Multiscale Graph Construction Using Non-local Cluster Features

TL;DR

This paper introduces a multiscale graph construction method that combines graph structure and node features, using hierarchical clustering with optimal transport and spectral clustering to better detect clusters with similar features, even if spatially separated.

Contribution

It proposes a novel multiscale clustering approach that integrates signal features and non-local relationships for hierarchical graph construction.

Findings

Effective in multiscale image segmentation

Improves clustering of spatially separated similar nodes

Demonstrates advantages over traditional graph clustering methods

Abstract

This paper presents a multiscale graph construction method using both graph and signal features. Multiscale graph is a hierarchical representation of the graph, where a node at each level indicates a cluster in a finer resolution. To obtain the hierarchical clusters, existing methods often use graph clustering; however, they may ignore signal variations. As a result, these methods could fail to detect the clusters having similar features on nodes. In this paper, we consider graph and node-wise features simultaneously for multiscale clustering of a graph. With given clusters of the graph, the clusters are merged hierarchically in three steps: 1) Feature vectors in the clusters are extracted. 2) Similarities among cluster features are calculated using optimal transport. 3) A variable $k$-nearest neighbor graph (V$k$NNG) is constructed and graph spectral clustering is applied to the V$k$NNG to obtain clusters at a coarser scale. Additionally, the multiscale graph in this paper has \textit{non-local} characteristics: Nodes with similar features are merged even if they are spatially separated. In experiments on multiscale image and point cloud segmentation, we demonstrate the effectiveness of the proposed method.