flow-based clustering and spectral clustering: a comparison

TL;DR

This paper introduces a new graph clustering method that uses total variation minimization to create feature vectors, offering advantages over spectral clustering in handling certain challenging graph structures.

Contribution

The paper presents a novel clustering approach that replaces eigenvector computation with total variation minimization solutions, improving performance on specific graph structures.

Findings

Our method effectively handles challenging graph structures.

Total variation-based features outperform spectral clustering in certain cases.

The approach is adaptable with domain knowledge or heuristics for seed nodes.

Abstract

We propose and study a novel graph clustering method for data with an intrinsic network structure. Similar to spectral clustering, we exploit an intrinsic network structure of data to construct Euclidean feature vectors. These feature vectors can then be fed into basic clustering methods such as k-means or Gaussian mixture model (GMM) based soft clustering. What sets our approach apart from spectral clustering is that we do not use the eigenvectors of a graph Laplacian to construct the feature vectors. Instead, we use the solutions of total variation minimization problems to construct feature vectors that reflect connectivity between data points. Our motivation is that the solutions of total variation minimization are piece-wise constant around a given set of seed nodes. These seed nodes can be obtained from domain knowledge or by simple heuristics that are based on the network structure of data. Our results indicate that our clustering methods can cope with certain graph structures that are challenging for spectral clustering methods.