Graph Nodes Clustering Based on the Commute-Time Kernel

Abstract

This work presents a kernel method for clustering the nodes of a weighted, undirected, graph. The algorithm is based on a two-step procedure. First, the sigmoid commute-time kernel (K CT ), providing a similarity measure between any couple of nodes by taking the indirect links into account, is computed from the adjacency matrix of the graph. Then, the nodes of the graph are clustered by performing a kernel k-means or fuzzy k-means on this CT kernel matrix. For this purpose, a new, simple, version of the kernel k-means and the kernel fuzzy k-means is introduced. The joint use of the CT kernel matrix and kernel clustering appears to be quite successful. Indeed, this methodology provides good results, outperforming the spherical k-means, on a document clustering problem involving the newsgroups database.

Modularity-Driven Kernel k-means for Community Detection

“…• an enhanced kernel k-means approach inspired from [46,47], that employs the modularity criterion to estimate the optimal kernel or distance parameters as well as the natural number of clusters, • the Louvain method [2], which also estimates the natural number of clusters on its own, on 15 graph datasets, the smallest of which (Zachary's Karate club, [49]) contains 34 nodes. The largest graph (a Newsgroup graph, [34,46] …”

“…This method is a simple extension of the kernel k-means algorithm for community detection [46,47]. This extended method optimizes kernel parameters and automatically estimates the natural number of clusters present in the dataset.…”

“…Given a meaningful, symmetric distance matrix Δ, containing the distances Δ ij , the goal is to partition the nodes by minimizing the total within-cluster sum of squared distances. For details, see [20,46,47]. The change between the standard kernel k-means and the kernel k-means coupled with modularity criterion is found in the two-step approach of the latter, which is more easily explained using the flowchart in Fig.…”

“…To address the shortcomings of using a k-means on a graph structure, approaches such as kernel k-means were developed [46]. Kernel k-means can use various kernels derived from the distance-based or proximity-based data, and is particularly useful in community detection, that is, finding similar nodes in a given graph and grouping them together [46,47].…”

Fast Katz and Commuters: Efficient Estimation of Social Relatedness in Large Networks

“…For example, the algorithm we propose for computing the Katz and commute time between a given pair of nodes extends to the case where one wants to find the aggregate score between a node and a set of nodes. This could be useful in methods that find clusters using commute time [16,17,25]. In these cases, the commute time between a node and a group of nodes (e.g., a cluster) measures their affinity.…”