Robust Graph Learning from Noisy Data (1812.06673v1)

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.

• The paper proposes a robust graph learning method that jointly decomposes noisy data into clean and error components and learns the graph from the clean data.
• The approach enhances Robust PCA by using a graph regularizer from the clean data, improving data recovery and the quality of the learned graph.
• Extensive experiments show the method outperforms existing techniques in clustering and classification on real data, demonstrating its practical effectiveness.

Analysis of "Robust Graph Learning from Noisy Data"

The paper "Robust Graph Learning from Noisy Data" introduces an innovative method for constructing graphs from real-world data that is often afflicted by noise and errors. Traditional graph learning methods are susceptible to noise in the input data, potentially leading to inaccurate or suboptimal graph representations that degrade the performance of downstream tasks such as clustering and semisupervised classification. The authors address these challenges by proposing a novel scheme that decomposes raw data into clean and noisy components and learns the graph based on the clean data using an adaptive neighbors approach.

Key Contributions

The key contributions of the paper lie in the robustification of graph learning through a joint optimization scheme that simultaneously deals with graph construction and data denoising. This framework enhances the construction of graph Laplacians, pivotal for manifold-based methods like regularized Robust PCA (RPCA), which is also embedded into the proposed solution. The methodological innovation is particularly noteworthy as it proceeds by leveraging smooth manifold assumptions to enhance the low-rank recovery of data.

1. Unified Robust Graph Learning Model: This work proposes a unified framework where the decomposition of raw data into clean and error components occurs concurrently with graph learning. This approach avoids the traditional two-step process and enhances the relationship between the clean data and the learned graph.
2. Enhanced RPCA: Incorporating a graph Laplacian regularizer derived from clean data, the proposed model transcends conventional RPCA models which typically utilize noisy data. This approach not only improves the graph quality but also enhances the recovery of the underlying low-rank structure.
3. Experimental Validation: Extensive experiments demonstrate the effectiveness of the proposed model across multiple tasks, including clustering and semisupervised classification on a variety of real-world data sets. The model consistently outperforms existing state-of-the-art techniques in clustering accuracy, NMI, and purity metrics.

Experimental Performance

The empirical evaluation involves benchmarking the proposed method against a range of existing methodologies, including Spectral Clustering, Robust Kernel K-means, and Manifold RPCA, among others. The reported results reveal that the proposed method typically exceeds the performance of competitors, with significant improvements noted in clustering accuracy. This supports the hypothesis that constructing a graph from clean data offers considerable advantages in terms of both robustness and the reliability of graph-based learning tasks.

Implications and Future Directions

The implications for practical applications are substantial. Graph-based learning methods are widespread in tasks such as image segmentation, object recognition, and document clustering. This new approach could vastly improve the robustness and precision of these applications, particularly in environments where data integrity is compromised by noise or outliers.

From a theoretical perspective, this work invites further research into alternative graph learning paradigms and optimization techniques that share a similar philosophy of robustness against noise. The methodology also sets a foundation for exploring extensions in other types of unsupervised or weakly supervised learning tasks. Future work could explore the integration of more complex non-linear data manifold assumptions or the amalgamation with deep learning-based representations to further improve performance.

In conclusion, the "Robust Graph Learning from Noisy Data" paper enriches the field of graph-based machine learning with a robust, theoretically grounded methodology that promises enhanced performance across a spectrum of challenging real-world applications. The approach showcases the critical importance of addressing data noise in graph learning and sets a course for ongoing research in robust machine learning frameworks.