION; INFORMATION RETRIEVAL; VISUALIZATION;

BLOCK COORDINATE DESCENTS; DOCUMENT CLUSTERING; NONNEGATIVE MATRIX FACTORIZATION; TOPIC MODELING; VISUAL ANALYTICS;

MATRIX ALGEBRA;

EID: 84944595142     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-3-319-09259-1_7     Document Type: Chapter

References (52)

1. Arora S., Ge R., Kannan R., Moitra A. (2012) Computing a nonnegative matrix factorization-provably. In: Proceedings of the 44th symposium on theory of computing (STOC), pp 145-162.
2. Arora S., Ge R., Halpern Y., Mimno D., Moitra A., Sontag D., Wu Y., Zhu M. (2013). A practical algorithm for topic modeling with provable guarantees. J Mach Learn Res 28 (2):280-288.
3. Berman A., Plemmons R. J. (1994) Nonnegative matrices in the mathematical sciences. SIAM, Philadelphia.
4. Bertsekas D. P. (1999) Nonlinear programming, 2nd edn. Athena Scientific, Belmont.
5. Blei D. M., Ng A. Y., Jordan M. I. (2003) Latent Dirichlet allocation. J Mach Learn Res 3:993-1022.
6. Brunet J-P., Tamayo P., Golub T. R., Mesirov J. P. (2004) Metagenes and molecular pattern discovery using matrix factorization. Proc Natl Acad Sci USA 101 (12):4164-4169.
7. Cai D., He X., Han J., Huang T. S. (2011) Graph regularized nonnegative matrix factorization for data representation. IEEE Trans Pattern Anal Mach Intell 33 (8):1548-1560.
8. Choo J., Park H. (2013) Customizing computational methods for visual analytics with big data. IEEE Comput Graph Appl 33 (4):22-28.
9. Choo J., Lee C., Reddy C. K., Park H. (2013) UTOPIAN: user-driven topic modeling based on interactive nonnegative matrix factorization. IEEE Trans Vis Comput Graph 19 (12):1992-2001.
10. Cichocki A., Zdunek R., Phan A. H., Amari S. (2009) Nonnegative matrix and tensor factorizations: applications to exploratory multi-way data analysis and blind source separation. Wiley, London.
11. Devarajan K. (2008) Nonnegative matrix factorization: an analytical and interpretive tool in computational biology. PLoS Comput Biol 4 (7):e1000029.
12. Dhillon I. S., Sra S. (2005) Generalized nonnegative matrix approximations with Breg-man divergences. In: Advances in neural information processing systems (NIPS), vol 18, pp 283-290.
13. Ding C., He X., Simon H. D. (2005) On the equivalence of nonnegative matrix factorization and spectral clustering. In: Proceedings of SIAM international conference on data mining (SDM), pp 606-610.
14. Ding C., Li T., Jordan M. (2008) Nonnegative matrix factorization for combinatorial optimization: spectral clustering, graph matching, and clique finding. In: Proceedings of the 8th IEEE international conference on data mining (ICDM), pp 183-192.
15. Ding C., T. Li, Jordan M. I. (2010) Convex and semi-nonnegative matrix factorization. IEEE Trans Pattern Anal Mach Intell 32 (1):45-55.
16. Duda R. O., Hart P. E., Stork D. G. (2000) Pattern classification. Wiley-Interscience, London
17. Globerson A, Chechik G, Pereira F, Tishby N (2007) Euclidean embedding of co-occurrence data. J Mach Learn Res 8:2265-2295.
18. Gonzales E. F., Zhang Y. (2005) Accelerating the Lee-Seung algorithm for non-negative matrix factorization. Technical Report TR05-02, Rice University.
19. Grippo L., Sciandrone M. (2000) On the convergence of the block nonlinear Gauss-Seidel method under convex constraints. Oper Res Lett 26:127-136.
20. Hofmann T. (1999) Probabilistic latent semantic indexing. In: Proceedings of the 22nd annual international ACM SIGIR conference on research and development in information retrieval (SIGIR).
21. Hoyer P. O. (2004) Non-negative matrix factorization with sparseness constraints. J Mach Learn Res 5:1457-1469.
22. Kim H., Park H. (2007) Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis. Bioinformatics 23 (12):1495-1502.
23. Kim H., Park H. (2008) Nonnegative matrix factorization based on alternating non-negativity-constrained least squares and the active set method. SIAM J Matrix Anal Appl 30 (2):713-730.
24. Kim D., Sra S., Dhillon I. (2007) Fast Newton-type methods for the least squares nonnegative matrix approximation problem. In: Proceedings of SIAM international conference on data mining (SDM), pp 343-354.
25. Kim J., He Y., Park H. (2014) Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework. J Global Optim 58 (2):285-319.
