Subspace clustering by simultaneously feature selection and similarity learning

Abstract

Learning a reliable affinity matrix is the key to achieving good performance for graph-based clustering methods. However, most of the current work usually directly constructs the affinity matrix from the raw data. It may seriously affect the clustering performance since the original data usually contain noises, even redundant features. On the other hand, although integrating manifold regularization into the framework of clustering algorithms can improve clustering results, some entries of the pre-computed affinity matrix on the original data may not reflect the true similarities between data points. To address the above issues, we propose a novel subspace clustering method to simultaneously learn the similarities between data points and conduct feature selection in a unified optimization framework. Specifically, we learn a high-quality graph under the guidance of a low-dimensional space of the original data such that the obtained affinity matrix can reflect the true similarities between data points as much as possible. A new algorithm based on augmented Lagrangian multiplier is designed to find the optimal solution to the problem effectively. Extensive experiments are conducted on benchmark datasets to demonstrate that our proposed method performs better against the state-of-the-art clustering methods.