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This paper proposes a Mixed-Integer Linear Programming approach for the Soft Graph Clustering Problem. This is the first method that simultaneously allocates membership proportion for vertices that lie in multiple clusters, and that…
An unsupervised classification method for point events occurring on a network of lines is proposed. The idea relies on the distributional flexibility and practicality of random partition models to discover the clustering structure featuring…
In this paper, we propose a new method called Clustering Topological PRM (CTopPRM) for finding multiple homotopically distinct paths in 3D cluttered environments. Finding such distinct paths, e.g., going around an obstacle from a different…
We consider a generalized version of the correlation clustering problem, defined as follows. Given a complete graph $G$ whose edges are labeled with $+$ or $-$, we wish to partition the graph into clusters while trying to avoid errors: $+$…
We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…
A recently proposed clustering method, called the Nearest Descent (ND), can organize the whole dataset into a sparsely connected graph, called the In-tree. This ND-based Intree structure proves able to reveal the clustering structure…
Clustering is an essential technique for network analysis, with applications in a diverse range of fields. Although spectral clustering is a popular and effective method, it fails to consider higher-order structure and can perform poorly on…
This paper is concerned with a constrained optimization problem over a directed graph (digraph) of nodes, in which the cost function is a sum of local objectives, and each node only knows its local objective and constraints. To…
Graph clustering is a fundamental computational problem with a number of applications in algorithm design, machine learning, data mining, and analysis of social networks. Over the past decades, researchers have proposed a number of…
Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning…
Recently, network lasso has drawn many attentions due to its remarkable performance on simultaneous clustering and optimization. However, it usually suffers from the imperfect data (noise, missing values etc), and yields sub-optimal…
Scientists in many fields have the common and basic need of dimensionality reduction: visualizing the underlying structure of the massive multivariate data in a low-dimensional space. However, many dimensionality reduction methods confront…
Graph clustering is an unsupervised machine learning method that partitions the nodes in a graph into different groups. Despite achieving significant progress in exploiting both attributed and structured data information, graph clustering…
We discuss topological aspects of cluster analysis and show that inferring the topological structure of a dataset before clustering it can considerably enhance cluster detection: theoretical arguments and empirical evidence show that…
In this paper we consider discrete robot path planning problems on metric graphs. We propose a clustering method, Gamma-Clustering for the planning graph that significantly reduces the number of feasible solutions, yet retains a solution…
Graph clustering is a basic technique in machine learning, and has widespread applications in different domains. While spectral techniques have been successfully applied for clustering undirected graphs, the performance of spectral…
Clustering is a fundamental task in data analysis, and spectral clustering has been recognized as a promising approach to it. Given a graph describing the relationship between data, spectral clustering explores the underlying cluster…
Clustering algorithms are one of the main analytical methods to detect patterns in unlabeled data. Existing clustering methods typically treat samples in a dataset as points in a metric space and compute distances to group together similar…
Autonomous intersection management has the potential to reduce road traffic congestion and energy consumption. To realize this potential, efficient algorithms are needed. However, most existing studies locally optimize one intersection at a…
We study large-scale, distributed graph clustering. Given an undirected graph, our objective is to partition the nodes into disjoint sets called clusters. A cluster should contain many internal edges while being sparsely connected to other…