Robust Principal Component Analysis on Graphs
This work addresses robustness and scalability problems in PCA for data analysis, offering a convex solution that enhances clustering and low-rank recovery, though it appears incremental as it builds on existing Robust PCA and graph methods.
The paper tackles the sensitivity of PCA to outliers and scalability issues by introducing Robust PCA on Graphs, which incorporates spectral graph regularization into the Robust PCA framework, resulting in outperformance of 10 other state-of-the-art models in clustering and low-rank recovery tasks across 13 datasets.
Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization model, which is however non-convex. Besides, PCA based clustering can also be enhanced by using a graph of data similarity. In this article, we introduce a new model called "Robust PCA on Graphs" which incorporates spectral graph regularization into the Robust PCA framework. Our proposed model benefits from 1) the robustness of principal components to occlusions and missing values, 2) enhanced low-rank recovery, 3) improved clustering property due to the graph smoothness assumption on the low-rank matrix, and 4) convexity of the resulting optimization problem. Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with corruptions clearly reveal that our model outperforms 10 other state-of-the-art models in its clustering and low-rank recovery tasks.