MULTIVARIATE ANALYSIS AND CLASSIFICATION OF GEOMETRIC OBJECTS BASED ON A SET OF PARAMETERS

This study examines the feasibility of automated classification of geometric objects using multivariate statistical analysis of their parameters, without relying on complex nonlinear machine learning techniques. Objects are described by a set of interrelated geometric and physical characteristics, including linear dimensions, areas, volumes, mass, and density, which leads to high feature correlation and complicates their interpretation.
To address this task, classical methods of multivariate data analysis are applied: correlation and regression analysis, principal component analysis (PCA), clustering, and linear discriminant analysis (LDA). The study is conducted on a synthetic dataset formed based on realistic parameter ranges derived from actual geometric relationships.
It is demonstrated that preliminary dimensionality reduction using PCA can eliminate multicollinearity among features and produce a compact, interpretable representation of the data. Clustering in the principal component space reveals a stable group structure of objects, while the application of linear discriminant analysis ensures high classification quality. The results confirm that interpretable statistical methods remain an effective tool for analyzing and classifying geometric objects and can be used in tasks of preliminary data analysis, support of expert systems, and development of intelligent ICT-based systems.

1. Aivazyan, S. A., & Mkhitaryan, V. S. (2001). Prikladnaya statistika v zadachakh i uprazhneniyakh: Uchebnik dlya VUZov. Moscow: UNITY DANA.

2. Draper, N. R., & Smith, G. (2017). Prikladnoy regressiynyy analiz (3rd ed.). Moscow: Dialektika.

3. Fedorov, V. V. (2018). Metody mnogomernogo statisticheskogo analiza. St. Petersburg: Piter.

4. Guo, L., & Qin, Y. (2024). An exploration of the application of principal component analysis in big data processing. Applied Mathematics and Nonlinear Sciences, 9(1), 1-24. https://doi.org/10.2478/amns-2024-0664

5. Jolliffe, I. T. (2016). Principal Component Analysis (2nd ed.). New York, NY: Springer. https://doi.org/10.1007/9781493944708

6. Nikolenko, S. I. (2025). Mashinnoye obucheniye: osnovy. Saint Petersburg; Moscow; Minsk: Piter.

7. Gyamerah, S., Soori, G. T., Korda, D. R., Tawiah, J. K., Akolgo, E. A., & Dapaah, E. O. (2023). Comparative analysis of feature extraction for high dimensional data reduction using machine learning techniques. American Journal of Electrical and Computer Engineering, 7(2), 27-39. https://doi.org/10.11648/i.aiece.20230702.12

8. Mathivanan, N. M. N., Md. Ghani, N. A., & Janor, R. M. (2023). A comparative study on dimensionality reduction between principal component analysis and K means clustering. Indonesian Journal of Electrical Engineering and Computer Science, 16(2), 752-758. https://doi.org/10.11591/iieecs.v16.i2.pp752-758

9. Ma, Z., Lopez Oriona, A., Ombao, H., & Sun, Y. (2026). ROBCPCA: robust multivariate time series clustering method based on common principal component analysis. Journal of Classification, 43(1). https://doi.org/10.1007/s00357-026-09536-7

10. Oshternian, S. R., Loipfinger, S., Bhattacharya, A., & Fehrmann, R. S. N. (2024). Exploring combinations of dimensionality reduction, transfer learning, and regularization methods for predicting binary phenotypes with transcriptomic data. BMC Bioinformatics, 25, 167. https://doi.org/10.1186/s12859-024-05795-6

11. Fisher, R. A. (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics, 7, 179-188.

12. Sinaga, B. (2024). Multivariate data analysis for customer segmentation using principal component analysis and K means clustering. Jurnal Info Sains: Informatika dan Sains, 3, 1-10.

13. Cheng, G., Lin, R., & Peng, L. (2024). High dimensional multivariate analysis of variance via geometric median and bootstrapping. Biometrics, 80(3), ujae088. https://doi.org/10.1093/biomtc/uiae088

14. Shen, Z. (2023). Comparison and evaluation of classical dimensionality reduction methods. Highlights in Science, Engineering and Technology, 70, 411-418. https://doi.org/10.54097/hset.v70i.13890

15. Qu, L., & Pei, Y. (2024). A comprehensive review on discriminant analysis for addressing challenges of class level limitations, small sample size, and robustness. Processes, 12(7), 1382. https://doi.org/10.3390/pr12071382

16. Munoz Pichardo, J. M., Pino Mej^as, R., Cubiles de la Vega, M. D., & Enguix Gonzalez, A. (2024). Dimensionality reduction through clustering of variables and canonical correlation. Journal of the Korean Statistical Society, 54(1), 63-90. https://doi.org/10.1007/s42952-024-00290-3