Abstract: The problem of classification, clusterization or patterns recognition is one the manifestation of grouping information problem (GIP) in applied researching. It involves, beside mentioned above, the problem of recovering function, represented by empirical data (observations). Solutions of GIP largely depend of on the choice of ”math representatives” of the objects under investigation. It`s usual to use a collection of real valued characteristics – “feature vector”, in classification form of the GIP. Feature vector is in the essence a vector from Euclidean space n R . This choice is due to the highly advanced ties - and correspond techniques- in mathematical structure of such type. This technique includes, particularly, spectrum of linear operator (SVD), Moore-Penrose? inversion, orthogonal projectors operators for fundamental subspaces of the linear operator, Grouping operators and so on. Euclidean spaces m n R  of all matrixes of fixed dimension are natural spaces of “representatives” for a great many important applied fields of investigations: speech recognition, image processing and so on. In the paper SVD and Moore – Penrose technique for m n R  , proposed and developed in the earlier paper of the authors published in 2012 is used for formulating and solution of linear discrimination of two classes, represented by matrix learning samples.

Keywords: Feature vectors, information aggregating, matrix corteges, matrix corteges operators, Single Valued Decomposition for cortege linear operators, linear discrimination.

ACM Classification Keywords: G.2.m. Discrete mathematics: miscellaneous, G.1.6. Numerical analysis, I.5.1. Pattern Recognition, H.1.m. Models and Principles: miscellaneous

Link:

MATRIX “FEATURE VECTORS” IN GROUPING INFORMATION PROBLEM: LINEAR DISCRIMINATION

Volodymyr Donchenko, Fedir Skotarenko

http://www.foibg.com/ijita/vol21/ijita21-01-p04.pdf