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.
Linear Discriminant Analysis (LDA) has been a popular method for extracting features that preserves class separability. The projection functions of LDA are commonly obtained by maximizing the between-class covariance and simultaneously minimizing the within-class covariance. It has been widely used in many fields of information processing, such as machine learning, data mining, information retrieval, and pattern recognition. However, the computation of LDA involves dense matrices eigendecomposition, which can be computationally expensive in both time and memory. Specifically, LDA has O(mnt + t3) time complexity and requires O(mn + mt + nt) memory, where m is the number of samples, n is the number of features, and t = min(m,n). When both m and n are large, it is infeasible to apply LDA. In this paper, we propose a novel algorithm for discriminant analysis, called Spectral Regression Discriminant Analysis (SRDA). By using spectral graph analysis, SRDA casts discriminant analysis into a regression framework that facilitates both efficient computation and the use of regularization techniques. Specifically, SRDA only needs to solve a set of regularized least squares problems, and there is no eigenvector computation involved, which is a huge save of both time and memory. Our theoretical analysis shows that SRDA can be computed with O(mn) time and O(ms) memory, where .s(les n) is the average number of nonzero features in each sample. Extensive experimental results on four real-world data sets demonstrate the effectiveness and efficiency of our algorithm. Abstract Tensors are valuable tools to represent Electroencephalogram (EEG) data. Tucker decomposition is the most used tensor decomposition in multidimensional discriminant analysis and tensor extension of Linear Discriminant Analysis (LDA), called Higher Order Discriminant Analysis (HODA), is a popular tensor discriminant method used for analyzing Event Related Potentials (ERP). In this paper, we introduce a new tensor-based feature reduction technique, named Higher Order Spectral Regression Discriminant Analysis (HOSRDA), for use in a classification framework for ERP detection. The proposed method (HOSRDA) is a tensor extension of Spectral Regression Discriminant Analysis (SRDA) and casts the eigenproblem of HODA to a regression problem. The formulation of HOSRDA can open a new framework for adding different regularization constraints in higher order feature reduction problem. Additionally, when the dimension and number of samples is very large, the regression problem can be solved via efficient iterative algorithms. We applied HOSRDA on data of a P300 speller from BCI competition III and reached average character detection accuracy of 96.5 for the two subjects. HOSRDA outperforms almost all of other reported methods on this dataset. Additionally, the results of our method are fairly comparable with those of other methods when 5 and 10 repetitions are used in the P300 speller paradigm.