The original K-nearest neighbour ( KNN) algorithm was meant to classify homogeneous complete data, that is, data with only numerical features whose values exist completely. Thus, it faces problems when used with heterogeneous incomplete (HI) data, which has also categorical features and is plagued with missing values. Many solutions have been proposed over the years but most have pitfalls. For example, some solve heterogeneity by converting categorical features into numerical ones, inflicting structural damage. Others solve incompleteness by imputation or elimination, causing semantic disturbance. Almost all use the same K for all query objects, leading to misclassification. In the present work, we introduce KNNHI, a KNN-based algorithm for HI data classification that avoids all these pitfalls. Leveraging rough set theory, KNNHI preserves both categorical and numerical features, leaves missing values untouched and uses a different K for each query. The end result is an accurate classifier, as demonstrated by extensive experimentation on nine datasets mostly from the University of California Irvine repository, using a 10-fold cross-validation technique. We show that KNNHI outperforms six recently published KNN-based algorithms, in terms of precision, recall, accuracy and F-Score. In addition to its function as a mighty classifier, KNNHI can also serve as a K calculator, helping KNN-based algorithms that use a single K value for all queries that find the best such value. Sure enough, we show how four such algorithms improve their performance using the K obtained by KNNHI. Finally, KNNHI exhibits impressive resilience to the degree of incompleteness, degree of heterogeneity and the metric used to measure distance.
Fuzzy Set-Valued Information Systems and the Algorithm of Filling Missing Values for Incomplete Information Systems