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Versions of least-squares k-means algorithm for interval data
Recently, k-means clustering has been extended to the so-called interval data. In contrast to conventional data case, the interval data feature values are intervals rather than single reals. This paper further explores the least-squares criterion for k-means clustering to tackle the issue of initialization, that is, finding a proper set of initial cluster centers at interval data clustering. Specifically, we extend, for the interval data, a Pythagorean decomposition of the data scatter in the sum of two items, one being a genuine k-means least-squares criterion, the other, a complementary criterion, requiring the clusters to be numerous and anomalous. Therefore we propose a method for one-byone obtaining anomalous clusters. After a run of the method, we start k-means iterations from the centers of the most numerous of the found anomalous clusters. We test and validate our proposed BIKM algorithm at versions of two newly introduced interval datasets.
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English
Publication based on the results of:
Teregulov T., Loubenets E. R., / Series Quantum Physics "arXiv". 2026. No. 2609.31472.
We develop a new three-party quantum secret-sharing (QSS) protocol based on a three-qubit W state. This protocol encodes the secret-sequence bits using X gates and employs randomly selected Hadamard operations and measurement bases to generate information and security-test rounds. We evaluate the efficiency of the proposed protocol and analyze its security against an internal adversary ...
Added: September 28, 2026
Levashev V., / Series arXiv "math". 2026. No. 2609.06010.
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Added: September 24, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
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Added: September 24, 2026
Medvedev V., / Series arXiv "math". 2026.
We study complete static manifolds with boundary admitting a nowhere-vanishing static potential. Our main result shows that, under a natural lower bound relating the scalar curvature and the boundary mean curvature, a simple static manifold with boundary must in fact have positive scalar curvature, negative boundary mean curvature, and be compact; we also obtain explicit ...
Added: September 19, 2026
Poddiakov A., / Series Social Science Research Network "Social Science Research Network". 2026. No. 7437658.
Clarity of knowledge and reasoning is necessary in many cases. Yet vagueness in scientific thinking related to surprise, curiosity, "ability to engage with not-knowing" (de Freitas) and abductive reasoning is also a crucially important source of scientific creativity which supplements combinatorial logic when dealing with the already known. Starting from studies by C. S. Peirce ...
Added: September 15, 2026
Glutsyuk A., / Series arXiv "math". 2026.
B.Josephson (Nobel Prize, 1973) predicted a tunnelling effect for a system of two superconductors separated by a narrow dielectric (such a system is called Josephson junction): existence of a supercurrent through it and equations governing it. The overdamped Josephson junction is modeled by the family of differential equations on the 2-torus, dθdτ=1ω(cosθ+B+Acosτ), which is known as ...
Added: September 8, 2026
Pochinka O., Shmukler V., / Series math.RT "arXiv:1808.06395 [math.RT]". 2026.
Anosov flows have a long and rich history, firstly motivated by the
study of geodesic flows in negative curvature surface by Anosov and Sinai.
Not every closed manifold admits an Anosov flow for well-known reasons:
the fundamental group of a 3-manifold M admitting an Anosov flow must
have exponential growth, and M must be universally covered by R3. Nevertheless,
there ...
Added: August 31, 2026
Shabanov N., Kuricheva O., Kurbatova J. et al., / Series Working Papers SSRN "Department of Economics Ca’ Foscari University of Venice". 2026.
The carbon balance of an ecosystem is the difference between Gross Primary Productivity (GPP) and Ecosystem Respiration (Reco) as expressed by Net Ecosystem Exchange (NEE). While remote sensing retrievals of GPP have reached maturity, Reco estimation remains underexplored and ultimately cast bias on NEE. Here we present an end-to-end multi-scale analysis of the mechanism of ...
Added: August 21, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Loubenets E. R., / Series arxiv.org "quant-ph". 2026. No. 2607.18050.
In many quantum applications it is important to know whether or not a Bell nonlocal two-qudit state exhibits its nonlocality under correlation scenarios with some given numbers S1,S2≥1 of generalized quantum measurements at two sites. In the present article, we find analytically a new general locality condition sufficient for a nonseparable Werner state with a ...
