The asymptotic behaviour of threshold-based classification rules in case of three prescribed classes

Oksana Kubaychuk

doi:10.24297/jam.v12i5.318

Abstract

We consider the problem of the classification of an object from the observation after its numerical characteristic in case of three prescribed classes. We also study a problem on finding and asymptotic behaviour of threshold-based classification rules constructed from a sample from a mixture with varying concentrations.

Highlights

Object classification by its numerical characteristic is an important theoretical problem and has practical significance, for example, the definition of a person as “not healthy”, if the temperature of its body exceeds 37°C
An object is classified to belong to the first class if its characteristic does not exceed a threshold 37°C; otherwise, an object is classified to belong to the second class
In what follows we assume that: ( A ) the threshold t B defined by (1) exists and it is the unique point of the global minimum for L1(t) ( t1B is the unique global minimum point for L11(t1), t2B is the unique global minimum point for L12 (t2 ) )

Summary

INTRODUCTION

Object classification by its numerical characteristic is an important theoretical problem and has practical significance, for example, the definition of a person as “not healthy”, if the temperature of its body exceeds 37°C. To solve this problem we consider the threshold-based rule. It is often necessary to classify an object in case of more than one threshold, for example, the definition of a person as «not healthy», if the temperature of its body exceeds 37°C or lower 36°C. A boiling point and a melting point are used

THE SETTING OF THE PROBLEM

MAIN RESULTS

SUMMARY AND CONCLUSIONS