Discriminative Subspace Method for Minimum Error Pattern Recognition

Subspace Method (SM) is one of fundamental frameworks for pattern recognition. In particular, its discriminative learning version, called Learning Subspace Method (LSM), has been shown quite useful in various applications. However, this important design method leaves much room for further analysis due to the lack of a link between LSM and the ultimate goal of pattern recognition, i.e. the minimum error situation. In this light, we investigate in this paper SM from the viewpoint of the Minimum Classification Error/Generalized Probabilistic Descent method (MCE/GPD). Applying MCE/GPD to SM, we formalize a new discriminative subspace method, called the Minimum Error Learning Subspace method (MELS), which enables one to directly pursue the minimum error recognition. This paper also provides a rigorous analysis of the MELS’s learning mechanism as well as a comparison between the conventional LSM and MELS.