A compressed PCA subspace method for anomaly detection in high-dimensional data

IEEE Transactions on Information Theory

Volumn 59, Issue 11, 2013, Pages 7419-7433

  Ding, Qi ^a   Kolaczyk, Eric D ^a  

^a Boston University   (United States)

Author keywords

Anomaly detection; principal component analysis; random projection

Indexed keywords

ALTERNATIVE HYPOTHESIS; ANOMALY DETECTION; COVARIANCE MODELING; DIMENSION REDUCTION; HIGH DIMENSIONAL DATA; RANDOM PROJECTIONS; SAMPLE COVARIANCES; SUBSPACE DETECTION;

PRINCIPAL COMPONENT ANALYSIS; STATISTICS;

STATISTICAL TESTS;

EID: 84886653855     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2013.2278017     Document Type: Article

References (33)

1. Z. D. Bai, "Methodologies in spectral analysis of large dimensional random matrices, a review," Statist. Sinica, vol. 9, pp. 611-677, 1999.
2. P. J. Bickel and E. Levina, "Regularized estimation of large covariance matrices," Ann. Statist., vol. 36, no. 1, pp. 199-227, 2008.
3. E. Bingham and H. Mannila, "Random projection in dimensionality reduction: Applications to image and text data," in Proc. Seventh ACM SIGKDD Int. Conf. Knowledge Discovery Data Mining, 2001, pp. 245-250.
4. D. W. Chang, "A matrix trace inequality for products of Hermitian matrices," J. Math. Analysis Appl., vol. 237, no. 2, pp. 721-725, 1999.
5. L. H. Chiang, E. Russell, and R.D. Braatz, Fault Detection and Diagnosis in Industrial Systems. NewYork, NY, USA: Springer-Verlag, 2001.
6. S. Dasgupta, "Experiments with random projection," in Proc. 16th Conf. Uncertainty Artificial Intelligence, 2000, pp. 143-151.
7. M. A. Davenport, P. T. Boufounos, M. B. Wakin, and R. G. Baraniuk, "Signal processing with compressive measurements," IEEE J. Sel. Topics Signal Process., vol. 4, no. 2, pp. 445-460, Apr. 2010.
8. D. Fradkin and D.Madigan, "Experiments with random projections for machine learning," in Proc. 9th ACM SIGKDD Int. Conf. Knowledge Discovery Data Mining, 2003, pp. 517-522.
9. A. Harvey, E. Ruiz, and N. Shephard, "Multivariate stochastic variance models," Rev. Econ. Stud., vol. 61, no. 2, pp. 247-264, 1994.
10. J. E. Jackson and R. H. Morris, "An application of multivariate quality control to photographic processing," J. Amer. Statist. Soc., vol. 52, no. 278, pp. 186-199, 1957.
11. J. E. Jackson and G. S. Mudholkar, "Control procedures for residual associated with principal component analysis," Technometrics, vol. 21, pp. 341-349, 1979. (Pubitemid 9472204)
12. W. Johnson and J. Lindenstrauss, "Extensions of Lipschitz mappings into a Hilbert space," Contemp. Math., vol. 26, pp. 189-206, 1984.
13. I. M. Johnstone, "On the distribution of the largest eigenvalue in principal components analysis," Ann. Statist., vol. 29, pp. 295-327, 2001.
14. I. M. Johnstone and A. Y. Lu, "Sparse principal components analysis," J. Amer. Statist. Assoc., vol. 104, pp. 682-693, Jun. 2009.
15. M. Journée, Y. Nesterov, P. Richtárik, and R. Sepulchre, "Generalized power method for sparse principal component analysis," J. Mach. Learning Res., vol. 11, pp. 517-553, 2010.
16. N. E. Karoui, "Operator norm consistent estimation of large-dimensional sparse covariance matrices," Ann. Statist., vol. 36, pp. 2717-2756, 2008.
17. A. Lakhina, M. Crovella, and C. Diot, "Diagnosing network-wide traffic anomalies," presented at the Proc. Conf. Applications, Technol., Architect., Protocols Comput. Commun., Portland, OR, USA, Aug.-Sep. 30-03, 2004.
18. A. Lakhina, M. Crovella, and C. Diot, "Mining anomalies using traffic feature distributions," in Proc. Conf. Appl., Technol., Architect., Protocols Comput. Commun., Philadelphia, PA, USA, Aug. 22-26, 2005.
19. L. Laloux, P. Cizeau, J. P. Bouchaud, and M. Potters, "Noise dressing of financial correlation matrices," Phys. Rev. Lett., vol. 83, pp. 1467-1470, 1999. (Pubitemid 129690137)
20. D. R. Lessard, "International portfolio diversification: A multivariate analysis for a group of Latin American countries," J. Finance, vol. 28, no. 3, pp. 619-633, Jun. 1973.
21. E. Levina, A. Rothman, and J. Zhu, "Sparse estimation of large covariance matrices via a nested Lasso penalty," Ann. Appl. Statist., vol. 2, pp. 245-263, 2008.
22. P. Li, T. J. Hastie, and K. W. Church, "Very sparse random projections," in Proc. 12th ACM SIGKDD Int. Conf. Knowl. Discov. Data Mining, 2006, pp. 287-296. (Pubitemid 44535525)
23. X. Luo, "High dimensional low rank and sparse covariance matrix estimation via convex minimization," 2011 [Online]. Available: arXiv:1111.1133
24. S. Negahban and M. J. Wainwright, "Estimation of (near) low-rank matrices with noise and high-dimensional scaling," Ann. Statist., vol. 39, no. 2, pp. 1069-1097, 2011.
25. P. Nomikos and J. F. MacGregor, "Multivariate spc charts for monitoring batch processes," Technometrics, vol. 37, no. 1, pp. 41-59, Feb. 1995.
26. C. H. Papadimitriou, P. Raghavan, H. Tamaki, and S. Vempala, "Latent semantic indexing: A probabilistic analysis," J. Comput. Syst. Sci., vol. 61, no. 2, pp. 217-235, 2000.
27. P. G. Park, "On the trace bound of a matrix product," IEEE Trans. Autom. Control, vol. 41, no. 12, pp. 1799-1802, 1996.
28. D. Paul, "Asymptotics of sample eigenstructure for a large dimensional spiked covariance model," Statist. Sinica, vol. 17, pp. 1617-1642, 2007.
29. S. J. Qin, "Statistical process monitoring: Basics and beyond," J. Chemometrics, vol. 17, no. 8-9, pp. 480-502, 2003.
30. H. Shen and J. Z. Huang, "Sparse principal component analysis via regularized low rankmatrix approximation," J.Multivariate Anal., vol. 99, no. 6, pp. 1015-1034, 2008.
31. S. S. Vempala, The Random Projection Method. Providence, RI, USA: AMS, 2004.
32. G. S. Watson, Statistics on Spheres. New York, NY, USA: Wiley, 1983.
33. H. Zou, T. Hastie, and R. Tibshirani, "Sparse principal components analysis," J. Comput. Graph. Statist., vol. 15, pp. 265-286, 2006.