Approximate information discriminant analysis: A computationally simple heteroscedastic feature extraction technique

In this article we develop a novel linear dimensionality reduction technique for classification. The technique utilizes the first two statistical moments of data and retains the computational simplicity, characteristic of second-order techniques, such as linear discriminant analysis. Formally, the technique maximizes a criterion that belongs to the class of probability dependence measures, and is naturally defined for multiple classes. The criterion is based on an approximation of an information-theoretic measure and is capable of handling heteroscedastic data. The performance of our method, along with similar feature extraction approaches, is demonstrated based on experimental results with real-world datasets. Our method compares favorably to similar second-order linear dimensionality techniques.