Research On Structure Learning Of Block Diagonal Subspace Clustering

The traditional clustering algorithms are usually ineffective on high-dimensional data sets because the cluster structure of high-dimensional data only lies in the low-dimensional subspace.Subspace clustering assumes that high-dimensional data comes from the union of several subspaces,and the latent low-dimensional subspace structure can be found through clustering,and the data set is divided into multiple clusters according to the distribution of subspace.The key of subspace clustering is to construct the affine matrix that correctly reflects the data distribution.Sparse subspace clustering and low-rank subspace clustering use sparse representation and low-rank representation respectively to construct affine matrices that are input into spectral clustering to obtain the final clustering result.However,sparse and low-rank constraints do not achieve the desired results on some data sets.Block Diagonal Representation(BDR)subspace clustering algorithm was proposed recently,which can obtain more accurate affine matrix by adding Laplacian rank constraint to improve the clustering accuracy.However,all the above algorithms belong to linear subspace clustering,and their basic assumptions are self-expression property,noise-free data and independent subspaces,which are difficult to be satisfied by real data.In this paper,we take BDR as the benchmark algorithm,and design the structure learning algorithms for practical problems such as overlapped subspaces and corrupted data with outliers.The proposed algorithms correct the errors in subspace clustering through active learning,and improve the clustering performance and robustness.The main work of this paper is summarized as follows:(1)An Active Structured Block Diagonal Representation algorithm(ASBDR)is proposed.We design an active learning strategy for valuable pairwise constraint and incorporate it into Structured Block Diagonal Representation(SBDR)clustering algorithm to guide the algorithm to explore local structure of data on the basis of global structure and improve clustering performance.Experiments on face data set ORL and handwritten data set MNIST show the effectiveness of the proposed algorithm.(2)An Active Block Diagonal Representation algorithm(ABDR)is proposed and an active learning strategy for data labels is proposed to acquire labels of the informative data points from the framework and boundary of the clusters,and then the labeled data are converted into pairwise constraints,which are incorporated into BDR to improve the clustering performance.Experimental results on three images datasets(MNIST,ORL and COIL-20)and one UCI dataset(ISOLET)show that ABDR is superior to multiple state-of-the-art active clustering and learning techniques in complex clustering tasks,and ABDR is still robust in the case of data labels containing noise.(3)Aiming at the noise and outliers of real data,a new objective function and the corresponding algorithm OBDR(r Obust Block Diagonal Representation)are proposed by combining L_2,1 norm with the Laplacian rank constraint to improve the robustness of subspace clustering on dataset with outliers.Experimental results on noisy data sets show that the proposed algorithm has better robustness.To sum up,this paper combines active learning,semi-supervised learning methods and L_2,1 norm into block diagonal representation clustering algorithm to overcome data noises and improve the clustering performance of the algorithm.