Publications

In this article, we introduce novel reinforced hybrid fuzzy rule-based neural networks (RHFNNs). This article is concerned with the development of the design methodologies of hybrid fuzzy rule-based model for constructing the network structure and enhancing its predictive abilities through the combination of inhomogeneous neurons [i.e., clustering-based polynomial neurons (CPNs) and polynomial neurons (PNs)] and tournament selection. The key points of the proposed RHFNN are enumerated as follows: The first layer of the proposed network consists of CPNs. CPN can effectively reflect the complex nonlinear structure encountered in the data space, and refine (granulate) it with the help of the clustering algorithm. Two types of CPNs including hard C-means (HCM) clustering-based polynomial neuron (HCPN) and fuzzy C-means (FCM) clustering-based polynomial neuron (FCPN) are designed. According to the type of CPN used in the first layer, RHFNN can be categorized into two types, namely, RHFNN based on HCPN (HRHFNN) and RHFNN based on FCPN (FRHFNN). We use PNs to construct the second and consecutive layers. PN can identify and approximate the nonlinear relationship among system's inputs and outputs. A tournament-based performance selection (TPS) algorithm stemming from evolutionary computation is used for selection of neuron. TPS not only ensures that the candidate nodes have sufficient fitting ability but also enhances the individual diversity in the node set and provides the abilities to generate better prediction nodes. In addition, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm regularization is considered to reduce the deviation between coefficients and ameliorate overfitting as well as boost generalization ability. The performance of RHFNN is discussed through a variety of publicly available machine learning datasets. From the experimental results, we conclude that RHFNN achieves the best prediction accuracy on 13 of 15 datasets; the statistical analysis also confirms the superiority of RHFNN.

Learning a proper distance for clustering from prior knowledge falls into the realm of semisupervised fuzzy clustering. Although most existing learning methods take prior knowledge (e.g., pairwise constraints) into account, they pay little attention to local knowledge of data, which, however, can be utilized to optimize the distance. In this article, we propose a novel distance learning method, which learns from the Group-level information, for semisupervised fuzzing clustering. We first present a new format of constraint information, called Group-level constraints, by elevating the pairwise constraints (must-links and cannot-links) from point level to Group level. The Groups, generated around data points contained in the pairwise constraints, carry not only the local information of data (the relation between close data points) but also more background information under some given limited prior knowledge. Then, we propose a novel method to learn a distance by using the Group-level constraints, namely, Group-based distance learning, in order to optimize the performance of fuzzy clustering. The distance learning process aims to pull must-link Groups as close as possible while pushing cannot-link Groups as far as possible. We formulate the learning process with the weights of constraints by invoking some linear and nonlinear transformations. The linear Group-based distance learning method is realized by means of semidefinite programming, and the nonlinear learning method is realized by using the neural network, which can explicitly provide nonlinear mappings. Experimental results based on both synthetic and real-world datasets show that the proposed methods yield much better performance compared to other distance learning methods using pairwise constraints.