Abstract
We propose a multi-linear algebra based subspace learning approach for finding linear projection which preserves some implicit structural or locally-spatial information among the original feature space. Our method uses a new tensor data representation model, in which, each group of data points are partitioned into several equal-sized sub-groups with its neighbors affiliated to them, and all sub-groups are concatenated to represent as the tensor space product of the original feature space. Then, a new optimization algorithm called Lagrangian multiplier mode (L-mode) is presented for computing the optimal linear projections. We show that our method has three ways for resolving the Small Sample Size problem: by applying the fuzzy matrix model to avoid the disturbance from non-interested determinant, by a quadratic sample correlation model, and by projecting the samples into a manifold using linear programming. Extensive experimental results conducted on two benchmark face biometrics datasets i.e. Yale-B and CMU-PIE, and a nutrition surveillance dataset demonstrate that our method is effective and robust than the state-of-the-arts such as Principal Component Analysis, Linear Discriminant Analysis, Locality Preserving Projections and their variations on both classification accuracies and computational expenses.
Similar content being viewed by others
References
Belhumeur PN, Hespanha J, Kriegman D (1997) Eigenfaces versus fisherfaces: recognition using class specific linear projection. IEEE Trans Pattern Anal Mach Intell 19: 711–720
Cai D, Xiaofei H, Yuxiao H, Jiawei H, Huang T (2007) Learning a spatially smooth subspace for face recognition. In: Proceedings of the international conference on computer vision and pattern recognition, pp 1–7
Casabiell X, Pineiro V, Tome MA, Peino R, Dieguez C, Casanueva FF (1997) Presence of leptin in colostrum and breast milk from lactating mothers: a potential role in the regulation of neonatal food intake. J Clin Endocr Metab 82(4): 270–273
Chen L, Liao H, Ko M, Lin J, Yu G (2000) A new LDA-based face recognition system which can solve the small sample size problem. Pattern Recognit 33: 1713–1726
Douglas P (1976) The Cobb–Douglas production function once again: its history, its testing, and some new empirical values. J Polit Econ 84(5): 903–916
Friedman JH (1989) Regularized discriminant analysis. J Am Stat Assoc 84: 165–175
Georghiades A, Kriegman D, Belhumeur P (2001) From few to many: generative models for recognition under variable pose and illumination. IEEE Trans Pattern Anal Mach Intell 40: 643–660
Grassmann H (2000) Extension theory, American Mathematical Society
Hastie T, Buja A, Tibshirani R (1995) Penalized discriminant analysis. Ann Stat 23: 73–102
He Q (2001) Leptin and procreation. Qinghai Med J 31(12): 53–55
Jiang L (2003) The effect of leptin in the pathogenic mechanism of female infertility. J Med Postgrad 16(10): 792–794
Li X, Li H (2003) the root cause of infertility. Chin Gen Pract 6(11): 887–889
Li J, Lei Z, Jing W (2006) Detection for ureaplasma urealyticum in infertile women and men. Matern Child Health Care China 21(11): 1567–1568
Long YJ, Huang YZ (2006) Image based source camera identification using demosaicking. In: Proceedings of the 8th international conference on workshop multimedia signal processing, pp 419–424
Lu J, Plataniotis K, Venetsanopoulos A (2003) Regularized discriminant analysis for the small sample size problem in face recognition. Pattern Recognit Lett 24: 3079–3087
Lu J, Plataniotis K, Venetsanopoulos A (2005) Regularization studies of linear discriminant analysis in small sample size scenarios with application to face recognition. Pattern Recognit Lett 26: 181–191
Sim T, Baker S, Bsat M (2003) The CMU pose, illumination, and expression database. IEEE Trans Pattern Anal Mach Intell 25: 1615–1618
Tjonneland A, Overvad K, Haraldsdottir J, Bang S, Ewertz M, Jensen OM (1991) Validation of a semi-quantitative food frequency questionnaire development in Denmark. Int J Epidemiol 20(4): 906–912
Turk M, Pentland A, Bsat M (1991) Face recognition using eigenfaces. In: Proceedings of the international conference on computer vision and pattern recognition, pp 586–591
Wang H, Ahuja N (2008) A tensor approximation approach to dimensionality reduction. Int J Comput Vis 76: 217–229
Wang S, Zhang X, Luo L, Feng X (2006) Investigation of serum proteomic spectra in the patients suffering from primary infertility with unknown reasons during midluteal phase. Chin J Pract Gynecol 22(7): 509–511
Xu C (1994) Chlamydiatrachomatis and infertility. J Androl 8(3): 180–184
Yang J, Zhang D, Frangi A, Yang J (2004) Two-dimensional PCA: a new approach to appearance-based face representation and recognition. IEEE Trans Pattern Anal Mach Intell 26: 131–137
Yan S, Xu D, Zhang B, Zhang H, Yang Q, Lin S (2007a) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1): 40–51
Yan S, Xu D, Yang Q, Zhang L, Tang X, Zhang H (2007b) Multilinear discriminant analysis for face recognition. IEEE Trans Image Process 16: 212–220
Ye J, Janardan C, Park C, Park H (2004) An optimization criterion for generalized discriminant analysis on undersampled problems. IEEE Trans Pattern Anal Mach Intell 26: 982–994
Ye J, Janardan R, Li Q (2005) Two-dimensional linear discriminant analysis. In: Proceedings of the advances in neural information processing systems, pp 1569–1576
Yu H, Yang J (2001) A direct LDA algorithm for high-dimensional data with application to face recognition. Pattern Recognit 34: 2067–2070
Zhang Y, Proenca R, Maffei M, Barone M, Leopold L, Friedman J (1995) Positional cloning of the mouse obese gene and its human homologue. Nature 327: 425–432
Zheng W, Lai J, Li S (2008) 1D-LDA versus 2D-LDA: when is vector-based linear discriminant analysis better than matrix-based?. Pattern Recognit 41: 2156–2172
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jin, Q., Huang, Y. & Wang, C. Modular discriminant analysis and its applications. Artif Intell Rev 39, 285–303 (2013). https://doi.org/10.1007/s10462-011-9273-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10462-011-9273-3