A New Approach to Quantifying Cluster Analysis Results
УДК 519.6 + 519.25
Abstract
The paper proposes a unified approach to several variants of solving the problem of quantifying clusters of a pre-built cluster partition of a finite set. Generally speaking, each cluster gets vector labels when any of the mentioned variants are applied. For this purpose, a technique close to the analysis of latent classes is used. The first latent-object group of methods identifies each object with a vector with coordinates equal to the of the observed characteristics of this object. The second latent-indicative group of methods replaces each characteristic of all objects in a given cluster by a vector of its values. After that, the central vector being the closest to all vectors of the bunch, is selected from the bundle of vectors of a given cluster. The latent-object approach declares such a vector the vector label of the cluster. When using the latent-indicative approach, the obtained labels of different clusters have different dimensions. Thus, possible methods to reduce them to the one-dimensional numeric form are provided along with the recommendations for reducing the dimensionality of data-object labels. A numerical example is considered.
Downloads
References
Samuels J.A. One-Hot Encoding and Two-Hot Encoding: An Introduction. London: Imperial college London. 2024. 5 P. DOI: : 10.13140/RG.2.2.21459.76327
Manning c.D., Raghavan P., Schutze H. Introduction to Information Retrieval. cambridge: University Press. 2009. 581 p. DOI: : 10.1017/cBO9780511809071
Moreo A., Francisco M., Sebastiani F. Multi-label Quantification // AcM Transactions on Knowledge Discovery from Data. 2024. Vol. 18. No 1. DOI: : 10.48550/ arXiv.2211.08063
Bunse M., Moreo A., Sebastiani F., Senz M. Ordinal Quantification Through Regularization // Data Mining and Knowledge Discovery. 2024. Vol 38. No 6. P. 4076-4121. DOI: : 10.1007/978-3-031-26419-1-3
cheung Kwok-Wai, Tsui Kwok-ching, Liu Jiming. Extended Latent class Models for collaborative Recommendation // IEEE Transactions on Systems, Man, and cybernetics — Part A: Systems and Humans. 2004. Vol. 34. No 1. P. 143-148. DOI: : 10.1109/TSMcA.2003.818877
Rindskopf D. Latent Class Analysis. In: The SAGE Handbook of Quantitative Methods in Psychology. N.Y.: Sage. 2009. P. 226-244. DOI: : 10.4135/9780857020994
Дронов С.В., Шеларь А.Ю. Латентный кластерный анализ для случая двух кластеров // МАК: «Математики — Алтайскому краю» : сборник трудов Всероссийской конференции по математике. Барнаул: Изд-во Алтайского гос. университета. 2018. С. 23-26.
Дронов С.В., Еськов С.Ю. Геометрический подход в post-hoc задаче кластерного анализа // Труды семинара по геометрии и математическому моделированию. 2024. Т. 10. С. 48-53.
Dronov S.V., Sazonova A.S. Two Approaches to Cluster Variable Quantification // Model Assisted Statistics and Applications. 2015. Vol. 10. P. 155-162. DOI: : 10.3233/ MAS-140314
Gewers EL. et al. Principal Component Analysis: A Natural Approach to Data Exploration // ACM Computing Surveys. 2021. Vol. 54. No 4. P. 1-34. DOI: : 10.1145/3447755
Copyright (c) 2025 Сергей Вадимович Дронов, Юлия Алексеевна Дударева, Святослав Юрьевич Еськов
This work is licensed under a Creative Commons Attribution 4.0 International License.
Izvestiya of Altai State University is a golden publisher, as we allow self-archiving, but most importantly we are fully transparent about your rights.
Authors may present and discuss their findings ahead of publication: at biological or scientific conferences, on preprint servers, in public databases, and in blogs, wikis, tweets, and other informal communication channels.
Izvestiya of Altai State University allows authors to deposit manuscripts (currently under review or those for intended submission to Izvestiya of Altai State University) in non-commercial, pre-print servers such as ArXiv.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
