Recursive Sample Scaling Low-Rank Representation

The low-rank representation (LRR) method has recently gained enormous popularity due to its robust approach in solving the subspace segmentation problem, particularly those concerning corrupted data. In this paper, the recursive sample scaling low-rank representation (RSS-LRR) method is proposed. The advantage of RSS-LRR over traditional LRR is that a cosine scaling factor is further introduced, which imposes a penalty on each sample to minimize noise and outlier influence better. Specifically, the cosine scaling factor is a similarity measure learned to extract each sample’s relationship with the low-rank representation’s principal components in the feature space. In order words, the smaller the angle between an individual data sample and the low-rank representation’s principal components, the more likely it is that the data sample is clean. Thus, the proposed method can then effectively obtain a good low-rank representation influenced mainly by clean data. Several experiments are performed with varying levels of corruption on ORL, CMU PIE, COIL20, COIL100, and LFW in order to evaluate RSS-LRR’s effectiveness over state-of-the-art low-rank methods. The experimental results show that RSS-LRR consistently performs better than the compared methods in image clustering and classification tasks.

One-Step Robust Low-Rank Subspace Segmentation for Tumor Sample Clustering

Clustering of tumor samples can help identify cancer types and discover new cancer subtypes, which is essential for effective cancer treatment. Although many traditional clustering methods have been proposed for tumor sample clustering, advanced algorithms with better performance are still needed. Low-rank subspace clustering is a popular algorithm in recent years. In this paper, we propose a novel one-step robust low-rank subspace segmentation method (ORLRS) for clustering the tumor sample. For a gene expression data set, we seek its lowest rank representation matrix and the noise matrix. By imposing the discrete constraint on the low-rank matrix, without performing spectral clustering, ORLRS learns the cluster indicators of subspaces directly, i.e., performing the clustering task in one step. To improve the robustness of the method, capped norm is adopted to remove the extreme data outliers in the noise matrix. Furthermore, we conduct an efficient solution to solve the problem of ORLRS. Experiments on several tumor gene expression data demonstrate the effectiveness of ORLRS.