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In this study we propose a new feature extraction algorithm, dNMF (discriminant non-negative matrix factorization), to learn subtle class-related differences while maintaining an accurate generative capability. In addition to the minimum representation error for the standard NMF (non-negative matrix factorization) algorithm, the dNMF algorithm also results in higher between-class variance for discriminant power. The multiplicative NMF learning algorithm has been modified to cope with this additional constraint. The cost function was carefully designed so that the extraction of feature coefficients from a single testing pattern with pre-trained feature vectors resulted in a quadratic convex optimization problem in non-negative space for uniqueness. It also resolves issues related to the previous discriminant NMF algorithms. The developed dNMF algorithm has been applied to the emotion recognition task for speech, where it needs to emphasize the emotional differences while de-emphasizing the dominant phonetic components. The dNMF algorithm successfully extracted subtle emotional differences, demonstrated much better recognition performance and showed a smaller representation error from an emotional speech database.

A new discriminant NMF algorithm and its application to the extraction of subtle emotional differences in speech