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Fisher's Linear Discriminant Analysis (LDA) is a traditional dimensionality reduction method that has been proven to be successful for decades. To enhance the LDA's power for high-dimensional pattern classification, such as face recognition, numerous LDA-extension approaches have been proposed in the literature. This paper proposes a new method that improves the performance of LDA-based classification by simply increasing the number of (sub)-classes through clustering a few of classes of the training set prior to the execution of LDA. This is based on the fact that the eigen space of the training set consists of the range space and the null space, and that the dimensionality of the range space increases as the number of classes increases. Therefore, when constructing the transformation matrix, through minimizing the null space, the loss of discriminative information resulted from this space can be minimized. To select the classes to be clustered, in the present paper, the intraset distance is employed as a criterion and the k-means clustering is performed to divide them. Our experimental results for an artificial data set of XOR-type samples and a well-known benchmark face database of Yale demonstrate that the classification efficiency of the proposed method could be improved.

On Using a Pre-clustering Technique to Optimize LDA-Based Classifiers for Appearance-Based Face Recognition