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.
The kernelization of the SDA can be easily obtained by exploiting the modified representation of @math and @math (7) @cite_17 . Here we can assume that data is centered in @math . The kernel matrix of the centered data can be obtained as in (12) @cite_48 where @math is a vector of ones.
@cite_48 @cite_17
2140095548 2047737850
A new method for performing a nonlinear form of principal component analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in high-dimensional feature spaces, related to input space by some nonlinear map—for instance, the space of all possible five-pixel products in 16 × 16 images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition. In order to overcome the restricts of linear discriminant analysis (LDA), such as multivariate Normal distributed classes with equal covariance matrix but different means and the single-cluster structure in each class, subclass discriminant analysis (SDA) is proposed recently. In this paper the kernel SDA is presented, called KSDA. Moreover, we reformulate SDA so as to avoid the complicated derivation in the feature space. The encouraging experimental results on eight UCI data sets demonstrate the efficiency of our method.