Generalized multiple maximum scatter difference feature extraction using QR decomposition

• GMMSD employs QR decomposition rather than SVD.
• GMMSD allows relatively-free selection of a suitable matrix to reduce dimension.
• We reveal GMMSD’s relationship to other feature extraction methods.
• Experimental results are presented to demonstrate the effectiveness of GMMSD.

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, rendering this method impractical for high dimensional data. In this paper, we propose a generalized MMSD (GMMSD) criterion for feature extraction and classification. GMMSD allows relatively-free selection of a suitable transformation matrix to reduce dimensions. Based on GMMSD criterion, we demonstrate that the same discriminant information can be extracted by QR decomposition, which is more efficient than SVD. Next, GMMSD is compared with several classical feature extraction methods to justify the validity of the proposed method. Our experiments on three face databases and two facial expression databases demonstrate that GMMSD provides favorable recognition performance with high computational efficiency.