Comparative Analysis of Visualizing Methods for Multidimensional Data

The article deals with data of large dimensions, the problem of their visualization and analysis. As visualizers, methods from different classes of dimensionality reduction algorithms were chosen: PCA, t-SNE and the modified Thorgerson principal projection method based on constructing a subspace of initial data projection by changing the method of factorization of the scalar product matrix using the cumulative curve analysis method. A technique for comparing the methods under consideration is proposed, based on assessing the information content of representing multidimensional data in a two-dimensional space using the Hartigan criterion, as well as the Shepard diagram with obtaining a correlation coefficient from it. To form a test multidimensional base, it is convenient to use hyperspherical coordinates, while the samples themselves are a collection of two types of uniformly distributed observations in a multidimensional ellipsoid: regular observations and outliers, which are balls whose centers are at some distance from each other.