Multilinear Discriminant Analysis for Face Recognition

By Shuicheng Yan, Dong Xu, Qiang Yang, Lei Zhang, Xiaoou Tang, HongJiang Zhang. IEEE Transactions on Image Processing, 2007

355 citations recorded by the source corpus.

There is a growing interest in subspace learning techniques for face recognition; however, the excessive dimension of the data space often brings the algorithms into the curse of dimensionality dilemma. In this paper, we present a novel approach to solve the supervised dimensionality reduction problem by encoding an image object as a general tensor of second or even higher order. First, we propose a discriminant tensor criterion, whereby multiple interrelated lower dimensional discriminative subspaces are derived for feature extraction. Then, a novel approach, called k-mode optimization, is presented to iteratively learn these subspaces by unfolding the tensor along different tensor directions. We call this algorithm multilinear discriminant analysis (MDA), which has the following characteristics: 1) multiple interrelated subspaces can collaborate to discriminate different classes, 2) for classification problems involving higher order tensors, the MDA algorithm can avoid the curse of dimensionality dilemma and alleviate the small sample size problem, and 3) the computational cost in the learning stage is reduced to a large extent owing to the reduced data dimensions in k-mode optimization. We provide extensive experiments on ORL, CMU PIE, and FERET databases by encoding face images as second- or third-order tensors to demonstrate that the proposed MDA algorithm based on higher order tensors has the potential to outperform the traditional vector-based subspace learning algorithms, especially in the cases with small sample sizes

Subfields: Computational Mathematics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/42350e28d11e33641775bef4c7b41a2c3437e4fd

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Citations in the corpus

Discriminative multi-manifold analysis for face recognition from a single training sample per person (2011, methodology): “Representative and popular algorithms include principal component analysis (PCA) [41], linear discriminant analysis (LDA) [2], locality preserving projections (LPPs) [15], marginal fisher analysis (MFA) [49], and their weighted, kernelized, and tensorized variants [23], [24], [49], [50], [53].”
A survey of multilinear subspace learning for tensor data (2011, methodology): “They result in very high-dimensional vectors, lead to the estimation of a large number of parameters, and also break the natural structure and correlation in the original data [2, 21, 22].”
Maximum Neighborhood Margin Discriminant Projection for Classification (2014, methodology): “Among the DR techniques, principal component analysis (PCA) [2, 3], linear discriminant analysis (LDA) [3, 4], locality preserving projection (LPP) [5, 6], and their kernelized and tensorized variants [7–18] are the most representative and well-known algorithms.”
Neighborhood repulsed metric learning for kinship verification (2012, neutral): “Representative examples include face recognition [5], [8], [10], [20], [22], [27], [28], [35], [37], [40], [41], [42], [43], [54], [55], [56], [58], [64], [65], [66], [67], [68], facial expression recognition [11], [18], [70], facial age estimation [19], [21], [24], [25], [31], [39], gender classifi”
MPCA: Multilinear Principal Component Analysis of Tensor Objects (2008, methodology): “Remark 3: There are other choices of initialization such as truncated identity matrices [20], [23], [31] (named as pseudo identity matrices) and random matrices.”
Multilinear Discriminant Analysis for Higher-Order Tensor Data Classification (2014, methodology): “Index Terms—Linear discriminant analysis (LDA), multilinear discriminant analysis (MDA), direct general tensor discriminant analysis (DGTDA), constrained multilinear discriminant analysis (CMDA), pattern classification, higher-order tensor Ç”