Related papers: Clustered Planarity = Flat Clustered Planarity
We present a structural clustering algorithm for large-scale datasets of small labeled graphs, utilizing a frequent subgraph sampling strategy. A set of representatives provides an intuitive description of each cluster, supports the…
Fair clustering is the process of grouping similar entities together, while satisfying a mathematically well-defined fairness metric as a constraint. Due to the practical challenges in precise model specification, the prescribed fairness…
We consider the clustering aggregation problem in which we are given a set of clusterings and want to find an aggregated clustering which minimizes the sum of mismatches to the input clusterings. In the binary case (each clustering is a…
Consider the following two ways to colour the vertices of a graph where the requirement that adjacent vertices get distinct colours is relaxed. A colouring has "defect" $d$ if each monochromatic component has maximum degree at most $d$. A…
Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…
Document clustering is an unsupervised approach in which a large collection of documents (corpus) is subdivided into smaller, meaningful, identifiable, and verifiable sub-groups (clusters). Meaningful representation of documents and…
Given a graph G, we investigate the question of determining the parity of the number of homomorphisms from G to some other fixed graph H. We conjecture that this problem exhibits a complexity dichotomy, such that all parity graph…
Modern methods of graph theory describe a graph up to isomorphism, which makes it difficult to create mathematical models for visualizing graph drawings on a plane. The topological drawing of the planar part of a graph allows representing…
We prove that if $G$ is a sparse graph --- it belongs to a fixed class of bounded expansion $\mathcal{C}$ --- and $d\in \mathbb{N}$ is fixed, then the $d$th power of $G$ can be partitioned into cliques so that contracting each of these…
The objective of clustering is to discover natural groups in datasets and to identify geometrical structures which might reside there, without assuming any prior knowledge on the characteristics of the data. The problem can be seen as…
Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…
We establish basic properties of cluster algebras associated with oriented bordered surfaces with marked points. In particular, we show that the underlying cluster complex of such a cluster algebra does not depend on the choice of…
While spectral clustering algorithms for undirected graphs are well established and have been successfully applied to unsupervised machine learning problems ranging from image segmentation and genome sequencing to signal processing and…
Graph-based subspace clustering methods have exhibited promising performance. However, they still suffer some of these drawbacks: encounter the expensive time overhead, fail in exploring the explicit clusters, and cannot generalize to…
We study supervised learning problems using clustering constraints to impose structure on either features or samples, seeking to help both prediction and interpretation. The problem of clustering features arises naturally in text…
We address the problem of un-supervised soft-clustering called micro-clustering. The aim of the problem is to enumerate all groups composed of records strongly related to each other, while standard clustering methods separate records at…
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…
A graph is $\ell$-choosable if, for any choice of lists of $\ell$ colors for each vertex, there is a list coloring, which is a coloring where each vertex receives a color from its list. We study complexity issues of choosability of graphs…
Identifying clusters of vertices in graphs continues to be an important problem, and modularity continues to be used as a tool for solving the problem. Modularity, which measures the quality of a division of the vertices into clusters,…
Correlation clustering seeks a partition of the vertex set of a given graph/network into groups of closely related, or just close enough, vertices so that elements of different groups are not close to each other. The problem has been…