GRASPEL: Graph Spectral Learning at Scale

TL;DR

GRASPEL introduces a scalable spectral method for learning ultra-sparse, graph Laplacian-based graphs from data, significantly improving efficiency and accuracy in applications like spectral clustering and t-SNE.

Contribution

The paper presents the first highly-scalable spectral approach for learning large, sparse graphs that integrates recent spectral methods for graph sparsification and embedding.

Findings

Achieved superior spectral clustering efficiency and accuracy.

Enabled learning of ultra-sparse, spectrally-robust graphs from large data.

Improved computational efficiency over prior graph learning methods.

Abstract

Learning meaningful graphs from data plays important roles in many data mining and machine learning tasks, such as data representation and analysis, dimension reduction, data clustering, and visualization, etc. In this work, for the first time, we present a highly-scalable spectral approach (GRASPEL) for learning large graphs from data. By limiting the precision matrix to be a graph Laplacian, our approach aims to estimate ultra-sparse (tree-like) weighted undirected graphs and shows a clear connection with the prior graphical Lasso method. By interleaving the latest high-performance nearly-linear time spectral methods for graph sparsification, coarsening and embedding, ultra-sparse yet spectrally-robust graphs can be learned by identifying and including the most spectrally-critical edges into the graph. Compared with prior state-of-the-art graph learning approaches, GRASPEL is more scalable and allows substantially improving computing efficiency and solution quality of a variety of data mining and machine learning applications, such as spectral clustering (SC), and t-Distributed Stochastic Neighbor Embedding (t-SNE). {For example, when comparing with graphs constructed using existing methods, GRASPEL achieved the best spectral clustering efficiency and accuracy.