Kernel methods for data analysis are frequently considered to be restricted to positive definite kernels. In practice, however, indefinite kernels arise e.g. from problem-specific kernel construction or optimized similarity measures. We, therefore, present formal extensions of some kernel discriminant analysis methods which can be used with indefinite kernels. In particular these are the multi-...

Fisher criterion has achieved great success in dimensionality reduction. Two representative methods based on Fisher criterion are Fisher Score and Linear Discriminant Analysis (LDA). The former is developed for feature selection while the latter is designed for subspace learning. In the past decade, these two approaches are often studied independently. In this paper, based on the observation th...

Automatic facial expression recognition is an interesting and challenging subject in signal processing, pattern recognition, artificial intelligence, etc. In this paper, a new method of facial expression recognition based on local binary patterns (LBP) and local Fisher discriminant analysis (LFDA) is presented. The LBP features are firstly extracted from the original facial expression images. T...

Automatic Linguistic Annotation is a promising solution to bridge the semantic gap in content-based image retrieval. However, two crucial issues are not well addressed in state-of-art annotation algorithms: 1. The Small Sample Size (3S) problem in keyword classifier/model learning; 2. Most of annotation algorithms can not extend to real-time online usage due to their low computational efficienc...

Fisher linear discriminant analysis (LDA) and its kernel extension— kernel discriminant analysis (KDA)—are well known methods that consider dimensionality reduction and classification jointly. While widely deployed in practical problems, there are still unresolved issues surrounding their efficient implementation and their relationship with least mean squared error procedures. In this paper we ...

The null space of the within-class scatter matrix is found to express most discriminative information for the small sample size problem (SSSP). The null space-based LDA takes full advantage of the null space while the other methods remove the null space. It proves to be optimal in performance. From the theoretical analysis, we present the NLDA algorithm and the most suitable situation for NLDA....

A novel scatter-difference-based local Fisher discriminant analysis(SDLFDA) algorithm for tissue classification is proposed in this paper. SDLFDA explicitly considers the local manifold structure and interclass discrimination in gene expression data space. By using SDLFDA, each gene expression data can be projected into a lower-dimensional discriminative feature space. In addition, SDFLDA reduc...

The Fisher discriminant analysis (FDA) is a common technique for binary classification. A parametrized extension, which we call the extended FDA, has been introduced from the viewpoint of robust optimization. In this work, we first give a new probabilistic interpretation of the extended FDA. We then develop algorithms for solving an optimization problem that arises from the extended FDA: comput...

Fisher linear discriminant analysis (FLDA) based on variance ratio is compared with scatter linear discriminant (SLDA) analysis based on determinant ratio. It is shown that each optimal FLDA data model is optimal SLDA data model but not opposite. The novel algorithm 2SS4LDA (two singular subspaces for LDA) is presented using two singular value decompositions applied directly to normalized multi...