A nested-loop Fisher discriminant analysis algorithm

Fisher discriminant analysis (FDA), as a very important method for feature extraction, has been widely used in different applications. However, some drawbacks of the conventional FDA algorithm have limited its success and applications. In order to improve the discriminant power, a new discriminant analysis algorithm is proposed based on Fisher's linear discriminant objective by developing a nested loop algebra, called nested-loop Fisher discriminant analysis (NeLFDA). The basic idea of the proposed NeLFDA is to overcome three important problems of the conventional Fisher discriminant analysis algorithm: (1) the within-class scatter matrix may be singular for eigenvalue decomposition, (2) the number of extracted discriminant components is limited by rank deficiency of the between-class scatter matrix, and (3) the discriminant components are correlated with each other for each class. The above problems are addressed in a nested-loop iterative process including inner-loop and outer-loop calculations. Using the proposed algorithm, its application to classification and fault diagnosis is evaluated on two examples. Illustration results show that the proposed algorithm can better separate different classes with improved discriminant power and provide more promising fault diagnosis performance.