Self-representative kernel concept factorization

Abstract

Kernel concept factorization (KCF) has successfully utilized kernel trick to conduct matrix factorization in the kernel space. However, conventional KCF methods usually define kernel in advance, which limits their ability to exploit the power of kernel. This paper proposes a semi-supervised self-representative kernel concept factorization (S3RKCF) method to integrate adaptive kernel learning and low-dimensional data representation learning into a unified model. Technically, an adaptive local geometric structure is acquired in the KCF-induced self-representation space, and then it facilitates data representation learning simultaneously. Furthermore, to enhance the discriminability of data representation, limited supervisory information is imposed in the formulated optimization problem as constraints. In this way, our model can learn kernel and discriminative low-dimensional representation adaptively and iteratively. To solve the optimization problem, an alternating iterative algorithm is designed with convergence guarantee. The performance of our proposed S3RKCF is evaluated through clustering and classification tasks, and the experimental results on eight real-world data sets demonstrate its effectiveness compared to state-of-the-art methods.