Graph-Laplacian PCA: Closed-Form Solution and Robustness

Principal Component Analysis (PCA) is a widely used to learn a low-dimensional representation. In many applications, both vector data X and graph data W are available. Laplacian embedding is widely used for embedding graph data. We propose a graph-Laplacian PCA (gLPCA) to learn a low dimensional representation of X that incorporates graph structures encoded in W. This model has several advantages: (1) It is a data representation model. (2) It has a compact closed-form solution and can be efficiently computed. (3) It is capable to remove corruptions. Extensive experiments on 8 datasets show promising results on image reconstruction and significant improvement on clustering and classification.