Individual approximate clusters: methods, properties, applications

B. Mirkin

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Individual approximate clusters: methods, properties, applications

P. 26–37.

A least-squares data approximation approach to finding individual clusters is advocated. A simple local optimization algorithm leads to suboptimal clusters satisfying some natural tightness criteria. Three versions of an iterative extraction approach are considered, leading to a portrayal of the cluster structure of the data. Of these, probably most promising is what is referred to as the incjunctive clustering approach. Applications are considered to the analysis of semantics, to integrating different knowledge aspects and consensus clustering.

Language: English

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Keywords: consensus clustering data recovery approach single cluster kernel cluster

Publication based on the results of:

Методы визуализации текстовой информации с помощью построения суффиксных деревьев, мультифасетных классификаций и иерархических онтологий: алгоритмическое и программное обеспечение (2013)

In book

Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing

Issue 8170: Lecture Notes in Artificial Intelligence. , Heidelberg: Springer, 2013.

Агломеративный консенсусный кластер-анализ с автоматическим выбором числа кластеров

Mirkin B., Parinov A., Автоматика и телемеханика 2024 № 3 С. 6–22

This paper reports of theoretical and computational results related to an original concept of consensus clustering involving what we call the projective distance between partitions. This distance is defined as the squared difference between a partition incidence matrix and its image over the orthogonal projection in the linear space spanning the other partition incidence matrix. ...

Added: February 24, 2025

Piece‐wise constant cluster modelling of dynamics of upwelling patterns

Nascimento S., Martins A., Relvas P. et al., Expert Systems: The Journal of Knowledge Engineering 2023 P. 1–16

A comprehensive approach is presented to analyse season's coastal upwelling represented by weekly sea surface temperature (SST) image grids. Our three-stage data recovery clustering method assumes that the season's upwelling can be divided into shorter periods of stability, ranges, each to be represented by a constant core and variable shell parts. Corresponding clustering algorithms parameters ...

Added: October 16, 2023

Community Detection in Feature-Rich Networks Using Data Recovery Approach

Mirkin B., Shalileh S., Journal of Classification 2022 Vol. 39 P. 432–462

The problem of community detection in a network with features at its nodes takes into account both the graph structure and node features. The goal is to find relatively dense groups of interconnected entities sharing some features in common. There have been several approaches proposed for that. We apply the so-called data recovery approach to ...

Added: August 1, 2022

A One-by-One Method for Community Detection in Attributed Networks

Shalileh S., Mirkin B., , in: Intelligent Data Engineering and Automated Learning – IDEAL 2020/ 21st International Conference, Guimaraes, Portugal, November 4–6, 2020, Proceedings, Part IIVol. 12490: Lecture Notes in Computer Science.: Cham: Springer, 2020. P. 413–422.

The problem of community detection in a network with features at its nodes takes into account both the graph structure and node features. The goal is to find relatively dense groups of interconnected entities sharing some features in common. We apply the so-called data recovery approach to the problem by combining the least-squares recovery criteria ...

Added: November 14, 2020

A Lattice-based Consensus Clustering Algorithm

Бочаров А. А., Gnatyshak D. V., Ignatov D. I. et al., , in: CLA 2016: Proceedings of the Thirteenth International Conference on Concept Lattices and Their Applications. CEUR Workshop ProceedingsVol. 1624.: M.: Higher School of Economics, National Research University, 2016. P. 45–56.

We propose a new algorithm for consensus clustering, FCA-Consensus, based on Formal Concept Analysis. As the input, the algorithm takes T partitions of a certain set of objects obtained by k-means algorithm after T runs from different initialisations. The resulting consensus partition is extracted from an antichain of the concept lattice built on a formal ...

Added: October 24, 2016

A Note on the Effectiveness of the Least Squares Consensus Clustering

Mirkin B., Shestakoff A., , in: Clusters, orders, trees: methods and applications. In Honor of Boris Mirkin's 70th BirthdayVol. 92.: Berlin: Springer, 2014.

We develop a consensus clustering framework proposed three decades ago in Russia and experimentally demonstrate that our least squares consensus clustering algorithm consistently outperforms several recent consensus clustering methods. ...

Added: January 23, 2015

Summary and semi-average similarity criteria for individual clusters

Mirkin B., , in: Models, Algorithms, and Technologies for Network AnalysisVol. 59.: NY: Springer, 2013. P. 101–126.

There exists much prejudice against the within-cluster summary similarity criterion which supposedly leads to collecting all the entities in one cluster. This is not so if the similarity matrix is pre-processed by subtraction of ``noise'', of which two ways, the uniform and modularity, are mentioned in the paper. Another criterion under consideration is the semi-average ...

Added: November 22, 2013

Least squares consensus clustering: criteria, methods, experiments

Mirkin B., Shestakoff A., , in: Advances in Information Retrieval.: L.: Springer, 2013. P. 764–768.

We develop a consensus clustering framework developed three decades ago in Russia and experimentally demonstrate that our least squares consensus clustering algorithm consistently outperforms several recent consensus clustering methods. ...

Added: April 15, 2013