Feature Selection for Adaptive Dual-Graph Regularized Concept Factorization for Data Representation

Abstract

Recently, manifold regularization with the affinity graph in matrix factorization-related studies, such as dual-graph regularized concept factorization (GCF), have yielded impressive results for clustering. However, due to the noisy and irrelevant features of the data samples, the affinity graph constructed directly from the original feature space is not necessarily a reliable reflection of the intrinsic manifold of the data samples. To overcome this problem, we integrate feature selection into the construction of the data (feature) graph and propose a novel algorithm called adaptive dual-graph regularized CF with Feature selection $(\hbox {ADGCF}_{\mathrm{FS}})$, which simultaneously considers the geometric structures of both the data manifold and the feature manifold. We unify feature selections, dual-graph regularized CF into a joint objective function and minimize this objective function with iterative and alternative updating optimization schemes. Moreover, we provide the convergence proof of our optimization scheme. Experimental results on TDT2 and Reuters document datasets, COIL20 and PIE image datasets demonstrate the effectiveness of our proposed method.