Using Local Spectral Methods to Robustify Graph-Based Learning Algorithms

TitleUsing Local Spectral Methods to Robustify Graph-Based Learning Algorithms
Publication TypeConference Paper
Year of Publication2015
AuthorsGleich, D., & Mahoney M. W.
Published inProceedings of the 21st Annual SIGKDD

Graph-based learning methods have a variety of names including semi-supervised and transductive learning. They typically use a diffusion to propagate labels from a small set of nodes with known class labels to the remaining nodes of the graph. While popular, these algorithms, when implemented in a straightforward fashion, are extremely sensitive to the details of the graph construction. Here, we provide four procedures to help make them more robust: recognizing implicit regularization in the diffusion, using a scalable push method to evaluate the diffusion, using rank-based rounding, and densifying the graph through a matrix polynomial. We study robustness with respect to the details of graph constructions, errors in node labeling, degree variability, and a variety of other real-world heterogeneities, studying these methods through a precise relationship with mincut problems. For instance, the densification strategy explicitly adds new weighted edges to a sparse graph. We find that this simple densification creates a graph where multiple diffusion methods are robust to several types of errors. This is demonstrated by a study with predicting product categories from an Amazon co-purchasing network.


Gleich is supported by NSF CAREER CF-1149756; Mahoney is partially supported from the Army Research Office and the DARPA GRAPHS program

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