Application of tensors in multivariate component analysis of categorized features

When modeling social processes and phenomena, it is often necessary to process data related to categorized features, identify cause-and-effect relationships between such data, and determine the most significant indicators. A study of existing approaches to analyzing dependencies between categorized variables revealed several problems when applying these methods to multidimensional categorized data (tensors). Therefore, this article proposes an approach to studying dependencies between such variables using multidimensional component analysis. This approach involves applying tensor unfolding matrices obtained for each of its axes (categorized features). The method allows for the construction of integral characteristics (components) based on the elements of the original tensor, the formation of component loading matrices, and the calculation of the tensor core, which has fewer gradations of categorized features (lower number of dimensions in the tensor axes) than the original tensor. The article proposes a method for ranking the gradations of categorized variables by the degree of cumulative influence of component loadings, based on the calculation of vector norms. The described approach to studying dependencies between multidimensional categorized variables is demonstrated using a three-dimensional tensor with the shape (4;10;10) and categorized features: nosology group, field of activity, and group of professionally significant qualities. The algorithm for analyzing multidimensional categorized data using multidimensional component analysis, discussed in this article, is intended to be incorporated as an analytical tool into the regional information and analytical portal "PERSPEKTIVA-PRO." This tool can be used to develop a digital support trajectory for people with disabilities and special needs, taking into account their personal and variable characteristics.

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