  In this paper, we use semi-definite programming and generalized principal
component analysis (GPCA) to distinguish between two or more different facial
expressions. In the first step, semi-definite programming is used to reduce the
dimension of the image data and "unfold" the manifold which the data points
(corresponding to facial expressions) reside on. Next, GPCA is used to fit a
series of subspaces to the data points and associate each data point with a
subspace. Data points that belong to the same subspace are claimed to belong to
the same facial expression category. An example is provided.
