Methods and characteristics of locality-preserving transformations in the problems of computational intelligence

Abstract

EN: The problem of the development of mathematical support for data dimensionality reduction is solved. Its results can be used to automate the process of diagnostic and recognizing model construction by precedents. The set of rapid transformations from the original multi-dimensional space to the one-dimensional axis was firstly proposed. They provide a solution of the feature extraction and feature selection problems. The complex of indicators characterizing the properties of transformations was firstly proposed. On the basis of the proposed indicators the set of criteria was defined. It facilitate comparison and selection of the best transformations and results of their work in diagnosis and recognition problems solving on the basis of computational intelligence methods. The software realizing proposed transformations and indicators characterizing their properties was developed. The experimental study of proposed transformations and indicators was conducted, which results allow to recommend the proposed transformations for use in practice. UK: Вирішено проблему розроблення математичного забезпечення для скорочення розмірності даних. Вперше запропоновано набір швидких перетворень з багатовимірного простору на одновимірну вісь, що дозволяють вирішувати завдання витягу та відбору ознак. Вперше запропоновано комплекс показників і критеріїв якості перетворень на узагальнену вісь. Запропоновані перетворення і показники програмно реалізовано і досліджено при вирішенні практичних завдань.