Min-max discriminant analysis based on gradient method for feature extraction

Feature extraction is an essential step in pattern classification, which is normally divided into two tasks: transforming the input vector into a feature vector and/or reducing its dimensionality. A well-defined feature extraction algorithm makes the subsequent classification process more effective and efficient. One of the most important feature extraction algorithms is linear discriminant analysis (LDA). However, there is a critical drawback for LDA. For a classification task with c classes, since the rank of the between class matrix cannot be larger than c - 1, the dimension of the projected subspace is at most c - 1 for LDA. From this viewpoint, min-max discriminant analysis based on gradient method (MMDA-GM) is derived in this paper. With the proposed MMDA-GM, a set of features can be extracted simultaneously. It is shown that the proposed method achieves good performance for data sets from UCI Machine Learning Repository.