Related papers: Clustering and Arnoux-Rauzy words
A balanced word is one in which any two factors of the same length contain the same number of each letter of the alphabet up to one. Finite binary balanced words are called Sturmian words. A Sturmian word is bispecial if it can be extended…
The avalanche quantity of the information developed by mankind has led to concept of automation of knowledge extraction - Data Mining ([1]). This direction is connected with a wide spectrum of problems - from recognition of the fuzzy set to…
$k$-means and $k$-median clustering are powerful unsupervised machine learning techniques. However, due to complicated dependences on all the features, it is challenging to interpret the resulting cluster assignments. Moshkovitz, Dasgupta,…
The cognitive constraints that humans exhibit in their social interactions have been extensively studied by anthropologists, who have highlighted their regularities across different types of social networks. We postulate that similar…
The (bitwise) complement $\overline{x}$ of a binary word $x$ is obtained by changing each $0$ in $x$ to $1$ and vice versa. An $\textit{antisquare}$ is a nonempty word of the form $x\, \overline{x}$. In this paper, we study infinite binary…
A word $u=u_1\dots u_n$ is a scattered factor of a word $w$ if $u$ can be obtained from $w$ by deleting some of its letters: there exist the (potentially empty) words $v_0,v_1,..,v_n$ such that $w = v_0u_1v_1...u_nv_n$. The set of all…
Clustering is an unsupervised machine learning methodology where unlabeled elements/objects are grouped together aiming to the construction of well-established clusters that their elements are classified according to their similarity. The…
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…
We study the problem of explainability-first clustering where explainability becomes a first-class citizen for clustering. Previous clustering approaches use decision trees for explanation, but only after the clustering is completed. In…
We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We…
This paper aims to use term clustering to build a modular ontology according to core ontology from domain-specific text. The acquisition of semantic knowledge focuses on noun phrase appearing with the same syntactic roles in relation to a…
In this paper we introduce and study a new property of infinite words: An infinite word $x\in A^\mathbb{N}$, with values in a finite set $A$, is said to be $k$-self-shuffling $(k\geq 2)$ if $x$ admits factorizations: $x=\prod_{i=0}^\infty…
Consider the set of those binary words with no non-empty factors of the form $xxx^R$. Du, Mousavi, Schaeffer, and Shallit asked whether this set of words grows polynomially or exponentially with length. In this paper, we demonstrate the…
We consider the robust algorithms for the $k$-means clustering problem where a quantizer is constructed based on $N$ independent observations. Our main results are median of means based non-asymptotic excess distortion bounds that hold…
This paper (cmp-lg/yymmnnn) has been accepted for publication in the student session of EACL-95. It outlines ongoing work using statistical and unsupervised neural network methods for clustering words in untagged corpora. Such approaches…
Enumerating the number of times one word occurs in another is a much-studied combinatorial subject. By utilizing a method that we call ``lexicographic extreme referencing'', we provide a formula for computing occurrences of one binary word…
We consider the number of occurrences of subwords (non-consecutive sub-sequences) in a given word. We first define the notion of subword entropy of a given word that measures the maximal number of occurrences among all possible subwords. We…
This paper concerns a specific class of strict standard episturmian words whose directive words resemble those of characteristic Sturmian words. In particular, we explicitly determine all integer powers occurring in such infinite words,…
Many of the kinds of language model used in speech understanding suffer from imperfect modeling of intra-sentential contextual influences. I argue that this problem can be addressed by clustering the sentences in a training corpus…
We analyze here a particular kind of linguistic network where vertices representwords and edges stand for syntactic relationships between words. The statisticalproperties of these networks have been recently studied and various features…