Revisiting Spectral Graph Clustering with Generative Community Models

Abstract

The methodology of community detection can be divided into two principles: imposing a network model on a given graph, or optimizing a designed objective function. The former provides guarantees on theoretical detectability but falls short when the graph is inconsistent with the underlying model. The latter is model-free but fails to provide quality assurance for the detected communities. In this paper, we propose a novel unified framework to combine the advantages of these two principles. The presented method, SGC-GEN, not only considers the detection error caused by the corresponding model mismatch to a given graph, but also yields a theoretical guarantee on community detectability by analyzing Spectral Graph Clustering (SGC) under GENerative community models (GCMs). SGC-GEN incorporates the predictability on correct community detection with a measure of community fitness to GCMs. It resembles the formulation of supervised learning problems by enabling various community detection loss functions and model mismatch metrics. We further establish a theoretical condition for correct community detection using the normalized graph Laplacian matrix under a GCM, which provides a novel data-driven loss function for SGC-GEN. In addition, we present an effective algorithm to implement SGC-GEN, and show that the computational complexity of SGC-GEN is comparable to the baseline methods. Our experiments on 18 real-world datasets demonstrate that SGC-GEN possesses superior and robust performance compared to 6 baseline methods under 7 representative clustering metrics.

Unsupervised Learning for Subterranean Junction Recognition Based on 2D Point Cloud

“…In this work, we propose to identify the number of junctions in uncertain subterranean environments using an unsupervised learning framework. Cluster analysis is one of the most fundamental problems in machine learning for finding groups of similar data points without any supervi-sion [21]. Many existing clustering methods such as K-means clustering learn hidden structures from data points that are connected within convex boundaries.…”

Incremental eigenpair computation for graph Laplacian matrices: theory and applications

“…Over the past two decades, the graph Laplacian matrix and its variants have been widely adopted for solving various research tasks, including graph partitioning [42], data clustering [5,32,56], community detection [7,13,50], consensus in networks [37,53], accelerated distributed optimization [29], dimensionality reduction [2,52], entity disambiguation [46,[60][61][62][63][64], link prediction [15,19,20,59], graph signal processing [12,48], centrality measures for graph connectivity [6], multi-layer network analysis [11,30], interconnected physical systems [43], network vulnerability assessment [9], image segmentation [18,47], gene expression [28,31,39], among others. The fundamental task is to represent the data of interest as a graph for analysis, where a node represents an entity (e.g., a pixel in an image or a user in an online social network) and an edge represents similarity between two multivariate data samples or actual relation (e.g., friendship) between nodes [32].…”