Related papers: A mixed-integer linear programming approach for so…
An uncertain graph $\mathcal{G} = (V, E, p : E \rightarrow (0,1])$ can be viewed as a probability space whose outcomes (referred to as \emph{possible worlds}) are subgraphs of $\mathcal{G}$ where any edge $e\in E$ occurs with probability…
In this paper, we establish a method for model order reduction of a certain class of physical network systems. The proposed method is based on clustering of the vertices of the underlying graph, and yields a reduced order model within the…
Nonlinear reformulations of the spectral clustering method have gained a lot of recent attention due to their increased numerical benefits and their solid mathematical background. However, the estimation of the multiple nonlinear…
The goal of fair clustering is to find clusters such that the proportion of sensitive attributes (e.g., gender, race, etc.) in each cluster is similar to that of the entire dataset. Various fair clustering algorithms have been proposed that…
We present a graph-theoretical approach to data clustering, which combines the creation of a graph from the data with Markov Stability, a multiscale community detection framework. We show how the multiscale capabilities of the method allow…
Flow-based methods for local graph clustering have received significant recent attention for their theoretical cut improvement and runtime guarantees. In this work we present two improvements for using flow-based methods in real-world…
Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance.…
We introduce a principled and theoretically sound spectral method for $k$-way clustering in signed graphs, where the affinity measure between nodes takes either positive or negative values. Our approach is motivated by social balance…
We propose two spectral algorithms for partitioning nodes in directed graphs respectively with a cyclic and an acyclic pattern of connection between groups of nodes. Our methods are based on the computation of extremal eigenvalues of the…
In today's data-driven digital era, the amount as well as complexity, such as multi-view, non-Euclidean, and multi-relational, of the collected data are growing exponentially or even faster. Clustering, which unsupervisely extracts valid…
We consider the problem of simultaneously clustering and learning a linear representation of data lying close to a union of low-dimensional manifolds, a fundamental task in machine learning and computer vision. When the manifolds are…
We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for…
We consider a problem of grouping multiple graphs into several clusters using singular value thesholding and non-negative factorization. We derive a model selection information criterion to estimate the number of clusters. We demonstrate…
We study the complexity of finding an optimal hierarchical clustering of an unweighted similarity graph under the recently introduced Dasgupta objective function. We introduce a proof technique, called the normalization procedure, that…
Motivated by applications in social network community analysis, we introduce a new clustering paradigm termed motif clustering. Unlike classical clustering, motif clustering aims to minimize the number of clustering errors associated with…
We introduce a dynamic version of the NP-hard graph problem Cluster Editing. The essential point here is to take into account dynamically evolving input graphs: Having a cluster graph (that is, a disjoint union of cliques) that represents a…
Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the…
Graph clustering, which aims to divide a graph into several homogeneous groups, is a critical area of study with applications that span various fields such as social network analysis, bioinformatics, and image segmentation. This paper…
Cut-based directed graph (digraph) clustering often focuses on finding dense within-cluster or sparse between-cluster connections, similar to cut-based undirected graph clustering methods. In contrast, for flow-based clusterings the edges…
Graph clustering is a fundamental and challenging task in the field of graph mining where the objective is to group the nodes into clusters taking into consideration the topology of the graph. It has several applications in diverse domains…