Matrix clustering as a clustering matrices of the same dimension

Author(s):  V.M. Moskovkin, Dr., Prof., Belgorod National Research University, Belgorod, Russia,

Herinelto Casimiro, Belgorod National Research University, Belgorod, Russia,

Issue:  Volume 44, №23

Rubric:  System analysis and processing of knowledge

Annotation:  The paper presents an overview research on matrix clustering and shows lack of works on clustering for matrices of the same dimension. In order to accomplish this problem, it is proposed to convert such matrices into vectors of the same length and carry out their already known clustering methods. Such clustering of matrix objects is proposed to be compared with their clustering according to the method of natural boundaries for the scalar characteristics of matrix objects. In the simplest case, it is calculated according to the formula of the arithmetical mean of the normalized values of the elements of the original matrix. There has been given seven examples of matrix objects which can be clustered leading them to the vectors of the same dimension. In view of the fact that the clustering of any object essentially depends on the selected metrics and clustering techniques, it is therefore suggested to carry out scenario calculations in the number of a×b, where a is the number of metrics, and b is the number of clustering methods

Keywords:  Cluster Metrics, clustering matrices of the same dimension, clustering methods, clustering algorithms, matrix objects, vector objects, scalar integral characteristics

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