Learning Multi-layer Graphs and a Common Representation for Clustering

TL;DR

This paper introduces a novel method for learning multi-layer graphs from multi-view data to improve spectral clustering by jointly estimating graph Laplacians and low-dimensional embeddings, outperforming existing techniques.

Contribution

It proposes a joint graph learning and embedding framework with a rank constraint for multi-view clustering, along with an efficient alternating minimization solver.

Findings

Outperforms state-of-the-art multi-view clustering methods on synthetic datasets.

Demonstrates effectiveness on real-world datasets with improved clustering accuracy.

Provides a scalable and efficient algorithm for multi-layer graph learning.

Abstract

In this paper, we focus on graph learning from multi-view data of shared entities for spectral clustering. We can explain interactions between the entities in multi-view data using a multi-layer graph with a common vertex set, which represents the shared entities. The edges of different layers capture the relationships of the entities. Assuming a smoothness data model, we jointly estimate the graph Laplacian matrices of the individual graph layers and low-dimensional embedding of the common vertex set. We constrain the rank of the graph Laplacian matrices to obtain multi-component graph layers for clustering. The low-dimensional node embeddings, common to all the views, assimilate the complementary information present in the views. We propose an efficient solver based on alternating minimization to solve the proposed multi-layer multi-component graph learning problem. Numerical experiments on synthetic and real datasets demonstrate that the proposed algorithm outperforms state-of-the-art multi-view clustering techniques.