Mixtures of robust probabilistic principal component analyzers

Neurocomputing

Volumn 71, Issue 7-9, 2008, Pages 1274-1282

  Archambeau, Cédric ^a   Delannay, Nicolas ^b   Verleysen, Michel ^b  

^a UNIVERSITY COLLEGE LONDON   (United Kingdom)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Dimensionality reduction; EM algorithm; Mixture model; Non Gaussianity; Principal component analysis; Robustness to outliers

Indexed keywords

CLUSTERING ALGORITHMS; COMPUTER SIMULATION; DATA REDUCTION; PRINCIPAL COMPONENT ANALYSIS; PROBABILITY;

LINEAR MODEL; ROBUST PROBABILISTIC PRINCIPAL COMPONENT ANALYZER;

DATA PROCESSING;

ALGORITHM; ARTICLE; CLUSTER ANALYSIS; DATA ANALYSIS; DATA MINING; FACTORIAL ANALYSIS; NONLINEAR SYSTEM; PRINCIPAL COMPONENT ANALYSIS; PRIORITY JOURNAL; PROBABILITY; SENSITIVITY AND SPECIFICITY; STATISTICAL DISTRIBUTION; STATISTICAL MODEL; STUDENT T TEST;

EID: 40649094216     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.neucom.2007.11.029     Document Type: Article

References (28)

1. C. Archambeau, Probabilistic models in noisy environments-and their application to a visual prosthesis for the blind, Ph.D. Thesis, Université catholique de Louvain, Louvain-la-Neuve, Belgium, 2005.
2. Archambeau C., Delannay N., and Verleysen M. Robust probabilistic projections. In: Cohen W.W., and Moore A. (Eds). 23rd International Conference on Machine Learning (ICML) (2006), ACM, New York 33-40
3. C. Archambeau, N. Delannay, M. Verleysen, Mixtures of robust probabilistic principal component analyzers, in: 15th European Symposium on Artificial Neural Networks (ESANN), 2007, pp. 229-234.
4. Bishop C.M. Pattern Recognition and Machine Learning (2006), Springer, New York
5. Cox T., and Cox M. Multidimensional Scaling (2001), Chapman & Hall, London
6. Dempster A.P., Laird N.M., and Rubin D.B. Maximum likelihood from incomplete data via EM algorithm. J. R. Stat. Soc. B 39 1 (1977) 1-38
7. Efron B., and Tibshirani R.J. An Introduction to the Bootstrap (1993), Chapman & Hall, London
8. Everitt B.S. An Introduction to Latent Variable Models (1983), Chapman & Hall, London
9. Fisher R.A. Applications of "Student's" distribution. Metron 5 (1925) 90-104
10. Z. Ghahramani, G.E. Hinton, The EM algorithm for mixtures of factor analyzers, Technical Report CRG-TR-96-1, Department of Computer Science, University of Toronto, 1996.
11. Hinton G.E., Dayan P., and Revow M. Modeling the manifolds of images of handwritten digits. IEEE Trans. Neural Networks 8 (1997) 65-74
12. Hotelling H. Analysis of a complex of statistical variables into principal components. J. Educ. Psychol. 24 (1933) 417-441
13. Huang K., Ma Y., and Vidal R. Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications. 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR) vol. 2 (2004) 631-638
14. Jolliffe I.T. Principal Component Analysis (1986), Springer, New York
15. Liu C., and Rubin D.B. ML estimation of the t distribution using EM and its extensions, ECM and ECME. Stat. Sinica 5 (1995) 19-39
16. Minka T.P. Automatic choice of dimensionality for PCA. In: Leen T.K., Dietterich T.G., and Tresp V. (Eds). Advances in Neural Information Processing Systems (NIPS) vol. 13 (2001), MIT Press, Cambridge, MA 598-604
17. Neal R.M., and Hinton G.E. A view of the EM algorithm that justifies incremental, sparse, and other variants. In: Jordan M.I. (Ed). Learning in Graphical Models (1998), MIT Press, Cambridge, MA 355-368
18. Nocedal J., and Wright S.J. Numerical Optimization (2000), Springer, Berlin
19. Peel D., and McLachlan G.J. Robust mixture modelling using the t distribution. Stat. Comput. 10 (2000) 339-348
20. Roweis S.T. EM algorithms for PCA and SPCA. In: Jordan M.I., Kearns M.J., and Solla S.A. (Eds). Advances in Neural Information Processing Systems (NIPS) vol. 10 (1998), MIT Press, Cambridge, MA
21. Roweis S.T., and Saul L.K. Nonlinear dimensionality reduction by locally linear embedding. Science 290 (2000) 2323-2326
22. Rubin D.B., and Thayer D.T. EM algorithms for ML factor analysis. Psychometrika 47 1 (1982) 69-76
23. Sammon Jr. J.W. A nonlinear mapping for data structure analysis. IEEE Trans. Comput. 18 (1969) 401-409
24. Shoham S. Robust clustering by deterministic agglomeration EM of mixtures of multivariate t-distributions. Pattern Recognition 35 5 (2002) 1127-1142
25. Tenenbaum J.B., de Silva V., and Langford J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (2000) 2319-2323
26. Tipping M.E., and Bishop C.M. Probabilistic principal component analysis. J. R. Stat. Soc. B 61 (1999) 611-622
27. Tipping M.E., and Bishop C.M. Mixtures of probabilistic principal component analyzers. Neural Comput. 11 2 (1999) 443-482
28. Xu L., and Yuille A.L. Robust principal component analysis by self-organizing rules based on statistical physics approach. IEEE Trans. Neural Networks 6 1 (1995) 131-143