In this paper, we propose reinforced fuzzy clustering-based ensemble neural networks (FCENNs) classifier. The objective of this paper is focused on the development of the design methodologies of ensemble neural networks classifier for constructing the network structure and enhancing the learning methods of fuzzy clustering-based neural networks through the combination of the probabilistic model and its learning mechanism. The proposed FCENNs classifier takes into consideration a cross-entropy error function to improve learning while L2 norm regularization is used to reduce overfitting as well as enhance generalization abilities. The essential points of the proposed reinforced FCENNs classifier can be enumerated as follows: First, in the proposed classifier, the cross-entropy error function is used as a cost function; to do this, a softmax function is applied to represent a categorical distribution located at the nodes of the output layer. Second, the learning mechanism is composed of two parts. First, fuzzy C-means clustering forms the connections (weights) of the hidden layer while the connections of the output layer are adjusted with the aid of the nonlinear least squares method using Newton's method-based learning. Third, L2 norm-regularization is considered to avoid the degradation of generalization ability caused by overfitting. The learning mechanism similar to ridge regression is realized by adding L2 penalty term to the cross-entropy error function. From the viewpoint of performance improvement achieved through the proposed novel learning method, the design methodology for the ensemble neural networks classifier is discussed and analyzed with the aid of a diversity of two-dimensional synthetic data and machine learning datasets.

中文翻译：

---

基于强化模糊聚类的集成神经网络


在本文中，我们提出了基于强化模糊聚类的集成神经网络（FCENN）分类器。本文的目标是开发集成神经网络分类器的设计方法，用于构建网络结构，并通过概率模型及其学习机制的结合来增强基于模糊聚类的神经网络的学习方法。所提出的 FCENN 分类器考虑了交叉熵误差函数来改进学习，同时使用 L2 范数正则化来减少过度拟合并增强泛化能力。所提出的强化FCENNs分类器的要点可以列举如下：首先，在所提出的分类器中，交叉熵误差函数被用作成本函数；为此，应用 softmax 函数来表示位于输出层节点的分类分布。其次，学习机制由两部分组成。首先，模糊C均值聚类形成隐藏层的连接（权重），而输出层的连接则借助基于牛顿法的学习的非线性最小二乘法进行调整。第三，L2范数正则化被认为可以避免过度拟合导致的泛化能力下降。通过在交叉熵误差函数中添加L2惩罚项，实现了类似于岭回归的学习机制。从通过所提出的新颖学习方法实现性能改进的角度来看，借助各种二维合成数据和机器学习数据集，讨论和分析了集成神经网络分类器的设计方法。