Communications Inspired Linear Discriminant Analysis
This work addresses dimensionality reduction for classification tasks, offering an incremental improvement over existing information-theoretic methods.
The paper tackles supervised linear dimensionality reduction by designing a projection matrix that maximizes mutual information between projected signals and class labels, using a Shannon entropy measure and gradient descent optimization. It achieves promising results compared to Linear Discriminant Analysis, Information Discriminant Analysis, and a Renyi entropy-based method on real datasets.
We study the problem of supervised linear dimensionality reduction, taking an information-theoretic viewpoint. The linear projection matrix is designed by maximizing the mutual information between the projected signal and the class label (based on a Shannon entropy measure). By harnessing a recent theoretical result on the gradient of mutual information, the above optimization problem can be solved directly using gradient descent, without requiring simplification of the objective function. Theoretical analysis and empirical comparison are made between the proposed method and two closely related methods (Linear Discriminant Analysis and Information Discriminant Analysis), and comparisons are also made with a method in which Renyi entropy is used to define the mutual information (in this case the gradient may be computed simply, under a special parameter setting). Relative to these alternative approaches, the proposed method achieves promising results on real datasets.