Added: July 21, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Let K be a field of characteristic zero. We prove that its motivic cohomology in degree m−1 and weight m is rationally isomorphic to the cohomology of the polylogarithmic complex. This gives a partial extension of A. Suslin theorem describing the indecomposable K3 of a field. ...
Added: July 16, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Konakov V., Kucher D., Mammen E., / Series arXiv "math". 2026. No. 2606.11142v1.
In this paper, we construct strong approximations for discrete-time Markov chains weakly converging to continuous diffusion processes, as well as for their perturbed counterparts. Under the assumption of bounded coefficients, we construct closely coupled versions of these processes on a shared probability space. In particular, for both non-degenerate and degenerate cases, we maximize the probability ...
Added: June 11, 2026
Медведева Е. Г., Khayrov E., Поляков Н. А. et al., Системы и средства информатики 2020 Т. 30 № 4 С. 25–37
The paper provides an overview of tasks that arise in wireless networks with mobile base stations located on unmanned aerial vehicles (UAV). The authors choose two methods of adaptive navigation based on user clustering for a comparative analysis of effectiveness of network deployment - the k- means method and the particle swarm method. The solution ...
Added: May 19, 2023
Klochkov Y., Kroshnin A., Zhivotovskiy N., Annals of Statistics 2021 Vol. 49 No. 4 P. 2206–2230
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 nonasymptotic excess distortion bounds that hold under the two bounded moments assumption in a general separable Hilbert space. In particular, our results extend the renowned asymptotic result of (Ann. Statist. 9 (1981) ...
Added: October 6, 2021
Абдурахманова Э. М., Социология: методология, методы, математическое моделирование 2020 № 50-51 С. 37–62
In the social sciences, researchers are often faced with the task of classifying objects into meaningful groups, including in education. However, homogeneous groups can be extracted basing on various conceptual foundations leading to the identification of different group structures which might influence the interpretation of the results. The purpose of this study is to compare the ...
Added: July 6, 2021
Egorova L., Torop V., , in: New Perspectives in Science Education 9th Edition - International Conference (Florence, Italy, 19-20 March 2020).: Filodiritto Publisher, 2020. P. 112–116.
Recently appeared online courses rapidly gained their popularity due to the great opportunities. Absolutely different people can study any discipline for various purposes. Online courses can be useful both to children in preparing for lessons, and to adults in advanced training. Gradually, courses are becoming not only part of the additional curriculum at the university, ...
Added: September 3, 2020
de Amorim R. C., Makarenkov V., Mirkin B., Journal of Classification 2020 Vol. 37 No. 1 P. 143–157
Real-world data sets often contain mislabelled entities. This can be particularly problematic if the data set is being used by a supervised classification algorithm at its learning phase. In this case, the accuracy of this classification algorithm, when applied to unlabelled data, is likely to suffer considerably. In this paper, we introduce a clustering-based method ...
Added: August 6, 2020
Gorchakov A., В кн.: 2nd International Scientific Conference "Convergent Cognitive Information Technologies", Convergent 2017Т. Volume 2064.: CEUR-WS, 2017. С. 202–208.
In this paper, an example is given of using the OpenMP Application Programming Interface to accelerate the calculation of the matrix of the first derivatives of a vector function (the Jacobi matrix) in the solution of least-squares problems by the Levenberg-Marquardt method. The calculation of the Jacobi matrix is produced using the methodology of fast ...
Added: November 18, 2018
Gorchakov A., CEUR Workshop Proceedings, 2017.
In this paper, an example is given of using the OpenMP Application Programming Interface to accelerate the calculation of the matrix of the first derivatives of a vector function (the Jacobi matrix) in the solution of least-squares problems by the Levenberg-Marquardt method. The calculation of the Jacobi matrix is produced using the methodology of fast ...
Added: October 30, 2018
Zhukova L., Polyakov K., Polyakova M. V., Современная наука и инновации 2013 № 3 С. 75–81
Authors suggests some advices in the field of client base segmentation construction for retail profit-making organizations concerning their possible reaction on marketing campaigns. Advices are based on the results of research in one of the largest Russian retail network in the segment of mobile devices. ...
Added: February 2, 2015