USING THE MAIN COMPONENTS METHOD AND CANONICAL CORRELATIONS FOR BREEDING NEW VARIETIES OF CULTURAL PLANTS

Abstract

To develop new varieties of cultivated plants, the article proposes the use of the method of principal components at the first stage of the calculation and the method of canonical correlations at the second. Analysis of the methods of genetics and breeding on the issue of breeding new varieties of cultivated plants led to the following assumptions: a change in the basic property of any plant species is associated with the possible magnitude of the scatter of individual particular properties, and the greatest changes in the desired properties can be obtained as a result of crossing individuals that have the greatest variability of these properties. Based on this, in purposeful selection, first of all, only those features should be taken into account that show the greatest scatter in the transition from one object to another, which is possible when using the method of principal components.

Principal component method is one of the main ways to reduce the dimension of data, losing the least amount of information. The problem is reduced to the classical problem of finding the eigenvalues and eigenvectors of a symmetric matrix. Among the existing approaches to solving the problem by the principal components (factors) method, this study used an approach where, to maximize a function associated with a number of additional conditions, we use the method of Lagrange multipliers.

The canonical correlations method at the second stage makes it possible to find the maximum correlations between two groups of random variables, being, as it were, a generalization of the correlation analysis in the case of two sets of random variables. This dependence is determined by using new arguments - canonical values (canonical variables), calculated as linear combinations of the original features for each of the groups. Canonical values should be maximally correlated with each other, and their number is determined by the number of variables in a smaller set (if the number of variables in them is not the same). That is, at the second stage, the residence of the canonical correlations is determined for the found pairs of principal components and secondary vectors, the elements of which are the found principal components. Thus, an algorithm for directed search for pairs for crossing cultivated plants has been developed, which consists of two stages of calculation by the methods of principal components and canonical correlations.