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Abstract: Semi-supervised (or partial) fuzzy clustering plays an important and unique role in discovering hidden structure in data realized in presence of a certain quite limited fraction of labeled patterns. The objective of this study is to investigate and quantify the effect of various distance functions (distances) on the performance of the clustering mechanisms. The underlying goal of endowing the clustering algorithms with a higher level of flexibility is done via the use of various distances. The enhancement of this character is evaluated by means of a comprehensive assessment of quality of clusters, their ensuing discrimination abilities and the accuracy of clusters themselves. In addition to the standard Euclidean distance being commonly exploited in fuzzy clustering, three more versatile and adaptive distance measures are considered such as its weighted version, a full adaptive distance, and a kernel-based distance. Using Fuzzy C-Means (FCM) coming in its generic format, we show its semi-supervised enhancements, derive detailed formulas and analyze their effectiveness. The improvements of semi-supervised clustering are empirically evaluated and numerically quantified with the use of several Machine Learning data sets. [Copyright &y& Elsevier]

Abstract Fuzzy rule-based classifiers have been used in many applications showing better performance due to simple modular architectures and significant interpretability. Generally, researchers design this type of classifiers along with two incompatible directions: some of them devote to mine more rules from data for enhancing the accuracy of classifiers and others focus on reducing the number of rules for simplifying the classifier with high accuracy. However, from the perspective of practicability, the tradeoff between the accuracy of model and the number of rules including in the model should be carefully considered when designing classifiers. Further, these classifiers also encounter two evident limitations in the process of design: one is that the contribution of each sample versus individual attributions is equally important and another is that the concept of information granularity is not considered. These two limitations result in the reduction of accuracy of the ensuing classifier. To alleviate these two limitations and make compromise between the accuracy and the number of rules of formed classifier, in this study, a novel method is proposed to construct a fuzzy classifier by means of the principle of justifiable granularity with weighted data. The proposed method involves two main stages: the first stage concerns with the formation of an initial classification model. The initial model is constructed by engaging a synergy of Fuzzy C-Means clustering (FCM) and the principle of justifiable granularity with weighted data. The second stage focuses on the refinement of the initial classification model. The number of rules of the completely formed fuzzy classification model is equal to that of classes of experimental data. A series of experiments concerning synthetic datasets and ten UCI datasets are also implemented to exhibit the feasibility and effectiveness of the proposed classification method as well as reveal the impact of information granularity on resulting classification model. [ABSTRACT FROM AUTHOR]