Multi-Class Classification Based on Fisher Criteria with Weighted Distance

Linear discriminant analysis (LDA) is an efficient dimensionality reduction algorithm. In this paper we propose a new Fisher criteria with weighted distance (FCWWD) to find an optimal projection for multi-class classification tasks. We replace the classical linear function with a nonlinear weight function to describe the distances between samples in Fisher criteria. What's more, we give a new algorithm based on this criteria along with a theoretical explanation that our algorithm benefits from an approximation of the ROC optimization. Experimental results demonstrate the efficiency of our method to improve the multi-class classification performance.