Subspace Clustering via Adaptive Non-Negative Representation Learning and Its Application to Image Segmentation

Abstract

Self-representation subspace clustering based on graphs has the merits of capability and efficiency. However, the graph built by the self-representation methods has two issues: (i) usually lacking conciseness and informativeness due to the negative representation coefficients. (ii) no guarantee of an overall optimal solution due to the separation of representation learning and graph construction. To alleviate these issues, we propose a novel subspace clustering via learning non-negative representation with an adaptive graph. Specifically, we explicitly impose the non-negative constraint on the self-representation learning, ensuring that each data point is approximated from a group of homogeneous samples and enhancing the distinguishability of data representation. Meanwhile, an adaptive graph is developed so that both representation and the geometric structure of data are simultaneously learned in a unified procedure. Moreover, the learned representation is less sensitive to data noise imposed by the ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2,1</sub> -norm, so the adaptive graph will be further improved. An efficient optimization procedure is developed to find the optimal solution. Extensive experiments on subspace clustering and the extension application to image segmentation validate the advantages of our method against state-of-the-art methods.