Face recognition is one of those unstructured tasks that the human brain excels at, but that is difficult for computers to perform. But as it becomes crucial for many modern activities, it would be a great help for us humans if we could automate this task at least in part. More specifically, face recognition is hard for computers because a face is composed of content, or main features, that have low data dimensionality. These features can be drowned in style or background noise, such as expression, illumination and so on, that have instead high data dimensionality. The challenge is thus to reduce data dimensionality, or get rid of unimportant features without losing substantial ones; this is called feature extraction. A wide variety of algorithms--linear, nonlinear, matricial, or tensorial--already exist to do that; feature extraction can already be performed with any of these algorithms.

This paper presents factor analysis, a new framework to lower data dimensionality by mapping high to low data dimensionality. It involves two steps: in step one, it designs a factor separating function. In step two, it designs a mapping function. Both steps can be run in supervised or unsupervised mode. This framework can be applied to any of the algorithms mentioned above; it can even be thought of as a tool to unify them all.

In the paper, the authors apply factor analysis to face identification, facial pose classification, and facial age grouping; these applications differ only in definition of content and style factors. In face identification, content includes frontal and normalized face views, and style includes pose, illumination, and expression. In facial pose identification, content includes facial poses, and styles are identity, illumination, and expression. In facial age grouping, content includes facial ages, and styles are identity, facial pose, illumination, and expression. To test their framework, the authors fed different facial sets to a number of the algorithms mentioned above and then they ran the algorithms with different weights for each factor. They found that recognition precision was greatly improved by the appropriate design of weight and partition in the factor analysis framework.

At the beginning of the paper, the authors state that they want to show relationships among existing algorithms and facilitate the design of new ones. The paper fully succeeds in doing so because it shows that by varying parameters, a relatively easy task, the same algorithms can be used for a variety of tasks.