Subspace Semi-supervised Fisher Discriminant Analysis

Fisher discriminant analysis (FDA) is a popular method for supervised dimensionality reduction. FDA seeks for an embedding transformation such that the ratio of the between-class scatter to the within-class scatter is maximized. Labeled data, however, often consume much time and are expensive to obtain, as they require the efforts of human annotators. In order to cope with the problem of effectively combining unlabeled data with labeled data to find the embedding transformation, we propose a novel method, called subspace semi-supervised Fisher discriminant analysis (SSFDA), for semi-supervised dimensionality reduction. SSFDA aims to find an embedding transformation that respects the discriminant structure inferred from the labeled data and the intrinsic geometrical structure inferred from both the labeled and unlabeled data. We also show that SSFDA can be extended to nonlinear dimensionality reduction scenarios by applying the kernel trick. The experimental results on face recognition demonstrate the effectiveness of our proposed algorithm.