Abstract: When training data in the noisy environment, the generalization performance of traditional RBF (radial basis function) neural network is degraded because of the deficiency of feature extraction mechanism. This paper proposes a novel modeling method, i.e., RBF neural network modeling using fuzzy subspace clustering (FSC-RBF-NN) which adds feature extraction mechanism to overcome this challenge. Compared with traditional RBF neural network modeling, the proposed method can extract different subspace features for different nodes in hidden layer according to the subspace features of FSC (fuzzy subspace clustering) method and the feature extraction mechanism. When the training data contain lots of noise features, the proposed method can still keep good generalization performance by using the feature extraction mechanism to remove noise features. The experimental results on the synthetic and real-
world datasets prove that the FSC-RBF-NN method has strong robustness in the noisy environment.

Key words: robustness, radial basis function (RBF), RBF neural network, fuzzy subspace clustering (FSC), ε-insensitive loss function

摘要： 传统径向基函数（radial basis function，RBF）神经网络模型在处理噪声环境下的数据时，会因缺乏去除噪音特征的机制而使得受训模型的泛化性能下降。针对此缺陷，根据模糊子空间聚类（fuzzy subspace clustering，FSC）算法的子空间特性，为RBF神经网络添加特征抽取机制，提出了一种模糊子空间聚类RBF神经网络建模新方法（RBF neural network modeling using fuzzy subspace clustering，FSC-RBF-NN）。与传统RBF神经网络建模方法相比，FSC-RBF-NN方法可根据FSC的子空间特性和特征抽取机制，为不同的隐含层节点选取不同的特征子空间。当训练数据中含有大量噪音特征时，FSC-RBF-NN方法可通过特征抽取机制去除噪音特征，只保留对建模有积极作用的特征，使模型能保持良好的泛化性能。模拟和真实数据集上的实验结果亦验证了FSC-RBF-NN方法在噪声环境下具有更好的鲁棒性。

关键词: 鲁棒性, 径向基函数（RBF）, RBF神经网络, 模糊子空间聚类, &epsilon, -不敏感损失函数