Abstract:

For linear non-separated problems, many dimensionality reduction methods which are based on the definite kernel were proposed. The Fisher discriminant analysis method,  one of the commonly used methods,  was improved and extended. The definite kernel was extended to the indefinite kernel, and then indefinite kernel discriminant analysis based on fuzzy memberships was proposed. In addition, weighted generalized IKDA algorithms were achieved according to the weighting function. Experimental results showed that the proposed methods could achieve good classification results, and the choice of the weighting function could have a significant effect on the classification results.

Key words: indefinite kernel, fuzzy discriminant analysis, fuzzy membership, weighting function, misclassification rate