Smooth Non-negative Low-Rank Graph Representation for Clustering

Abstract

The existing low-rank graph representation algorithms fail to capture the global representation structure of data accurately, and cannot make full use of the valid information of data to guide the construction of the representation graph, then the constructed representation graph does not have a connected structure suitable for clustering. A smooth non-negative low-rank graph representation method for clustering (SNLRR) is proposed to solve these problems. To more accurately capture the global representation structure of data, SNLRR uses a logarithmic determinant function that is more consistent with the rank characteristics of the matrix to replace the kernel norm to estimate the rank function smoothly, which can effectively reduce the impact of larger singular values of the matrix on the rank estimation, balance the contribution of all singular values to the rank estimation, enhance the accuracy of the rank estimation, so as to more accurately capture the global representation structure of the data. The distance regularization term is also introduced to adaptively assign the optimal nearest neighbor learning representation matrix for each data point to capture the local representation structure of data. Besides, SNLRR applies rank constraint on the Laplace matrix of representation matrix so that the learned representation graph has the same number of connected components as the real number of clusters, that is, the resulting representation graph has a interconnected structure suitable for clustering. Experimental results on seven datasets with high dimensions and complex distribution, using eight comparison algorithms, show that the clustering performance of SNLRR algorithm is better than that of the eight comparison algorithms, with an average increase of 0.2073 in accuracy and 0.1758 in NMI. Therefore, SNLRR is a graph representation clustering algorithm that can effectively handle data with high dimensions and complex distribution.

Keywords

• clustering; low-rank representation; rank constraint; logarithmic determinant low rank