THE SIGNIFICANCE AND APPLICATION OF COMPACTNESS MEASURES IN MACHINE LEARNING
Main Article Content
Abstract
This article explores the concept of compactness as one of the factors that contribute to the generalization ability of models in machine learning. Compactness is a characteristic that reflects the closeness, density, and organization of data, significantly impacting a model's performance on test data. The article provides both an intuitive and formal description of compactness measures, explains how they can be evaluated, and in which scenarios their use is justified. It also discusses the relationship between generalization ability and compactness using practical examples. The results of the study open new possibilities for improving model quality through compactness assessment.
Downloads
Article Details
Section

This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors retain the copyright of their manuscripts, and all Open Access articles are disseminated under the terms of the Creative Commons Attribution License 4.0 (CC-BY), which licenses unrestricted use, distribution, and reproduction in any medium, provided that the original work is appropriately cited. The use of general descriptive names, trade names, trademarks, and so forth in this publication, even if not specifically identified, does not imply that these names are not protected by the relevant laws and regulations.
How to Cite
References
1. Zagoruiko N.G. Hypotheses of compactness and λ-compactness in data analysis methods // Sib. Zh. Industr. Mathematics, Vol. 1. – No. 1. – 1998. – P. 1 14–126.
2. Zhuravlev Yu.I. On algebraic methods in recognition and classification problems // Recognition, classification, forecasting. Mathematical methods and their application. – 1989. − P. 9-16.
3. Jambeu M. Hierarchical cluster - analysis and correspondence // Translated from French. - M.: Finance and Statistics, - 1988. - 342 p.
4. https://www.kaggle.com/datasets
5. Duda R. O., Hart P. E., Stork D. G. Pattern Classification. 2nd ed. - Wiley-Interscience, 2001. - 654 p
6. Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Springer.
7. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The Elements of Statistical Learning: Data Mining, Inference, and Prediction. Springer.
8. Tan, P.-N., Steinbach, M., & Kumar, V. (2019). Introduction to Data Mining. Pearson.
9. Xu, R., & Wunsch, D. (2005). Survey of clustering algorithms. IEEE Transactions on Neural Networks, 16(3), 645–678.
10.Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20, 53–65.
11.Biehl, M., Hammer, B., & Villmann, T. (2016). Prototype-based models in machine learning. Wiley Interdisciplinary Reviews: Cognitive Science, 7(2), 92–111.
12.Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep Learning. MIT Press.
13. Schölkopf, B., & Smola, A. J. (2002). Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press.
14. Pedregosa, F., et al. (2011). Scikit-learn: Machine Learning in Python. Journal of Machine Learning Research, 12, 2825–2830.