Multilinear Discriminant Analysis for Face Recognition

• Published in: IEEE transactions on image processing Vol. 16; no. 1; pp. 212 - 220
• Main Authors: Yan, Shuicheng, Xu, Dong, Yang, Qiang, Zhang, Lei, Tang, Xiaoou, Zhang, Hong-Jiang
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2007; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: 2-D LDA; 2-D PCA; Algorithm design and analysis; Algorithms; Applied sciences; Artificial Intelligence; Asia; Biometry - methods; Computer Simulation; Discriminant Analysis; Exact sciences and technology; Face - anatomy & histology; Face recognition; Feature extraction; Humans; Image coding; Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Information Storage and Retrieval - methods; Information, signal and communications theory; Iterative algorithms; Learning; Linear discriminant analysis; linear discriminant analysis (LDA); Linear Models; Mathematical analysis; Miscellaneous; Models, Biological; multilinear algebra; Numerical Analysis, Computer-Assisted; Pattern recognition; Pattern Recognition, Automated - methods; Principal component analysis; principal component analysis (PCA); Signal processing; Studies; subspace learning; Subspaces; Telecommunications and information theory; Tensile stress; Tensors; Unsupervised learning; Biometrics; Performance evaluation; Second order; Image processing; Multicriteria analysis; Iterative method; multilinear algebra; Optimization; Learning; Image coding; Database; Learning algorithm; 2-D LDA; Discriminant analysis; Face recognition; Third order; principal component analysis (PCA); Subspace method; Pattern recognition; Computational complexity; Statistical method; subspace learning; Signal processing; 2-D PCA; Feature extraction; linear discriminant analysis (LDA); Automatic recognition; Algorithm analysis; Principal component analysis
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2006.884929

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