Related papers: Cluster algebras associated with open Richardson v…

A novel nonparametric clustering algorithm is proposed using the interpoint distances between the members of the data to reveal the inherent clustering structure existing in the given set of data, where we apply the classical nonparametric…

We propose a novel graph clustering method guided by additional information on the underlying structure of the clusters (or communities). The problem is formulated as the matching of a graph to a template with smaller dimension, hence…

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…

The description of complex configuration is a difficult issue. We present a powerful technique for cluster identification and characterization. The scheme is designed to treat with and analyze the experimental and/or simulation data from…

Clustering is a crucial task in various domains of knowledge, including medicine, epidemiology, genomics, environmental science, economics, and visual sciences, among others. Methodologies for inferring the number of clusters have often…

Initialisation of the EM algorithm in model-based clustering is often crucial. Various starting points in the parameter space often lead to different local maxima of the likelihood function and, so to different clustering partitions. Among…

In spectral clustering, one defines a similarity matrix for a collection of data points, transforms the matrix to get the Laplacian matrix, finds the eigenvectors of the Laplacian matrix, and obtains a partition of the data using the…

The method of Hol\'y, Sokol and \v{C}ern\'y (Applied Soft Computing, 2017, Vol. 60, p. 752-762) clusters objects based on their incidence in a large number of given sets. The idea is to minimize the occurrence of multiple objects from the…

We present a new geometrical method aimed at determining the members of open clusters. The methodology estimates, in an N-dimensional space, the membership probabilities by means of the distances between every star and the cluster central…

This is a preliminary draft of Chapters 4-5 of our forthcoming textbook "Introduction to Cluster Algebras." Chapters 1-3 have been posted as arXiv:1608.05735. This installment contains: Chapter 4. New patterns from old Chapter 5. Finite…

We give an explicit combinatorial description of cluster structures in Schubert varieties of the Grassmannian in terms of (target labelings of) Postnikov's plabic graphs. This description is a natural generalization of the description given…

This paper proposes a new paradigm and computational framework for identification of correspondences between sub-structures of distinct composite systems. For this, we define and investigate a variant of traditional data clustering, termed…

We give an introduction to the theory of cluster categories and cluster tilted algebras. We include some background on the theory of cluster algebras, and discuss the interplay with cluster categories and cluster tilted algebras.

We obtain the clustering coefficient, the degree-dependent local clustering, and the mean clustering of networks with arbitrary correlations between the degrees of the nearest-neighbor vertices. The resulting formulas allow one to determine…

Erikkson showed that singular value decomposition(SVD) of flattenings determined a partition of a phylogenetic tree to be a split. In this paper, based on his work, we develop new statistically consistent algorithms fit for grid computing…

We investigate the question of studying spectral clustering in a Hilbert space where the set of points to cluster are drawn i.i.d. according to an unknown probability distribution whose support is a union of compact connected components. We…

In this work, we propose a new clustering algorithm to group nodes in networks based on second-order simplices (aka filled triangles) to leverage higher-order network interactions. We define a simplicial conductance function, which on…

We introduce a new method for performing clustering with the aim of fitting clusters with different scatters and weights. It is designed by allowing to handle a proportion $\alpha$ of contaminating data to guarantee the robustness of the…

Clifford indices of vector bundles on algebraic curves were introduced in a previous paper of the authors. In this paper we study bundles of rank 2 which compute these Clifford indices. This is of particular interest in the light of…

In order to apply the recent successes of machine learning and automated plant phenotyping on a large scale using agricultural robotics, efficient and general algorithms must be designed to intelligently split crop fields into small, yet…