Elastic net regularized kernel non-negative matrix factorization algorithm for clustering guided image representation

Abstract

Due to the capacity of data representation, non-negative matrix factorization has been investigated widely by introducing a variety of constraints. The general processing of non-negative matrix factorization for image clustering consists of two steps: (i) achieving the r-dimensional non-negative image representations, where the rank r is set to the expected number of clusters; (ii) adopting the traditional clustering techniques to accomplish the clustering task. Nevertheless, the previous non-negative matrix factorization variants derive image representations from the original space which cannot handle the nonlinear structure of images. This paper focuses on the existing issues and proposes an elastic net regularized kernel non-negative matrix factorization algorithm for clustering guided image representation. In order to explore the nonlinear relations of images, this paper uses the kernel trick to extend original non-negative matrix factorization. A self-organized graph and elastic net regularization are incorporated into the proposed objective of kernel non-negative matrix factorization, besides, the rank is allowed to be larger than the expected number of clusters. By doing so, the graph defined in the feature space is more qualified to represent the intrinsic structure of images. As an accompanying advantage, the clusters of images can be determined using the graph directly without using the two-step trick. According to the proposed alternating update algorithm for solving the optimization problem, the image representation and clustering result can be obtained simultaneously. Extensive experiments on challenging data sets demonstrate the effectiveness of the proposed algorithm compared with the prominent non-negative matrix factorization variants for image clustering.