Graph Convolution RPCA With Adaptive Graph.

Area of Science:

• Machine Learning
• Data Science
• Dimensionality Reduction

Background:

• Principal Component Analysis (PCA) is widely used for dimensionality reduction but is sensitive to outliers.
• Existing robust PCA methods have limitations in representation ability.
• There is a need for robust and effective dimensionality reduction techniques that preserve data structure.

Purpose of the Study:

• To develop a novel robust PCA method that enhances both robustness and representation ability.
• To incorporate manifold structure into PCA for improved performance.
• To address the limitations of existing PCA techniques in handling outliers and preserving data characteristics.

Main Methods:

• A novel Graph Convolution Robust PCA (GRPCA) method is proposed.
• It constructs a sparse graph based on local sample connectivity.
• Graph auto-encoder with dual-decoder is used to solve robust PCA under low-rank and sparse constraints, learning embeddings that reconstruct manifold structure and low-rank approximation.
• The graph is refined using low-dimensional embeddings to mitigate misconnections from occlusions.

Main Results:

• GRPCA demonstrates superior performance in clustering low-dimensional embeddings.
• The method excels in low-rank recovery tasks.
• Extensive experiments on six real-world datasets validate the efficiency and superiority of GRPCA.

Conclusions:

• GRPCA effectively enhances the robustness and representation ability of PCA.
• The integration of manifold structure via graph convolution improves dimensionality reduction.
• The proposed method offers a significant advancement for robust PCA applications.