Projection-optimal local Fisher discriminant analysis for feature extraction

In this paper, a novel dimensionality reduction algorithm called projection-optimal local Fisher discriminant analysis (PoLFDA) is proposed in order to address the multimodal problem. Novel weight matrices defined on the projected space can represent the intraclass compactness and the interclass separability. Based on the novel weighted matrices, the local between-class scatter matrix and the local within-class scatter matrix are defined such that the local structure can be preserved. In order to enhance the discriminant ability, we impose an orthogonal constraint on the objective function, which can be regarded as a trace ratio problem. In general, a trace ratio problem does not have a closed-form solution; however, it can be solved using some efficient iterative algorithms. Therefore, we optimize the projection matrix by solving the trace ratio problem iteratively. Experiments on toy data, face, and handwritten digit data sets are conducted to evaluate the performance of PoLFDA; the results and comparisons verify the effectiveness of the proposed method.