Manifold elastic net: A unified framework for sparse dimension reduction

Data Mining and Knowledge Discovery

Volumn 22, Issue 3, 2011, Pages 340-371

  Zhou, Tianyi ^a   Tao, Dacheng ^a   Wu, Xindong ^b  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b University of Vermont ^*  (United States)

Author keywords

Dimensionality reduction; Elastic net; Manifold learning

Indexed keywords

CLASSIFICATION ERRORS; DATA REPRESENTATIONS; DATA SETS; DIMENSION REDUCTION; DIMENSIONALITY REDUCTION; DIMENSIONALITY REDUCTION ALGORITHMS; ELASTIC NET; EQUIVALENT TRANSFORMATIONS; EXPERIMENTAL EVIDENCE; LOCAL GEOMETRY; LOW DIMENSIONAL; MANIFOLD LEARNING; OVERFITTING; PENALIZED LEAST-SQUARES; PROJECTION MATRIX; SPARSE SOLUTIONS; UNIFIED FRAMEWORK;

FACE RECOGNITION; MATRIX ALGEBRA; OPTIMIZATION;

LEARNING ALGORITHMS;

EID: 79960810210     PISSN: 13845810     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10618-010-0182-x     Document Type: Article

References (54)

1. Belhumeur PN, Hespanha JP, Kriegman DJ (1997) Eigenfaces vs. fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19(7):711-720 (Pubitemid 127762263)
2. Belkin M, Niyogi P (2001) Laplacian eigenmaps and spectral techniques for embedding and clustering. Adv Neural Inf Process Syst 14:585-591
3. Belkin M, Niyogi P, Sindhwani V (2006) Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. J Mach Learn Res 7:2399-2434 (Pubitemid 44708005)
4. Bian W, Tao D (2008) Harmonic mean for subspace selection. In: IEEE ICPR, pp 1-4
5. Bishop CM,Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput 10:215-234
6. Cai D, He X, Han J (2007) Spectral regression for efficient regularized subspace learning. In: IEEE 11th international conference on computer vision, 2007. ICCV 2007, pp 1-8
7. Cai D, He X, Han J (2008) SRDA: an efficient algorithm for large-scale discriminant analysis. IEEE Trans Knowl Data Eng 20(1):1-12
8. Candes E, Tao T (2005) The dantzig selector: statistical estimation when p is much larger than n. Ann Stat 35:2392-2404
9. Candes EJ,Wakin MB, Boyd SP (2008) Enhancing sparsity by reweighted L1 minimization. Special issue on sparsity. J Fourier Anal Appl 14(5):877-905
10. D'aspremont A, Ghaoui LE, Jordan MI, Lanckriet GRG (2007) A direct formulation for sparse PCA using semidefinite programming. SIAM Rev 49(3):434-448 (Pubitemid 47377693)
11. Ding C, Li T (2007) Adaptive dimension reduction using discriminant analysis and k-means clustering. In: ICML '07: Proceedings of the 24th international conference on machine learning. ACM, New York, NY, USA, pp 521-528
12. Ding CHQ, Li T, Jordan MI (2008) Convex and semi-nonnegative matrix factorizations. IEEE Trans Pattern Anal Mach Intell 32(1):45-55
13. Donoho DL, Grimes C (2003) Hessian eigenmaps: locally linear embedding techniques for high-dimensional data. PNAS 100(10):5591-5596 (Pubitemid 36576852)
14. Efron B, Hastie T, Johnstone I, Tibshirani R (2004) Least angle regression. Ann Stat 32(2):407-499 (Pubitemid 41250302)
15. Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. J Am Stat Assoc 96:1348-1360 (Pubitemid 33695585)
16. Fan J, Lv J (2008) Sure independence screening for ultrahigh dimensional feature space. J R Stat Soc Ser B 70(5):849-911
17. Fisher RA (1936) The use of multiple measurements in taxonomic problems. Ann Eugen 7(2):179-188
18. Fyfe C (2007) Two topographic maps for data visualisation. Data Min Knowl Discov 14(2):207-224 (Pubitemid 46418255)
19. Golub GH, Van Loan CF (1996) Matrix computations. 3. Johns Hopkins University Press, Baltimore, MD
20. Graham DB, Allinson NM (1936) Characterizing virtual eigensignatures for general purpose face recognition. Face recognition: from theory to applications, NATO ASI series F. Comput Syst Sci 163:446-456
21. Hastie T, Tibshirani R, Friedman J (2009) The elements of statistical learning: data mining, inference, and prediction, 2nd edn. Springer Series in Statistics, Springer, 2nd edn. corr. 3rd printing edn
22. He X, Niyogi P (2004) Locality preserving projections. In: Advances in neural information processing systems. MIT Press, Cambridge, MA
23. He X, Cai D, Yan S, Zhang HJ (2005a) Neighborhood preserving embedding. In: Proceedings of IEEE international conference on computer vision, vol. 2. IEEE Computer Society,Washington, DC, USA, pp 1208-1213 (Pubitemid 44042318)
24. He X, Yan S, Hu Y, Niyogi P (2005b) Face recognition using laplacianfaces. IEEE Trans Pattern Anal Mach Intell 27(3):328-340 (Pubitemid 40377326)
