# Robust Graph Learning from Noisy Data

## TL;DR

This paper introduces a robust graph learning method that effectively handles noisy data, improving clustering, classification, and data recovery by adaptively removing noise and errors, and leveraging robust PCA and graph smoothness.

## Contribution

The paper presents a novel robust graph learning model that enhances low-rank recovery and graph construction from noisy data, outperforming existing methods across various applications.

## Key findings

- Outperforms state-of-the-art methods in image/document clustering.
- Significantly improves semi-supervised classification accuracy.
- Enhances data recovery in image shadow removal and video background subtraction.

## Abstract

Learning graphs from data automatically has shown encouraging performance on clustering and semisupervised learning tasks. However, real data are often corrupted, which may cause the learned graph to be inexact or unreliable. In this paper, we propose a novel robust graph learning scheme to learn reliable graphs from real-world noisy data by adaptively removing noise and errors in the raw data. We show that our proposed model can also be viewed as a robust version of manifold regularized robust PCA, where the quality of the graph plays a critical role. The proposed model is able to boost the performance of data clustering, semisupervised classification, and data recovery significantly, primarily due to two key factors: 1) enhanced low-rank recovery by exploiting the graph smoothness assumption, 2) improved graph construction by exploiting clean data recovered by robust PCA. Thus, it boosts the clustering, semi-supervised classification, and data recovery performance overall. Extensive experiments on image/document clustering, object recognition, image shadow removal, and video background subtraction reveal that our model outperforms the previous state-of-the-art methods.