Related papers: A determinantal formula for cluster variables in c…
We propose a node clustering method for time-varying graphs based on the assumption that the cluster labels are changed smoothly over time. Clustering is one of the fundamental tasks in many science and engineering fields including signal…
We present a new computation of the critical value of the random-cluster model with cluster weight $q\ge 1$ on $\mathbb{Z}^2$. This provides an alternative approach to the result of Beffara and Duminil-Copin. We believe that this approach…
We consider the problem of estimating the number of clusters (k) in a dataset. We propose a non-parametric approach to the problem that utilizes similarity graphs to construct a robust statistic that effectively captures similarity…
Let $\mathscr{C}$ be the category of finite dimensional modules over the quantum affine algebra $U_q(\widehat{\mathfrak{g}})$ of a simple complex Lie algebra ${\mathfrak{g}}$. Let $\mathscr{C}^-$ be the subcategory introduced by Hernandez…
Given a family of stable curves, we define a sheaf of factorization algebras associated to any universal factorization algebra, and prove a gluing formula for the corresponding sheaf of chiral homology, generalizing the sheaves of vertex…
Buan, Marsh and Reiten proved that if a cluster-tilting object $T$ in a cluster category $\mathcal C$ associated to an acyclic quiver $Q$ satisfies certain conditions with respect to the exchange pairs in $\mathcal C$, then the denominator…
Clustering of variables is as a way to arrange variables into homogeneous clusters, i.e., groups of variables which are strongly related to each other and thus bring the same information. These approaches can then be useful for dimension…
This paper is devoted to the presentation of combinatorial bialgebras whose coproduct is defined with the help of a commutative semigroup. We consider this setting in order to give a general framework which admits as special cases the…
Spectral clustering approaches have led to well-accepted algorithms for finding accurate clusters in a given dataset. However, their application to large-scale datasets has been hindered by computational complexity of eigenvalue…
We study two variants of the fundamental problem of finding a cluster in incomplete data. In the problems under consideration, we are given a multiset of incomplete $d$-dimensional vectors over the binary domain and integers $k$ and $r$,…
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…
VARCLUST algorithm is proposed for clustering variables under the assumption that variables in a given cluster are linear combinations of a small number of hidden latent variables, corrupted by the random noise. The entire clustering task…
Cluster algebras are a class of commutative algebras whose generators are defined by a recursive process called mutation. We give a brief introduction to cluster algebras, and explain how discrete integrable systems can appear in the…
Quantum Clustering is a powerful method to detect clusters in data with mixed density. However, it is very sensitive to a length parameter that is inherent to the Schr\"odinger equation. In addition, linking data points into clusters…
We develop a general approach to finding combinatorial models for cluster algebras. The approach is to construct a labeled graph called a framework. When a framework is constructed with certain properties, the result is a model…
This thesis is concerned with studying the properties of gradings on several examples of cluster algebras, primarily of infinite type. We first consider two finite type cases: $B_n$ and $C_n$, completing a classification by Grabowski for…
Cluster analysis requires many decisions: the clustering method and the implied reference model, the number of clusters and, often, several hyper-parameters and algorithms' tunings. In practice, one produces several partitions, and a final…
In this paper, we introduce the enough $g$-pairs property for a principal coefficients cluster algebra, which can be understood as a strong version of the sign-coherence of the $G$-matrices. Then we prove that any skew-symmetrizable…
Cluster analysis relates to the task of assigning objects into groups which ideally present some desirable characteristics. When a cluster structure is confined to a subset of the feature space, traditional clustering techniques face…
In many situations it is desirable to identify clusters that differ with respect to only a subset of features. Such clusters may represent homogeneous subgroups of patients with a disease, such as cancer or chronic pain. We define a…