Face recognition using nonnegative matrix factorization with fractional power inner product kernel

Abstract

Kernel nonnegative matrix factorization (KNMF) algorithms have been widely used to extract features for face recognition. The choice of kernel function is vital to facial feature extraction. The polynomial kernel function has been commonly used in KNMF. The power of the polynomial kernel is required to be a positive integer, thereby ensuring that the kernel generates a positive semi-definite matrix. In this paper, we investigate a new type of inner-product kernel that has a fractional power. The new kernel offers us flexibility in data representation as the power can be any positive real number. Based on the fractional power inner-product kernel, we present a novel KNMF algorithm called fractional power inner-product KNMF (FPKNMF). The FPKNMF algorithm is theoretically and experimentally validated to be convergent. The experimental results confirm that our algorithm exhibits a performance superior to the state-of-the-art methods in terms of facial representation and recognition accuracy.