An Unsupervised Learning Approach for Facial Expression Recognition using Semi-Definite Programming and Generalized Principal Component Analysis

In this paper, we consider facial expression recognition using an unsupervised learning framework. Specifically, given a data set composed of a number of facial images of the same subject with different facial expressions, the algorithm segments the data set into groups corresponding to different facial expressions. Each facial image can be regarded as a point in a high-dimensional space, and the collection of images of the same subject resides on a manifold within this space. We show that different facial expressions reside on distinct subspaces if the manifold is unfolded. In particular, semi-definite embedding is used to reduce the dimensionality and unfold the manifold of facial images. Next, generalized principal component analysis is used to fit a series of subspaces to the data points and associate each data point to a subspace. Data points that belong to the same subspace are shown to belong to the same facial expression.