Semi-supervised dimensionality reduction via harmonic functions

Traditional unsupervised dimensionality reduction techniques are widely used in many learning tasks, such as text classification and face recognition. However, in many applications, a few labeled examples are readily available. Thus, semi-supervised dimensionality reduction(SSDR), which could incorporate the label information, has aroused considerable research interests. In this paper, a novel SSDR approach, which employs the harmonic function in a gaussian random field to compute the states of all points, is proposed. It constructs a complete weighted graph, whose edge weights are assigned by the computed states. The linear projection matrix is then derived to maximize the separation of points in different classes. For illustration, we provide some deep theoretical analyses and promising classification results on different kinds of data sets. Compared with other dimensionality reduction approaches, it is more beneficial for classification. Comparing with the transductive harmonic function method, it is inductive and able to deal with new coming data directly.