Informatics and Applications

2026, Volume 20, Issue 3, pp 67-76

INTERPRETATION OF ELLIPSOID-BASED CLUSTER DATA STRUCTURE

  • M. P. Krivenko

Abstract

Equivalent definitions of ellipsoids are considered as well as formulations of analytic geometry problems aimed at interpreting the cluster structure of data. The corresponding solution algorithms are mathematically substantiated. Two examples from the field of data analysis are discussed based on a Gaussian mixture model. Ellipsoids are used to interpret the data clusters corresponding to the elements of the mixture. The first example focuses on modeling reference values by describing the empirical distribution of multivariate patient data, including age and PSA (Prostate-Specific Antigen) biomarker measurements. The proposed mixture-based solutions demonstrate clear advantages and enable the direct application of ellipse-based visualization methods to identify specific features of the object under study. The second example considers a consolidated approach for analyzing longitudinal data when a series of multidimensional object characteristics is represented as a single vector of observed values. To demonstrate the emerging capabilities of data analysis, the problem of early diagnosis of cancer using PSA biomarkers is investigated. The advantage of the consolidating method is confirmed by a high degree of separability of sets of cluster elements of the mixture measured by the number of pairwise intersections of the corresponding ellipsoids. Analysis of the degree of intersection of sets of ellipsoids for different classes of diagnoses can further help identify the contribution of individual data clusters to classification errors.

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