A comparative study of general fuzzy min-max neural networks for pattern classification problems

--General fuzzy min-max (GFMM) neural network is a generalization of fuzzy neural networks formed by hyperbox fuzzy sets for classification and clustering problems. Two principle algorithms are deployed to train this type of neural network, i.e., incremental learning and agglomerative learning. This paper presents a comprehensive empirical study of performance influencing factors, advantages, and drawbacks of the general fuzzy min-max neural network on pattern classification problems. The subjects of this study include (1) the impact of maximum hyperbox size, (2) the influence of the similarity threshold and measures on the agglomerative learning algorithm, (3) the effect of data presentation order, (4) comparative performance evaluation of the GFMM with other types of fuzzy min-max neural networks and prevalent machine learning algorithms. The experimental results on benchmark datasets widely used in machine learning showed overall strong and weak points of the GFMM classifier . These outcomes also informed potential research directions for this class of machine learning algorithms in the future. Pattern classification, which belongs to the class of supervised learning, aims to discover information and knowledge under data through taking advantage of the power of learning algorithms [1]. It plays a crucial role in many real-world applications ranging from medical diagnostic [2], electronic devices [3] to tourism [4] and energy [5]. Multidimensional hyperbox fuzzy sets can be used to deal with the pattern classification problems effectively by partitioning the pattern space and assigning a class label associated with a degree of certainty for each region. Each fuzzy min-max hyperbox is represented by minimum and maximum points along with a fuzzy membership function. The membership function is employed to compute the degree-of-fit of each input sample to a given hyperbox. Meanwhile, the hyperbox is continuously adjusted during the training process to cover the input patterns. Simpson was the first one who formulated a fuzzy min-max neural network (FMNN) using hyperbox representations and proposed the training algorithms for classification [6] and clustering [7] problems. Since then, many researchers have paid attention to enhancing the performance of the FMNN and addressing some of its major drawbacks. Recent surveys [8], [9] on the FMNN have divided modified variants into two groups, i.e., fuzzy min-max networks with and without contraction process. Representatives of improved models removing the contraction procedure from the training algorithms and replacing it with particular neurons for overlapping regions among hyperboxes comprise the inclusion/exclusion fuzzy hyperbox classifier [10], the fuzzy min-max neural network with compensatory neuron [11], the data-core-based FMM neural network [12], and the multilevel FMM neural network [13].