Robust Dimensionality Reduction via Low-rank Laplacian Graph Learning

Manifold learning is a widely used technique for dimensionality reduction as it can reveal the intrinsic geometric structure of data. However, its performance decreases drastically when data samples are contaminated by heavy noise or occlusions, which leads to unsatisfying data processing performance. We propose a novel robust dimensionality reduction method via low-rank Laplacian graph learning for classification and clustering tasks to solve the above problem. First, we construct a low-rank Laplacian graph by combining manifold learning and subspace learning. This graph can capture both global and local structural information of the data. And we introduce rank constraints for the Laplacian graph to make it more discriminative. Second, we put the learning of projection matrix and sample affinity graph into a unified framework. The projection matrix is embedded into a robust low-rank Laplacian graph so that the low-dimensional mapping of data can maintain the structural information in the graph well. Finally, we add a regularization term to the projection matrix to make it have the ability of both feature extraction and feature selection. Therefore, the proposed model can resist the interference of noise or data damage to learn the optimal projection to achieve better performance in dimensionality reduction through such a data dimensionality reduction joint framework. Comprehensive experiments on various benchmark datasets with varying degrees of occlusions or corruptions are carried out to evaluate the performance of the proposed method. Compared with the state-of-the-art dimensionality reduction methods in the literature, the experimental results are inspiring, showing our method’s effectiveness and robustness in classification and clustering, especially in object recognition scenarios with noise or occlusions.