Research On Sparse Subspace Estimation And Clustering Based On L_p Norm Regularization

Recently, subspace clustering has been widely attracted by the researchers for its clustering effects. The key point is to reveal the nature subspace that the data is located based on the data self-representation.That is to say, data clustering is conducted by similarity graph construction with sparse representation. Nevertheless, the clustering error will go up since the noises, missing entries and singular samples in the observation data which is used as dictionary to represent subspace. On the other hand, employ matrix l1 norm as sparse regularization to take place of l0 norm in optimization problem. Though the convex approximation can solve the uncontinuous and NP-hard l0 norm, the solution solved with convex approximation model will diverge the original model solution unless it satisfies stronger incoherence.In order to solve the problems mentioned, the paper proposed a model of sparse subspace estimation and clustering based on lp norm regularization. Specifically, lp norm can take place of l1 norm to be sparse regularization constraint. Meanwhile, dictionary learning is added into the model. And subspaces can be represented accurately. For the non-convex approximate model, an efficient algorithm is proposed based on Alternating Direction Method of Multipliers (ADMM). The effectiveness of the proposed algorithm for subspace clustering through experiments on synthetic data and face data can be demonstrated well.The main contributions of this paper are summarized as the following:(1)The dictionary learning is added into the sparse representation model. The dictionary consists of observation data would be taken place by learning dictionary. In case of observation data with noises, missing entries and outlying entries, the subspace can be represented accurately.(2)lp norm is regarded as sparse regularization constraint instead of l1 norm ,and the most sparse solution is obtained under the weak incoherence relatively. Hence, the correlations between the data can be described efficiently.(3)For the non-convex model, a fast solving algorithm based on ADMM is to be proposed.(4)The effectiveness and superiority of the proposed algorithm for subspace clustering through experiments on synthetic data and face data can be demonstrated.