Distance-based discriminant analysis method and its applications

A new approach to fuzzy quantities ordering based on distance method and its applications for solving fuzzy linear programming

Many ranking methods have been proposed so far. However, there is yet no method that can always give a satisfactory solution to every situation; some are counterintuitive, not discriminating; some use only the local information of fuzzy values; some produce different ranking for the same situation. For overcoming the above problems, we propose a new method for ranking fuzzy quantities based on ...

A New Reduced-Rank Linear Discriminant Analysis Method and Its Applications

We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component analysis (PCA). The proposed method is computationally efficient and can incorporate the correlation structure among the features. Besides the theoretical insi...

Laplacian MinMax Discriminant Projection and its Applications

A new algorithm, Laplacian MinMax Discriminant Projection (LMMDP), is proposed in this paper for supervised dimensionality reduction. LMMDP aims at learning a discriminant linear transformation. Specifically, we define the within-class scatter and the between-class scatter using similarities which are based on pairwise distances in sample space. After the transformation, the considered pairwise...

Lorentzian Discriminant Projection and Its Applications

This paper develops a supervised dimensionality reduction method, Lorentzian Discriminant Projection (LDP), for discriminant analysis and classification. Our method represents the structures of sample data by a manifold, which is furnished with a Lorentzian metric tensor. Different from classic discriminant analysis techniques, LDP uses distances from points to their within-class neighbors and ...

Iterative Majorization Approach to the Distance-based Discriminant Analysis