Kernel Non-Negative Matrix Factorization Using Self-Constructed Cosine Kernel

Abstract

Kernel-based non-negative matrix factorization (KNMF) can non-linearly extract non-negative features for image-data representation and classification. However, different kernel functions would lead to different performance. This means that selecting an appropriate kernel function plays an important role in KNMF algorithms. In this paper, we construct a novel Mercer kernel function, called cosine kernel function, which has the advantages of translation invariance and robustness to noise. Based on the self-constructed cosine kernel, we further propose a cosine kernel-based NMF (CKNMF) approach. The iterative formulas of CKNMF are deduced using the gradient descent method. We empirically validate that our CKNMF algorithm is convergent. Compared with some state of the art kernel-based algorithms, experimental results indicate that the proposed CKNMF algorithm achieves superior performance on face recognition.