Hong Xia
IEEE Trans Neural Netw. 2006 Jul;17(4):1064-9. doi: 10.1109/TNN.2006.875986.
In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.
在这封信中，介绍了一种基于Box-Cox变换的径向基函数（RBF）神经网络，该网络使用RBF神经网络来表示变换后的系统输出。首先，基于秩揭示正交矩阵三角分解（QR分解）导出一个固定且规模适中的RBF模型库。然后，引入一种新的快速识别算法，该算法基于最大似然估计器，使用高斯-牛顿算法来推导所需的Box-Cox变换。这封信的主要贡献在于利用矩阵块分解引理的逆来探索所提出的RBF神经网络的特殊结构，以提高计算效率。最后，基于推导得到的最优Box-Cox变换和基于D-最优性的正交前向回归算法，识别出具有良好泛化性和稀疏性的基于Box-Cox变换的RBF神经网络。通过一个示例展示了所提出的算法及其有效性，并与支持向量机回归进行了比较。
