Determination of regional variants in the versification of Estonian folksongs using an interpretable fuzzy rule-based classifier

Abstract

In this paper, a method of hierarchical clustering and a selection of fuzzy classification algorithms are applied successively to the data set that contains measured characteristics of folk verses collected from 104 historical parishes of Estonia. The aim of the study is to detect the groups of parishes that are similar in terms of folk verse characteristics and to give us insight into the reasoning that the separation into these groups is based upon. The process of classification separates the initial groups into further subsets represented by fuzzy rules, which can be analyzed thanks to the interpretability of such rules. To emphasize the latter, most important features in individual rules are brought out by rule compression. The results of the analysis are backed by what is known from linguistic sciences.

Interpretability improvement of fuzzy rule-based classifiers via rule compression

“…A class that is separated from other classes in product space is easy to classify correctly whereas high overlap of classes can make it very difficult to obtain a rule placement that would result in an accurate classifier and typically, such class distributions need to be modeled with increased level of granularity. For this purpose we employ the algorithms of rule granulation and consolidation [10] to obtain the zero-error classifiers on which to verify the performance of compression methods described in Section 4.…”

“…This procedure, however, usually creates too many rules the number of which can be substantially reduced by rule base consolidation [10]. During the consolidation, weaker rules (governing few samples) are constantly losing their samples to stronger rules (those governing many samples) and as a natural result, many of the weaker rules become obsolete.…”

“…It then allows one to create the rules directly in product space that helps to cope with the curse of dimensionality [7] (the number of rules is relatively low and does not depend on the number of features). This, however, comes at the cost of loss of global semantics, making it impossible to use meaningful linguistic labels for fuzzy sets and invalidates the partition-driven interpretation -therefore one has to revert to the rule-driven interpretation of a fuzzy system [10].…”

“…In the context of the latter, interpretability improvement is a matter of finding a small number of concise fuzzy rules (not too spread out in product space) with a limited number of conditions [9]. The degree at which the rules in a classifier overlap is also an important factor that influences how understandable the rules of the system can be [10].…”

Design of Fuzzy Rule-based Classifiers through Granulation and Consolidation

“…The procedure for reducing the number of rules of classifiers is outlined in [29] and termed rule base consolidation. During the consolidation, weaker rules (governing few samples) are constantly losing their samples to stronger rules (those governing many samples).…”