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Clustering is a fundamental task in unsupervised learning. Previous research has focused on learning-augmented $k$-means in Euclidean metrics, limiting its applicability to complex data representations. In this paper, we generalize…

Machine Learning · Computer Science 2025-06-17 Chenglin Fan , Kijun Shin

Biclustering is a class of techniques that simultaneously clusters the rows and columns of a matrix to sort heterogeneous data into homogeneous blocks. Although many algorithms have been proposed to find biclusters, existing methods suffer…

Machine Learning · Statistics 2020-02-11 Michelle N. Ngo , Dustin S. Pluta , Alexander N. Ngo , Babak Shahbaba

The cluster expansion formalism used in materials science is reconstructed on an axiomatic basis with the aims of clarifying underlying concepts and improving computational procedures, and without using conventional cluster functions.…

Materials Science · Physics 2022-10-21 Paul E. Lammert , Vincent H. Crespi

In this document we achieve exact and asymptotic enumeration of words, compositions over a finite group, and/or integer compositions characterized by local restrictions and, separately, subsequence pattern avoidance. We also count…

Combinatorics · Mathematics 2019-04-19 Andrew MacFie

Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…

Applications · Statistics 2016-11-30 Matthew Pietrosanu

In an age of increasingly large data sets, investigators in many different disciplines have turned to clustering as a tool for data analysis and exploration. Existing clustering methods, however, typically depend on several nontrivial…

Quantitative Methods · Quantitative Biology 2009-11-11 Noam Slonim , Gurinder Singh Atwal , Gasper Tkacik , William Bialek

Universal Cycles, or U-cycles, as originally defined by de Bruijn, are an efficient method to exhibit a large class of combinatorial objects in a compressed fashion, and with no repeats. de Bruijn's theorem states that U-cycles for $n$…

Combinatorics · Mathematics 2013-03-15 Michelle Champlin , Anant Godbole , Beverly Tomlinson

Cluster concepts have been extremely useful in elucidating many problems in physics. Percolation theory provides a generic framework to study the behavior of the cluster distribution. In most cases the theory predicts a geometrical…

Statistical Mechanics · Physics 2016-09-15 Antonio Coniglio , Annalisa Fierro

We review clustering as an analysis tool and the underlying concepts from an introductory perspective. What is clustering and how can clusterings be realised programmatically? How can data be represented and prepared for a clustering task?…

Machine Learning · Computer Science 2022-12-05 Jan-Oliver Felix Kapp-Joswig , Bettina G. Keller

Various specifiable combinatorial structures, with d extensive parameters, can be exactly sampled both by the recursive method, with linear arithmetic complexity if a heavy preprocessing is performed, or by the Boltzmann method, with…

Data Structures and Algorithms · Computer Science 2013-07-09 Frederique Bassino , Andrea Sportiello

The aim of this article is to define some new families of the special numbers. These numbers provide some further motivation for computation of combinatorial sums involving binomial coefficients and the Euler kind numbers of negative order.…

Number Theory · Mathematics 2018-05-16 Yilmaz Simsek

Let $G_{k,n}$ be a group of permutations of $kn$ objects which permutes things independently in disjoint blocks of size $k$ and then permutes the blocks. We investigate the probabilistic and/or enumerative aspects of random elements of…

Probability · Mathematics 2025-04-29 Persi Diaconis , Nathan Tung

We consider a component of the word statistics known as clump; starting from a finite set of words, clumps are maximal overlapping sets of these occurrences. This parameter has first been studied by Schbath with the aim of counting the…

Discrete Mathematics · Computer Science 2008-04-24 Frederique Bassino , Julien Clement , Julien Fayolle , Pierre Nicodeme

We revisit Pollard's classical result on consistency for $k$-means clustering in Euclidean space, with a focus on extensions in two directions: first, to problems where the data may come from interesting geometric settings (e.g., Riemannian…

Statistics Theory · Mathematics 2025-07-01 Adam Quinn Jaffe

Recently, clustering moving object trajectories kept gaining interest from both the data mining and machine learning communities. This problem, however, was studied mainly and extensively in the setting where moving objects can move freely…

Machine Learning · Statistics 2015-11-05 Mohamed Khalil El Mahrsi , Romain Guigourès , Fabrice Rossi , Marc Boullé

We develop a new, powerful method for counting elements in a multiset. As a first application, we use this algorithm to study the number of occurrences of patterns in a permutation. For patterns of length 3 there are two Wilf classes, and…

Combinatorics · Mathematics 2024-03-05 Andrew R Conway , Anthony J Guttmann

Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, Lehmer's generalized Euler numbers are studied to give certain…

Number Theory · Mathematics 2025-01-03 Takao Komatsu , Guo-Dong Liu

We propose a new method for Unsupervised clustering in particle physics named UCluster, where information in the embedding space created by a neural network is used to categorise collision events into different clusters that share similar…

Data Analysis, Statistics and Probability · Physics 2021-06-01 Vinicius Mikuni , Florencia Canelli

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…

Methodology · Statistics 2017-10-09 Katherine Morris , Paul D. McNicholas

A relational dataset is often analyzed by optimally assigning a label to each element through clustering or ordering. While similar characterizations of a dataset would be achieved by both clustering and ordering methods, the former has…

Machine Learning · Computer Science 2023-04-10 Tatsuro Kawamoto , Masaki Ochi , Teruyoshi Kobayashi
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