Generalized MMSD feature extraction using QR decomposition

Multiple Maximum scatter difference (MMSD) discriminant criterion is an effective feature extraction method that computes the discriminant vectors from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix. However, singular value decomposition (SVD) of two times is involved in MMSD, making this method impractical for high dimensional data. In this paper, we propose a novel method for feature extraction and classification based on MMSD criterion, called generalized MMSD (GMMSD), which employs QR decomposition rather than SVD. Unlike MMSD, GMMSD does not require the computation of the whole scatter matrix. Instead, it computes the discriminant vectors from both the range of whitenizated input data matrix and the null space of the within-class scatter matrix. We evaluate the effectiveness of the GMMSD method in terms of classification accuracy in the reduced dimensional space. Our experiments on two facial expression databases demonstrate that the GMMSD method provides favorable performance in terms of both recognition accuracy and computational efficiency.