Missing data imputation using fuzzy-rough methods

• We have proposed 3 missing value imputation methods based on fuzzy-rough nearest neighbors: FRNNI, OWANNI and VQNNI.
• The results show they perform excellently.
• FRNNI outperforms the others.
• OWANNI is as good as FRNNI but in some cases FRNNI outperforms it.

Missing values exist in many generated datasets in science. Therefore, utilizing missing data imputation methods is a common and important practice. These methods are a kind of treatment for uncertainty and vagueness existing in datasets. On the other hand, methods based on fuzzy-rough sets provide excellent tools for dealing with uncertainty, possessing highly desirable properties such as robustness and noise tolerance. Furthermore, they can find minimal representations of data and do not need potentially erroneous user inputs. As a result, utilizing fuzzy-rough sets for imputation should be an effective approach. In this paper, we propose three missing value imputation methods based on fuzzy-rough sets and its recent extensions; namely, implicator/t-norm based fuzzy-rough sets, vaguely quantified rough sets and also ordered weighted average based rough sets. These methods are compared against 11 state-of-the-art imputation methods implemented in the KEEL data mining software on 27 benchmark datasets. The results show, via non-parametric statistical analysis, that the proposed methods exhibit excellent performance in general.