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 M²SA, 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. M²SA 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 M² SA even when the majority of the values in the training tensor are missing.