Linear Discriminant Analysis Algorithms
نویسنده
چکیده
We propose new algorithms for computing linear discriminants to perform data dimensionality reduction from R to R, with p < n. We propose alternatives to the classical Fisher’s Distance criterion, namely, we investigate new criterions based on the: Chernoff-Distance, J-Divergence and Kullback-Leibler Divergence. The optimization problems that emerge of using these alternative criteria are non-convex and thus hard to solve. However, despite the non-convexity our algorithms guarantee global optimality for the linear discriminant when p = 1. This is possible due to problem reformulations and recent developments in optimization theory [8],[9]. A greedy suboptimal approach is developed for 1 < p < n.
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