Related papers: Clustering Cluster Algebras with Clusters
We provide a cluster-algebraic approach to the computation of the recently introduced generalised biadjoint scalar amplitudes related to Grassmannians ${\rm Gr}(k,n)$. A finite cluster algebra provides a natural triangulation for the…
The mixture models have become widely used in clustering, given its probabilistic framework in which its based, however, for modern databases that are characterized by their large size, these models behave disappointingly in setting out the…
We introduce a framework for $\mathbb{Z}$-gradings on cluster algebras (and their quantum analogues) that are compatible with mutation. To do this, one chooses the degrees of the (quantum) cluster variables in an initial seed subject to a…
We develop a version of cluster algebra extending the ring of Laurent polynomials by adding Grassmann variables. These algebras can be described in terms of `extended quivers' which are oriented hypergraphs. We describe mutations of such…
In \cite{JKS} we gave an (additive) categorification of Grassmannian cluster algebras, using the category $\CM(A)$ of Cohen-Macaulay modules for a certain Gorenstein order $A$. In this paper, using a cluster tilting object in the same…
This is a first step guide to the theory of cluster algebras. We especially focus on basic notions, techniques, and results concerning seeds, cluster patterns, and cluster algebras.
This paper demonstrates that the homogeneous coordinate ring of the Grassmannian $\Bbb{G}(k,n)$ is a {\it cluster algebra of geometric type} - as defined by S. Fomin and A. Zelevinsky. Grassmannians having {\it finite cluster type} are…
There are many clustering methods, such as hierarchical clustering method. Most of the approaches to the clustering of variables encountered in the literature are of hierarchical type. The great majority of hierarchical approaches to the…
Cluster algebras have recently become an important player in mathematics and physics. In this work, we investigate them through the lens of modern data science, specifically with techniques from network science and machine learning. Network…
This is an introductory survey on cluster algebras and their (additive) categorification using derived categories of Ginzburg algebras. After a gentle introduction to cluster combinatorics, we review important examples of coordinate rings…
We use a cluster ensemble to determine the number of clusters, k, in a group of data. A consensus similarity matrix is formed from the ensemble using multiple algorithms and several values for k. A random walk is induced on the graph…
We derive an efficient method to perform clustering of nodes in Gaussian graphical models directly from sample data. Nodes are clustered based on the similarity of their network neighborhoods, with edge weights defined by partial…
A general framework for dealing with both linear regression and clustering problems is described. It includes Gaussian clusterwise linear regression analysis with random covariates and cluster analysis via Gaussian mixture models with…
In this work, the possibility of clustering correlated random variables was examined, both because of their mutual similarity and because of their similarity to the principal components. The k-means algorithm and spectral algorithms were…
Cluster algebras are a recent topic of study and have been shown to be a useful tool to characterize structures in several knowledge fields. An important problem is to establish whether or not a given cluster algebra is of finite type.…
We consider clustering in group decision making where the opinions are given by pairwise comparison matrices. In particular, the k-medoids model is suggested to classify the matrices since it has a linear programming problem formulation…
The homogeneous coordinate ring of the Grassmannian $\rm{Gr}(k,n)$ has a well-known cluster structure. There is a categorification of this cluster structure via a category of modules for a ring $A_{k,n}$ due to Jensen-King-Su, building on…
The classification of Grassmannian cluster algebras resembles that of regular polygonal tilings. We conjecture that this resemblance may indicate a deeper connection between these seemingly unrelated structures.
In the cluster algebra literature, the notion of a graded cluster algebra has been implicit since the origin of the subject. In this work, we wish to bring this aspect of cluster algebra theory to the foreground and promote its study. We…
We continue the exploration of various appearances of cluster algebras in scattering amplitudes and related topics in physics. The cluster configuration spaces generalize the familiar moduli space ${\mathcal M}_{0,n}$ to finite-type cluster…