25. Hotelling H (1936) Analysis of a complex of statistical variables into principal components. J Educ Phychol 24:417-441
26. Huang H, Ding C (2008) Robust tensor factorization using r1 norm. In: IEEE conference on computer vision and pattern recognition, 2008. CVPR 2008, pp 1-8
27. James GM, Radchenko P, Lv J (2009) Dasso: connections between the dantzig selector and lasso. J R Stat Soc Ser B 71(1):127-142
28. Kriegel HP, Borgwardt KM, Kröger P, Pryakhin A, Schubert M, Zimek A (2007) Future trends in data mining. Data Min Knowl Discov 15(1):87-97 (Pubitemid 47142812)
29. Li T, Zhu S, Ogihara M (2008a) Text categorization via generalized discriminant analysis. Inf Process Manage 44(5):1684-1697
30. Li X, Lin S, Yan S, Xu D (2008b) Discriminant locally linear embedding with high-order tensor data. IEEE Trans Syst Man Cybern B 38(2):342-352 (Pubitemid 351479557)
31. Liu W, Tao D, Liu J (2008) Transductive component analysis. In: ICDM '08: Proceedings of the 2008 eighth IEEE international conference on data mining. IEEE Computer Society,Washington, DC, USA, pp 433-442
32. Lv J, Fan Y (2009) A unified approach to model selection and sparse recovery using regularized least squares. Ann Stat 37:3498
33. Park MY, Hastie T (2006) L1 regularization path algorithm for generalized linear models. Tech. rep., Department of Statistics, Stanford University
34. Phillips PJ, Moon H, Rizvi SA, Rauss PJ (2000) The feret evaluation methodology for face-recognition algorithms. IEEE Trans Pattern Anal Mach Intell 22(10):1090-1104
35. Roweis ST, Saul LK (2000) Nonlinear dimensionality reduction by locally linear embedding. Science 290(5500):2323-2326 (Pubitemid 32041578)
36. Shakhnarovich G, Moghaddam B (2004) Face recognition in subspaces. In: Li SZ, Jain AK (eds) Handbook of face recognition. Springer-Verlag
37. Sun L, Ji S, Ye J (2008) A least squares formulation for canonical correlation analysis. In: ICML '08: Proceedings of the 25th international conference on machine learning. ACM, New York, NY, USA, pp 1024-1031
38. Tao D, Li X, Wu X, Hu W, Maybank SJ (2007a) Supervised tensor learning. Knowl Inf Syst 13(1):1-42
39. Tao D, Li X, Wu X, Maybank SJ (2007b) General tensor discriminant analysis and gabor features for gait recognition. IEEE Trans Pattern Anal Mach Intell 29(10):1700-1715
40. Tao D, Li X, Wu X, Maybank SJ (2009) Geometric mean for subspace selection. IEEE Trans Pattern Anal Mach Intell 31(2):260-274
41. Tenenbaum JB (2000) A global geometric framework for nonlinear dimensionality reduction. Science 290(5500):2319-2323 (Pubitemid 32041577)
42. Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B 58:267-288
43. Turk MA, Pentland AP (1991) Face recognition using eigenfaces. In: IEEE computer society conference on computer vision and pattern recognition, 1991. Proceedings CVPR '91, pp 586-591
44. Wang F, Chen S, Zhang C, Li T (2008) Semi-supervised metric learning by maximizing constraint margin. In: CIKM '08: Proceeding of the 17th ACM conference on information and knowledge management. ACM, New York, NY, USA, pp 1457-1458
45. Yan S, Xu D, Zhang B, Zhang HJ, Yang Q, Lin S (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40-51 (Pubitemid 46415944)
46. Ye J (2007) Least squares linear discriminant analysis. In: ICML '07: Proceedings of the 24th international conference on machine learning. ACM, New York, NY, USA, pp 1087-1093 (Pubitemid 47275175)
47. Zass R, Shashua A (2007) Nonnegative sparse PCA. In: In neural information processing systems. pp 1561-1568
48. Zhang Z, Zha H (2005) Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. SIAM J Sci Comput 26(1):313-338 (Pubitemid 40297703)
49. Zhang T, Tao D, Yang J (2008) Discriminative locality alignment. In: ECCV '08: Proceedings of the 10th European conference on computer vision. Springer-Verlag, Berlin, Heidelberg, pp 725-738
50. Zhang T, Tao D, Li X, Yang J (2009) Patch alignment for dimensionality reduction. IEEE Trans Knowl Data Eng 21(9):1299-1313
51. Zou H (2006) The adaptive Lasso and its Oracle properties. J Am Stat Assoc 101(476):1418-1429
52. Zou H, Hastie T (2005) Regularization and variable selection via the elastic net. J R Stat Soc B 67:301-320 (Pubitemid 40465877)
53. ZouH,Hastie T, Tibshirani R. (2006) Sparse principal component analysis. JComput Graph Stat 15(2):262-286
54. Zou H, Zhang HH (2009) On the adaptive elastic-net with a diverging number of parameters. Ann Stat 37(4):1733-1751