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A notion of stability for k-means clustering
Electronic journal of statistics. 2018. Vol. 12. No. 2. P. 4239–4263.
Le Gouic T., Paris Q.
In this paper, we define and study a new notion of stability for the k-means clustering scheme building upon the field of quantization of a probability measure. We connect this definition of stability to a geometric feature of the underlying distribution of the data, named absolute margin condition, inspired by recent works on the subject.
Publication based on the results of:
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
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Vasilev A., Kapitanov A., Roman Solovyev et al., PeerJ Computer Science 2026 Vol. 12 Article 3724
This article introduces MinMAE, a novel activation calibration method for Post-Training Quantization (PTQ) that significantly reduces accuracy loss in Convolutional Neural Networks (CNN). Motivated by the need for high-fidelity quantization without costly retraining, MinMAE directly minimizes the Mean Absolute Error (MAE) between original and dequantized activations, making it robust to outliers that degrade standard methods. ...
Added: May 3, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Rubchinskiy A., Chubarova D., Technology and Investment 2025 Vol. 16 No. 4 P. 211–240
The article considers one of the most famous examples of socio-economic systems characterized by significant uncertainty—the S&P-500 stock market, where shares of 500 largest US companies are traded. The flexible algorithm for daily trading has been developed. It is based on known fixed data about cost of shares in previous days as well as on ...
Added: December 19, 2025
F. T. Aleskerov, A. L. Myachin, V. I. Yakuba, Doklady Mathematics 2024 Vol. 110 No. 3 P. 474–479
We propose a novel method for rapid pattern analysis of high-dimensional numerical data, termed tunnel clustering. The main advantages of the method are its relatively low computational complexity, endogenous determination of cluster composition and number, and a high degree of interpretability of final results. We present descriptions of three different variations: one with fixed hyperparameters, ...
Added: March 3, 2025
Гусейнов О., Degtyarev K. Y., IRETC MTÜ PAHTEI - Proceedings of Azerbaijan High Technical Educational Institutions 2025 Т. 48 № 1 С. 360–370
The concept of Z-number was proposed by Prof. Lotfi Zadeh to describe partial reliability of information, and it is a kind of fusion of fuzziness and probabilistic uncertainty. Z-number can be presented as a pair of fuzzy numbers Z(A,B) used to describe a value of a random variable X. The first component (A) is a ...
Added: February 20, 2025
Shalileh S., Social Network Analysis and Mining 2025 Vol. 15212 P. 137–148
Community detection in attributed networks aims to recover clusters in which the within-community nodes are as interconnected and as homogeneous as possible, while the between-communities nodes are as disconnected and as heterogeneous as possible. The current research proposes a straightforward data-driven model with an integrated regularization term to recover communities. For further improvement of the ...
Added: November 30, 2024
T. A. Alvandyan, S. Shalileh, Doklady Mathematics 2024 Vol. 110 No. S1 P. S236–S250
Clustering has always been in great demand by scientific and industrial communities. However, due to the lack of ground truth, interpreting its obtained results can be debatable. The current research provides an empirical benchmark on the efficiency of three popular and one recently proposed crisp clustering methods. To this end, we extensively analyzed these (four) ...
Added: November 30, 2024
Богданова Т. К., Жукова Л. В., В кн.: XI-я международная конференция «Многомерный статистический анализ, эконометрика и моделирование реальных процессов» имени С.А. Айвазяна.: М.: ЦЭМИ РАН, 2024. С. 41–44.
The paper is devoted to the analysis and forecasting of the average salary of teachers. For 84 regions on the basis of their socio-demographic characteristics according to Rosstat data using Ward's method we obtained a two-cluster solution, which allowed us to identify quite strong differences in the level of wages, GRP per capita, level of ...
Added: October 4, 2024
Penikas H. I., Феста Ю. Ю., Известия Дальневосточного федерального университета. Экономика и управление 2024 Vol. 2 P. 75–94
Кластерный анализ широко используется в различных научных и практических областях, связанных с анализом данных. Это важный инструмент для решения задач в таких областях, как машинное обучение, обработка изображений, распознавание текста и т.д. Отсутствие наблюдений не всегда означает отсутствие информации, поэтому предполагается, что наличие пробелов в данных, наличие“пустых” кластеров, также несёт в себе информацию об объекте исследования, как и реальные наблюдения. В этом исследовании предполагается, ...
Added: August 10, 2024
Koile E., Moroz G., Journal of Linguistic Geography 2024 Vol. 12 No. 1 P. 24–31
Geolectal variation is often present in settings where one language is spoken across a vast geographic area. This can be found in phonological, morphosyntactic, and lexical features. For practical reasons, it is not always possible to conduct fieldwork in every single location of interest in order to obtain the full pattern of variation, and a ...
Added: May 6, 2024
Gromov V., Dang Q. N., , in: 10th International Conference, PReMI 2023, Kolkata, India, December 12–15, 2023, Proceedings. Pattern Recognition and Machine Intelligence. LNCS, volume 14301.: Cham: Springer, 2023. Ch. 3 P. 20–27.
Added: November 29, 2023
Backs A., Al-Falou A., Vagov A. et al., Physical Review B: Condensed Matter and Materials Physics 2023 Vol. 107 No. 17 Article 174527
In the vicinity of the type-I/type-II crossover in conventional superconductors, vortices exhibit a nonmonotonic interaction, which leads to exotic vortex matter states. We perform molecular dynamics simulations on a model superconductor in the intertype regime. In a field cooled approach, we examine the transition of a homogeneous vortex lattice (VL) into a structure consisting of ...
Added: November 2, 2023