Discriminant Laplacian Embedding

Many real life applications brought by modern technologies often have multiple data sources, which are usually characterized by both attributes and pairwise similarities at the same time. For example in webpage ranking, a webpage is usually represented by a vector of term values, and meanwhile the internet linkages induce pairwise similarities among the webpages. Although both attributes and pairwise similarities are useful for class membership inference, many traditional embedding algorithms only deal with one type of input data. In order to make use of the both types of data simultaneously, in this work, we propose a novel Discriminant Laplacian Embedding (DLE) approach. Supervision information from training data are integrated into DLE to improve the discriminativity of the resulted embedding space. By solving the ambiguity problem in computing the scatter matrices caused by data points with multiple labels, we successfully extend the proposed DLE to multi-label classification. In addition, through incorporating the label correlations, the classification performance using multi-label DLE is further enhanced. Promising experimental results in extensive empirical evaluations have demonstrated the effectiveness of our approaches.