Proceedings of the International scientific and practical conference ―Education and Scientific Progress‖ (April 24-26, 2026) / Publisher website: www.naukainfo.com. – Manchester, United Kingdom, 2026. - 218 p.

198 integrate numerical sensor readings, textual descriptions, graphical content, and categorical attributes. Such data structures are classified as multimodal [2, p. 15]. Traditional clustering approaches, particularly the k-means algorithm, have been optimized primarily for use with Euclidean numerical spaces [3, p. 178]. Applying these methods to heterogeneous data requires significant preprocessing steps and does not always guarantee effective results. In contrast, algorithms based on density- based clustering (DBSCAN), probabilistic models (GMM), or spectral graph theory demonstrate greater adaptability to working with nonlinear structures and mixed feature types [4, p. 523]. Despite the existence of a significant number of studies devoted to individual algorithms, a comprehensive comparative analysis in the context of multimodal datasets remains under-explored. The aim of this article is to systematically compare four widely used clustering methods (k-means, DBSCAN, GMM, and spectral clustering) using a unified methodology on multimodal data, as well as to formulate practical recommendations for their application. The k-means algorithm aims to minimize the sum of the squares of the distances from each point to the centroid of its corresponding cluster. The objective function is formalized as follows: J = ∑ k ∑||x - μ k || 2 , where μ k denotes the centroid of the k-th cluster, and the summation is performed over all points within each cluster [3, p. 180]. Since the algorithm is sensitive to the choice of initial parameters, in practice it is advisable to use the k- means++ modification [5, p. 2], which ensures a distribution of initial centroids that minimizes the initial error. The main limitation of the k-means algorithm is the assumption that clusters are spherical and that the variance is homogeneous, which restricts its application when dealing with complex geometric structures and datasets containing significant outliers [6, p. 65].