26. Kim J., Park H. (2008) Sparse nonnegative matrix factorization for clustering. Technical Report GT-CSE-08-01, Georgia Institute of Technology.
27. Kim J., Park H. (2008) Toward faster nonnegative matrix factorization: a new algorithm and comparisons. In: Proceedings of the 8th IEEE international conference on data mining (ICDM), pp 353-362.
28. Kim J., Park H. (2011) Fast nonnegative matrix factorization: An active-set-like method and comparisons. SIAM J Sci Comput 33 (6):3261-3281.
29. Kuang D., Park H. (2013) Fast rank-2 nonnegative matrix factorization for hierarchical document clustering. In: Proceedings of the 19th ACM international conference on knowledge discovery and data mining (KDD), pp 739-747.
30. Kuang D., Ding C., Park H. (2012) Symmetric nonnegative matrix factorization for graph clustering. In: Proceedings of SIAM international conference on data mining (SDM), pp 106-117.
31. Kuhn H. W. (1955) The Hungarian method for the assignment problem. Nav Res Logistics Q 2:83-97.
32. Lawson C. L., Hanson R. J. (1974) Solving least squares problems. Prentice Hall, Englewood Cliffs.
33. Lee D. D., Seung H. S. (1999) Learning the parts of objects by non-negative matrix factorization. Nature 401:788-791.
34. Lee D. D., Seung H. S. (2001) Algorithms for non-negative matrix factorization. In: Advances in neural information processing systems (NIPS), vol 14, pp 556-562.
35. Lewis D. D., Yang Y., Rose T. G., Li F. (2004) Rcv1: a new benchmark collection for text categorization research. J Mach Learn Res 5:361-397.
36. Li S., Hou X. W., Zhang H. J., Cheng Q. S. (2001) Learning spatially localized, parts-based representation. In: Proceedings of the 2001 IEEE conference on computer vision and pattern recognition (CVPR), pp 207-212.
37. Li T., Ding C., Jordan M. I. (2007) Solving consensus and semi-supervised clustering problems using nonnegative matrix factorization. In: Proceedings of the 7th IEEE international conference on data mining (ICDM), pp 577-582.
38. Li L., Lebanon G., Park H. (2012) Fast Bregman divergence NMF using Taylor expansion and coordinate descent. In: Proceedings of the 18th ACM international conference on knowledge discovery and data mining (KDD), pp 307-315.
39. Lin C-J. (2007) Projected gradient methods for nonnegative matrix factorization. Neural Comput 19 (10):2756-2779.
40. Manning C. D., Raghavan P., Schütze H. (2008) Introduction to information retrieval. Cambridge University Press, Cambridge.
41. Mc Callum A. K. (2002) MALLET: a machine learning for language toolkit. http://mallet.cs.umass.edu.
42. Monti S., Tamayo P., Mesirov J., Golub T. (2003) Consensus clustering: a resampling-based method for class discovery and visualization of gene expression microarray data. Mach Learn 52 (1-2):91-118.
43. Paatero P., Tapper U. (1994) Positive matrix factorization: a non-negative factor model with optimal utilization of error estimates of data values. Environmetrics 5:111-126.
44. Pauca V. P., Shahnaz F., Berry M. W., Plemmons R. J. (2004) Text mining using non-negative matrix factorizations. In: Proceedings of SIAM international conference on data mining (SDM), pp 452-456.
45. Pauca V. P., Piper J., Plemmons R. J. (2006) Nonnegative matrix factorization for spectral data analysis. Linear Algebra Appl 416 (1):29-47.
46. Shahnaz F., Berry M. W., Pauca V. P., Plemmons R. J. (2006) Document clustering using nonnegative matrix factorization. Inf Process Manag 42:373-386.
47. Tibshirani R. (1994) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B Methodol 58:267-288.
48. Van der Maaten L., Hinton G. (2008) Visualizing data using t-SNE. J Mach Learn Res 9:2579-2605.
49. Vavasis S. A. (2009) On the complexity of nonnegative matrix factorization. SIAM J Optim 20 (3):1364-1377.
50. Wild S., Curry J., Dougherty A. (2004) Improving non-negative matrix factorizations through structured initialization. Pattern Recognit 37:2217-2232.
51. Xie B., Song L., Park H. (2013) Topic modeling via nonnegative matrix factorization on probability simplex. In: NIPS workshop on topic models: computation, application, and evaluation.
52. Xu W., Liu X., Gong Y. (2003) Document clustering based on non-negative matrix factorization. In: Proceedings of the 26th annual international ACM SIGIR conference on research and development in information retrieval (SIGIR), pp 267-273.