MeanCut: A Greedy-Optimized Graph Clustering via Path-based Similarity and Degree Descent Criterion

TL;DR

MeanCut introduces a path-based similarity and a greedy degree descent approach for graph clustering, enabling detection of arbitrary shapes, robustness to noise, and improved efficiency through a fast MST algorithm, with applications demonstrated on real data.

Contribution

It proposes a novel greedy optimization algorithm for graph clustering using path-based similarity and degree descent, overcoming limitations of spectral clustering.

Findings

Effective in identifying arbitrary shaped clusters

Robust to noise and non-spherical data distributions

Improved computational efficiency with FastMST

Abstract

As the most typical graph clustering method, spectral clustering is popular and attractive due to the remarkable performance, easy implementation, and strong adaptability. Classical spectral clustering measures the edge weights of graph using pairwise Euclidean-based metric, and solves the optimal graph partition by relaxing the constraints of indicator matrix and performing Laplacian decomposition. However, Euclidean-based similarity might cause skew graph cuts when handling non-spherical data distributions, and the relaxation strategy introduces information loss. Meanwhile, spectral clustering requires specifying the number of clusters, which is hard to determine without enough prior knowledge. In this work, we leverage the path-based similarity to enhance intra-cluster associations, and propose MeanCut as the objective function and greedily optimize it in degree descending order for a nondestructive graph partition. This algorithm enables the identification of arbitrary shaped clusters and is robust to noise. To reduce the computational complexity of similarity calculation, we transform optimal path search into generating the maximum spanning tree (MST), and develop a fast MST (FastMST) algorithm to further improve its time-efficiency. Moreover, we define a density gradient factor (DGF) for separating the weakly connected clusters. The validity of our algorithm is demonstrated by testifying on real-world benchmarks and application of face recognition. The source code of MeanCut is available at https://github.com/ZPGuiGroupWhu/MeanCut-Clustering.