Application of rough sets in k nearest neighbours algorithm for classification of incomplete samples

Abstract

Algorithm k-nn is often used for classification, but distance measures used in this algorithm are usually designed to work with real and known data. In real application the input values are imperfect—imprecise, uncertain and even missing. In the most applications, the last issue is solved using marginalization or imputation. These methods unfortunately have many drawbacks. Choice of specific imputation has big impact on classifier answer. On the other hand, marginalization can cause that even a large part of possessed data may be ignored. Therefore, in the paper a new algorithm is proposed. It is designed for work with interval type of input data and in case of lacks in the sample analyses whole domain of possible values for corresponding attributes. Proposed system generalize k-nn algorithm and gives rough specific answer, which states if the test sample may or must belong to the certain set of classes. The important feature of the proposed system is, that it reduces the set of the possible classes and specifies the set of certain classes in the way of filling the missing values by set of possible values.