An approximate closed-form solution to correlation similarity discriminant analysis
High-dimensional data often lie on relatively low-dimensional manifold, while the nonlinear geometry of that manifold is often embedded in the similarities between the data points. Correlation as a similarity measure is able to capture these similarity structures. In this paper, we present a new correlation-based similarity discriminant analysis (CSDA) method for class separability problem. Firstly, a new formula based on the trace of matrix is proposed for computing the correlation between data points. Then a criterion maximizing the difference between within-class correlation and between-class correlation is proposed to achieve maximum class separability. The optimization of the criterion function can be transformed to an eigen-problem and an approximate closed-form solution can be obtained. Theoretical analysis shows that CSDA can be interpreted in the framework of graph-based learning. Furthermore, we also show how to extend CSDA to a nonlinear case through kernel-based mapping. Extensive experiments on different data sets are reported to illustrate the effectiveness of the proposed method in comparison with other competing methods.
correlation similarity discriminant analysis similarity measure linear discriminant analysis feature extraction