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.

Spectral dimensionality reduction methods have recently emerged as powerful tools for various applications in pattern recognition, data mining and computer vision. These methods use information contained in the eigenvectors of a data affinity (i.e, item-item similarity) matrix to reveal the low dimensional structure of the high dimensional data. One of the limitations of various spectral dimensionality reduction methods is their high computational complexity. They all need to construct a data affinity matrix and compute the top eigenvectors. This leads to O(n2) computational complexity, where n is the number of samples. Moreover, when the data are highly non-linear distributed, some linear methods have to be performed in a reproducing kernel Hilbert space (leads to the corresponding kernel methods) to learn an effective non-linear mapping. The computational complexity of these kernel methods is O(n3). In this paper, we propose a novel nonlinear dimensionality reduction algorithm, called Compressed Spectral Regression, with O(n) computational complexity. Extensive experiments on data clustering demonstrate the effectiveness and efficiency of the proposed approach.