Diatom Ecological Modelling with Weighted Pattern Tree Algorithm by Using Polygonal and Gaussian Membership Functions

Abstract

Weighted Pattern Tree (WPT) algorithm is as an extension of the Pattern Tree (PT) algorithm, which could be used for fuzzy modelling. This algorithm utilizes the similarity between two fuzzy sets in order to quantify how much a particular tree model is confident to predict a given class. The Membership Functions (MFs) play an important role in model induction and thus on the model’s performance. Therefore, this paper aims to investigate the influence of different MFs, not only by analyzing different mathematical distributions, but also to investigate the influence of the number of MFs per attribute used for fuzzification of the datasets, as well as the different settings of the algorithm in the area of diatom ecological modelling. The experimental results show that WPTs with depth 10 using polygonal MFs with high number of MFs per attribute are excellent for describing the training data, while the models that are built with low number of MFs are excellent for making predictions for unseen data. The results from this research can be used for ecological modelling of diatoms, to classify a given diatom into a particular water quality class.