Related papers: Abstract Cluster Structures
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…
Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable…
Let $S$ be a surface, $G$ a simply-connected classical group, and $G'$ the associated adjoint form of the group. In \cite{FG1}, it was shown that the moduli spaces of framed local systems $\X_{G',S}$ and $\A_{G,S}$ have the structure of…
A general method to obtain a representation of the structural landscape of nanoparticles in terms of a limited number of variables is proposed. The method is applied to a large dataset of parallel tempering molecular dynamics simulations of…
Let $k$ be a field and $A$ a finite-dimensional $k$-algebra of global dimension $\leq 2$. We construct a triangulated category $\Cc_A$ associated to $A$ which, if $A$ is hereditary, is triangle equivalent to the cluster category of $A$.…
Understanding the global organization of complicated and high dimensional data is of primary interest for many branches of applied sciences. It is typically achieved by applying dimensionality reduction techniques mapping the considered…
We study the cluster algebras arising from cluster tubes with rank bigger than $1$. Cluster tubes are $2-$Calabi-Yau triangulated categories which contain no cluster tilting objects, but maximal rigid objects. Fix a certain maximal rigid…
Let $\mathcal{A}_{q}$ be an arbitrary quantum cluster algebra with principal coefficients. We give the fundamental relations between the quantum cluster variables arising from one-step mutations from the initial cluster in…
We put cluster tilting in ageneral framework by showing that any quotient of a triangulated category modulo a tilting subcategory (that is, a maximal one-orthogonal subcategory) carries an abelian structure. These abelian quotients turn out…
We introduce a family of cluster algebras of infinite rank associated with root systems of type $A$, $D$, $E$. We show that suitable completions of these cluster algebras are isomorphic to the Grothendieck rings of the categories…
We consider triangulated orbit categories, with the motivating example of cluster categories, in their usual context of algebraic triangulated categories, then present them from another perspective in the framework of topological…
We take a novel lattice-theoretic approach to the $\tau$-cluster morphism category $\mathfrak{T}(A)$ of a finite-dimensional algebra $A$ and define the category via the lattice of torsion classes $\mathrm{tors } A$. Using the lattice…
This paper considers networks where relationships between nodes are represented by directed dissimilarities. The goal is to study methods that, based on the dissimilarity structure, output hierarchical clusters, i.e., a family of nested…
We construct a cluster algebra structure within the quantum cohomology ring of a quiver variety associated with an $A$-type quiver. Specifically, let $Fl:=Fl(N_1,\ldots,N_{n+1})$ denote a partial flag variety of length $n$, and…
This paper proposes an early detection method for cluster structural changes. Cluster structure refers to discrete structural characteristics, such as the number of clusters, when data are represented using finite mixture models, such as…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
We give a presentation of a finite crystallographic reflection group in terms of an arbitrary seed in the corresponding cluster algebra of finite type and interpret the presentation in terms of companion bases in the associated root system.
Clustering is a widely-used data mining tool, which aims to discover partitions of similar items in data. We introduce a new clustering paradigm, \emph{accordant clustering}, which enables the discovery of (predefined) group level insights.…
Clustering ensemble has emerged as an important research topic in the field of machine learning. Although numerous methods have been proposed to improve clustering quality, most existing approaches overlook the need for interpretability in…
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…