Related papers: Clustering, order conditions, and languages of int…
Perfectly clustering words are one of many possible generalizations of Christoffel words. In this article, we propose a factorization of a perfectly clustering word on a $n$ letters alphabet into a product of $n-1$ palindromes with a letter…
In model-based clustering and classification, the cluster-weighted model constitutes a convenient approach when the random vector of interest constitutes a response variable Y and a set p of explanatory variables X. However, its…
The FM-index is a well-known compressed full-text index, based on the Burrows-Wheeler transform (BWT). During a pattern search, the BWT sequence is accessed at "random" locations, which is cache-unfriendly. In this paper, we are interested…
Clustering is a fundamental approach to understanding data patterns, wherein the intuitive Euclidean distance space is commonly adopted. However, this is not the case for implicit cluster distributions reflected by qualitative attribute…
A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the…
The emergence of unsupervised word embeddings, pre-trained on very large monolingual text corpora, is at the core of the ongoing neural revolution in Natural Language Processing (NLP). Initially introduced for English, such pre-trained word…
We revisit the mergeable dictionaries with shift problem, where the goal is to maintain a family of sets subject to search, split, merge, make-set, and shift operations. The search, split, and make-set operations are the usual well-known…
As a kind of basic machine learning method, clustering algorithms group data points into different categories based on their similarity or distribution. We present a clustering algorithm by finding hyper-planes to distinguish the data…
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…
Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the…
Transformers are neural networks that revolutionized natural language processing and machine learning. They process sequences of inputs, like words, using a mechanism called self-attention, which is trained via masked language modeling…
This paper reviews some results regarding symbolic dynamics, correspondence between languages of dynamical systems and combinatorics. Sturmian sequences provide a pattern for investigation of one-dimensional systems, in particular interval…
We consider the problem of learning overcomplete dictionaries in the context of sparse coding, where each sample selects a sparse subset of dictionary elements. Our main result is a strategy to approximately recover the unknown dictionary…
One of the remarkable properties of cluster algebras is that any cluster, obtained from a sequence of mutations from an initial cluster, can be written as a Laurent polynomial in the initial cluster (known as the "Laurent phenomenon").…
Text clustering is a fundamental task in natural language processing, yet traditional clustering algorithms with pre-trained embeddings often struggle in domain-specific contexts without costly fine-tuning. Large language models (LLMs)…
The Goulden-Jackson cluster method is a powerful tool for counting words by occurrences of prescribed subwords, and was adapted by Elizalde and Noy for counting permutations by occurrences of prescribed consecutive patterns. In this paper,…
The Burrows-Wheeler Transform (BWT) is an important technique both in data compression and in the design of compact indexing data structures. It has been generalized from single strings to collections of strings and some classes of labeled…
An important issue in clustering concerns the avoidance of false positives while searching for clusters. This work addressed this problem considering agglomerative methods, namely single, average, median, complete, centroid and Ward's…
We introduce the notion of unavoidable (complete) sets of word patterns, which is a refinement for that of words, and study certain numerical characteristics for unavoidable sets of patterns. In some cases we employ the graph of pattern…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…