id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-4713	Bagdasaryan, Armen	On the Partition of Space by Hyperplanes	2023	6	.pdf	application/pdf	2527	194	72	Direct problem: find the minimum number of hyperplanes (1) that divide Rd into s regions according to the rule (2); Inverse problem: determine the maximum number of regions into which Rd can be divided by means of n hyperplanes (1) according to the rule (2). The question of how many such partitions are possible arises in various applications, for example, in the theory of pattern classification and machine learning [3, 5, 10] which employs partitions using some number k of parallel hyperplanes; in cluster analysis [6] dealing with the methods of partitioning of a set of objects on the basis of their characteristics or properties into clusters or groups so that the objects of a cluster are closely related according to certain criteria; data analysis and classification in which space partitioning by hyperplanes may be used together with linear regression techniques based on least absolute value estimates approach and its generalizations; in the theory of hybrid systems and control [9].	cache/ejpam-4713.pdf	txt/ejpam-4713.txt