Experimental Evaluation of Different Membership Functions on Weighted Pattern Trees for Diatom Modelling

Abstract

Weighted Pattern Trees (WPT) algorithm is an extension of the pattern tree algorithm, which builds models with different weights and these weights are used for predicting the particular output attribute and they show how much a particular tree model is confident to predict such class. The WPT uses the similarity information between the fuzzy term leaf and the root of the tree model to weight the model. Each fuzzy term is acquired from the input dataset using different types of membership functions (MFs). The shape and mathematical formulation of the MFs plays an important role in the WPT algorithm induction, and thus on the model performance. In this direction, the paper aims to experimentally investigate the influence of three smoothed MFs on real measured ecological dataset using three different type of experiments. The first experiments evaluate the influence of the number of MFs per attribute, the second experiments examine the type of the MFs, and the third experiments investigate the influence of different WPT variants on both descriptive and predictive classification accuracy. The results for the statistical significance with the two-step procedure, showed that models with depth 10 with Sigmoidal +1 MF and high number of MFs per attribute are excellent for building models with high descriptive power. On the other side, the models with low number of MFs with Bell MF and model depth constrained to five have high predictive power. These results encourage us to further investigate the influence of different similarity metrics and fuzzy aggregation operators on the performance of WPT models.