In this paper, we propose a speed-up approach for subclass discriminant analysis and formulate a novel efficient multi-view solution to it. The speed-up approach is developed based on graph embedding and spectral regression approaches that involve eigendecomposition of the corresponding Laplacian matrix and regression to its eigenvectors. We show that by exploiting the structure of the between-class Laplacian matrix, the eigendecomposition step can be substituted with a much faster process. Furthermore, we formulate a novel criterion for multi-view subclass discriminant analysis and show that an efficient solution for it can be obtained in a similar to the single-view manner. We evaluate the proposed methods on nine single-view and nine multi-view datasets and compare them with related existing approaches. Experimental results show that the proposed solutions achieve competitive performance, often outperforming the existing methods. At the same time, they significantly decrease the training time.
In this paper, a novel approximate solution of the criterion used in non-linear class-specific discriminant subspace learning is proposed. We build on the class-specific kernel spectral regression method, which is a two-step process formed by an eigenanalysis step and a kernel regression step. Based on the structure of the intra-class and out-of-class scatter matrices, we provide a fast solution for the first step. For the second step, we propose the use of approximate kernel space definitions. We analytically show that the adoption of randomized and class-specific kernels has the effect of regularization and Nystrom-based approximation, respectively. We evaluate the proposed approach in face verification problems and compare it with the existing approaches. Experimental results show the effectiveness and efficiency of the proposed approximate class-specific kernel spectral regression method, since it can provide satisfactory performance and scale well with the size of the data.