Face image modeling by multilinear subspace analysis with missing values.

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. The MSA requires a large training set, which is well organized in a single tensor, which consists of data samples with all possible combinations 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 the MSA but has been hardly investigated up to present. To solve the problem, this paper proposes an algorithm named M(2)SA, which is advantageous in real applications due to the following: 1) it inherits the ability of the MSA to decompose the interlaced semantic factors; 2) it does not depend on any assumptions on the data distribution; and 3) it can deal with a high percentage of missing values. M(2)SA is evaluated by face image modeling on two typical multifactorial applications, i.e., face recognition and facial age estimation. Experimental results show the effectiveness of M(2) SA even when the majority of the values in the training tensor are missing.