Dealing with Missing Data: Algorithms Based on Fuzzy Set and Rough Set Theories

Missing data, commonly encountered in many fields of study, introduce inaccuracy in the analysis and evaluation. Previous methods used for handling missing data (e.g., deleting cases with incomplete information, or substituting the missing values with estimated mean scores), though simple to implement, are problematic because these methods may result in biased data models. Fortunately, recent advances in theoretical and computational statistics have led to more flexible techniques to deal with the missing data problem. In this paper, we present missing data imputation methods based on clustering, one of the most popular techniques in Knowledge Discovery in Databases (KDD). We combine clustering with soft computing, which tends to be more tolerant of imprecision and uncertainty, and apply fuzzy and rough clustering algorithms to deal with incomplete data. The experiments show that a hybridization of fuzzy set and rough set theories in missing data imputation algorithms leads to the best performance among our four algorithms, i.e., crisp K-means, fuzzy K-means, rough K-means, and rough-fuzzy K-means imputation algorithms.