Polynomial-fuzzy decision tree structures for classifying medical data

Decision tree induction has been studied extensively in machine learning as a solution for classification problems. The way the linear decision trees partition the search space is found to be comprehensible and hence appealing to data modelers. Comprehensibility is an important aspect of models used in medical data mining as it determines model credibility and even acceptability. In the practical sense though, inordinately long decision trees compounded by replication problems detracts from comprehensibility. This demerit can be partially attributed to their rigid structure that is unable to handle complex non-linear or/and continuous data. To address this issue we introduce a novel hybrid multivariate decision tree composed of polynomial, fuzzy and decision tree structures. The polynomial nature of these multivariate trees enable them to perform well in non-linear territory while the fuzzy members are used to squash continuous variables. By trading-off comprehensibility and performance using a multi-objective genetic programming optimization algorithm, we can induce polynomial-fuzzy decision trees (PFDT) that are smaller, more compact and of better performance than their linear decision tree (LDT) counterparts. In this paper we discuss the structural differences between PFDT and LDT (C4.5) and compare the size and performance of their models using medical data.