Ieee transactions on systems, man, and cybernetics. part b: Cybernetics. In Supervised Nonlinear Dimensionality Reduction for Visualization and Classification

Abstract—Multilinear subspace analysis (MSA) is a promising methodology for pattern recognition problems due to its ability in decomposing the data formed from the interaction of multiple factors. MSA requires a large training set, well organized in a single tensor, which consists of data samples with all possible com-binations of the contributory factors. However, such a ‘complete’ training set is difficult (or impossible) to obtain in many real applications. The missing value problem is therefore crucial to the practicality of MSA, but has hardly been investigated up to the present. To solve the problem, this paper proposes an algorithm named M2SA, which is advantageous in real applications since: 1) it inherits the ability of MSA to decompose the interlaced semantic factors; 2) it does not depend on any assumptions on the data distribution; 3) it can deal with a high percentage of missing values. M2SA is evaluated by face image modeling on two typical multifactorial applications: face recognition and facial age estimation. Experimental results show the effectiveness of M2SA even when the majority of values in the training tensor are missing. Index Terms—Multilinear subspace analysis, Missing values, Face recognition, Facial age estimation. I