Accelerated filtering on graphs using Lanczos method

TL;DR

This paper introduces an accelerated graph filtering algorithm using the Lanczos method, which adapts to the Laplacian spectrum without explicit computation, offering higher accuracy and scalability for large graphs.

Contribution

The paper presents a novel Lanczos-based filtering algorithm that improves accuracy and efficiency over Chebyshev polynomial methods, especially for graphs with large spectral gaps.

Findings

Achieves higher accuracy than Chebyshev polynomial methods

Maintains similar computational complexity while improving precision

Performs well on large graphs with significant spectral gaps

Abstract

Signal-processing on graphs has developed into a very active field of research during the last decade. In particular, the number of applications using frames constructed from graphs, like wavelets on graphs, has substantially increased. To attain scalability for large graphs, fast graph-signal filtering techniques are needed. In this contribution, we propose an accelerated algorithm based on the Lanczos method that adapts to the Laplacian spectrum without explicitly computing it. The result is an accurate, robust, scalable and efficient algorithm. Compared to existing methods based on Chebyshev polynomials, our solution achieves higher accuracy without increasing the overall complexity significantly. Furthermore, it is particularly well suited for graphs with large spectral gaps.