Face image modeling by multilinear subspace analysis with missing values

ABSTRACT

The main difficulty in face image modeling is to decompose those semantic factors contributing to the formation of the face images, such as identity, illumination and pose. One promising way is to organize the face images in a higher-order tensor with each mode corresponding to one contributory factor. Then, a technique called Multilinear Subspace Analysis (MSA) is applied to decompose the tensor into the mode-$n$ product of several mode matrices, each of which represents one semantic factor. In practice, however, it is usually difficult to obtain such a complete training tensor since it requires a large amount of face images with all possible combinations of the states of the contributory factors. To solve the problem, this paper proposes a method named M$^2$SA, which can work on the training tensor with massive missing values. Thus M$^2$SA can be used to model face images even when there are only a small number of face images with limited variations which will cause missing values in the training tensor). Experiments on face recognition show that M$^2$SA can work reasonably well with up to $70\%$ missing values in the training tensor.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
        I.2.10 Vision and Scene Understanding

General Terms:
Algorithms

Keywords:
face image, missing values, multilinear subspace analysis