Abstract
The paper considers the solution of one of the types of classification problems in data analysis. Let us assume that the set of objects under consideration is in some way divided into two groups (we call this a regular partition). Along with this, each of the objects in view has a certain binary indicator measured – for each of the objects it has only values 0 or 1. It is required to estimate the confidence to assign the object to one of the groups of the regular partition using the knowledge of this indicator. This problem is a variant of the so called discriminant analysis problem, where the rule for assigning an object to one of the groups is called prognostic. So, the introduced numerical characteristic of the indicator of the informational content is called the prognostic power of it. The characteristic is introduced by estimating the differences between the regular partition of the set and the partition constructed by the binary indicator being studied. The magnitude of the difference is determined by calculating the cluster metric previously introduced in the work of the first author. This characteristic is compared with the correlation coefficient and the relative risk ratio commonly used in such cases.DOI 10.14258/izvasu(2017)4-15
Highlights
The paper considers the solution of one of the types of classification problems in data analysis
Можно сказать, что прогностическая сила бинарного показателя выявляет новый вид связи, не совпадающий с ранее изучавшимися
Если два рассматриваемых разбиения совпадают, результаты оценки степени связи таких бинарных показателей окажутся одинаковыми – J(X, Y ) будет равен 1, коэффициент корреляции окажется равным ±1, а коэффициент относительного риска окажется либо 0, либо примет бесконечно большое значение
Summary
The paper considers the solution of one of the types of classification problems in data analysis. В [8] доказано также, что максимально возможное значение метрики на семействе всех разбиений множества из n элементов равно n(n − 1) Поэтому без ограничения общности можно считать, что множества в разбиениях пронумерованы таким образом, что s = |A1∆B1| ≤ [n/2] ([n/2] – целая часть числа n/2).
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