Robust graph representation clustering based on adaptive data correction

Impressive performance has been achieved when learning graphs from data in clustering tasks. However, real data often contain considerable noise, which leads to unreliable or inaccurate constructed graphs. In this paper, we propose adaptive data correction-based graph clustering (ADCGC), which can be used to adaptively remove errors and noise from raw data and improve the performance of clustering. The ADCGC method mainly contains three advantages. First, we design the weighted truncated Schatten p-norm (WTSpN) instead of the nuclear norm to recover the low-rank clean data. Second, we choose clean data samples that represent the essential properties of the data as the vertices of the undirected graph, rather than using all the data feature points. Third, we adopt the block-diagonal regularizer to define the edge weights of the graph, which helps to learn an ideal affinity matrix and improve the performance of clustering. In addition, an efficient iterative scheme based on the generalized soft-thresholding operator and alternating minimization is developed to directly solve the nonconvex optimization model. Experimental results show that ADCGC both quantitatively and visually outperforms existing advanced methods.