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We revisit the question of classification of balanced circular words and focus on the case of a ternary alphabet. We propose a $3$-dimensional generalisation of the discrete approximation representation of Christoffel words. By considering…

Combinatorics · Mathematics 2021-05-03 D. V. Bulgakova , N. Buzhinsky , Y. O. Goncharov

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…

Machine Learning · Computer Science 2016-09-20 Vincent Roulet , Fajwel Fogel , Alexandre d'Aspremont , Francis Bach

This paper studies balancedness for infinite words and subshifts, both for letters and factors. Balancedness is a measure of disorder that amounts to strong convergence properties for frequencies. It measures the difference between the…

Discrete Mathematics · Computer Science 2018-10-18 Valérie Berthé , Paulina Cecchi Bernales

In this paper, we characterize by lexicographic order all finite Sturmian and episturmian words, i.e., all (finite) factors of such infinite words. Consequently, we obtain a characterization of infinite episturmian words in a "wide sense"…

Combinatorics · Mathematics 2010-03-16 Amy Glen , Jacques Justin , Giuseppe Pirillo

Motivated by extracting and summarizing relevant information in short sentence settings, such as satisfaction questionnaires, hotel reviews, and X/Twitter, we study the problem of clustering words in a hierarchical fashion. In particular,…

Machine Learning · Computer Science 2023-12-08 Eliabelle Mauduit , Andrea Simonetto

Two words are $k$-binomially equivalent if each subword of length at most $k$ occurs the same number of times in both words. The $k$-binomial complexity of an infinite word is a counting function that maps $n$ to the number of $k$-binomial…

Combinatorics · Mathematics 2022-12-07 Michel Rigo , Manon Stipulanti , Markus A. Whiteland

A vocabulary is a list of words designating subsets from a grand set X. We model a vocabulary as a partition of X and study the aggregation of individual vocabularies into a collective one. We characterize aggregation rules when X is…

Theoretical Economics · Economics 2026-03-16 Marco LiCalzi , M. Alperen Yasar

Brown clustering is a hard, hierarchical, bottom-up clustering of words in a vocabulary. Words are assigned to clusters based on their usage pattern in a given corpus. The resulting clusters and hierarchical structure can be used in…

Computation and Language · Computer Science 2016-08-05 Manuel R. Ciosici

We obtain a multiplication formula for cluster characters on (stably) 2-Calabi-Yau (Frobenius or) triangulated categories. This formula generalizes those known for arbitrary pairs of objects and for Auslander-Reiten triangles. As an…

Representation Theory · Mathematics 2023-01-11 Bernhard Keller , Pierre-Guy Plamondon , Fan Qin

We introduce two different approaches for clustering semantically similar words. We accommodate ambiguity by allowing a word to belong to several clusters. Both methods use a graph-theoretic representation of words and their paradigmatic…

Other Condensed Matter · Physics 2009-09-29 Beate Dorow , Dominic Widdows , Katarina Ling , Jean-Pierre Eckmann , Danilo Sergi , Elisha Moses

Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…

Formal Languages and Automata Theory · Computer Science 2026-05-28 Richard Mandel , Corto Mascle , Georg Zetzsche

Clustering is a popular form of unsupervised learning for geometric data. Unfortunately, many clustering algorithms lead to cluster assignments that are hard to explain, partially because they depend on all the features of the data in a…

Machine Learning · Computer Science 2020-09-23 Sanjoy Dasgupta , Nave Frost , Michal Moshkovitz , Cyrus Rashtchian

We present a clustering-based language model using word embeddings for text readability prediction. Presumably, an Euclidean semantic space hypothesis holds true for word embeddings whose training is done by observing word co-occurrences.…

Computation and Language · Computer Science 2017-09-07 Miriam Cha , Youngjune Gwon , H. T. Kung

We compare the performance of different clustering algorithms applied to the task of unsupervised text categorization. We consider agglomerative clustering algorithms, principal direction divisive partitioning and (for the first time)…

Disordered Systems and Neural Networks · Physics 2007-05-23 D. Volk , M. G. Stepanov

We present a global optimization algorithm for clustering data given the ratio of likelihoods that each pair of data points is in the same cluster or in different clusters. To define a clustering solution in terms of pairwise relationships,…

Machine Learning · Computer Science 2015-06-11 Vijay Kumar , Dan Levy

Clustering a lexicon of words is a well-studied problem in natural language processing (NLP). Word clusters are used to deal with sparse data in statistical language processing, as well as features for solving various NLP tasks (text…

Computation and Language · Computer Science 2018-08-17 Effi Levi , Saggy Herman , Ari Rappoport

We address the problem of automatically constructing a thesaurus (hierarchically clustering words) based on corpus data. We view the problem of clustering words as that of estimating a joint distribution over the Cartesian product of a…

cmp-lg · Computer Science 2008-02-03 Hang Li , Naoki Abe

Considering that words with different characteristic in the text have different importance for classification, grouping them together separately can strengthen the semantic expression of each part. Thus we propose a new text representation…

Computation and Language · Computer Science 2019-06-19 Xiaoye Tan , Rui Yan , Chongyang Tao , Mingrui Wu

Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…

Formal Languages and Automata Theory · Computer Science 2023-11-30 Jeffrey Shallit , Xinhao Xu

We introduce the notion of $\alpha$-numbers and formal intercept of sturmian words, and derive from this study general factorisations formula for sturmian words. Sturmian words are defined as infinite words with lowest unbound complexity,…

Combinatorics · Mathematics 2025-04-21 Caius Wojcik