Su Shun-Feng, Chuang Chen-Chia, Tao C W, Jeng Jin-Tsong, Hsiao Chih-Ching
Department of Electrical Engineering, National Taiwan University of Science and Technology, Taipei 106, Taiwan.
IEEE Trans Syst Man Cybern B Cybern. 2012 Feb;42(1):69-80. doi: 10.1109/TSMCB.2011.2161468. Epub 2011 Aug 18.
This paper introduces a new structure of radial basis function networks (RBFNs) that can successfully model symbolic interval-valued data. In the proposed structure, to handle symbolic interval data, the Gaussian functions required in the RBFNs are modified to consider interval distance measure, and the synaptic weights of the RBFNs are replaced by linear interval regression weights. In the linear interval regression weights, the lower and upper bounds of the interval-valued data as well as the center and range of the interval-valued data are considered. In addition, in the proposed approach, two stages of learning mechanisms are proposed. In stage 1, an initial structure (i.e., the number of hidden nodes and the adjustable parameters of radial basis functions) of the proposed structure is obtained by the interval competitive agglomeration clustering algorithm. In stage 2, a gradient-descent kind of learning algorithm is applied to fine-tune the parameters of the radial basis function and the coefficients of the linear interval regression weights. Various experiments are conducted, and the average behavior of the root mean square error and the square of the correlation coefficient in the framework of a Monte Carlo experiment are considered as the performance index. The results clearly show the effectiveness of the proposed structure.
本文介绍了一种新型径向基函数网络（RBFN）结构，它能够成功地对符号区间值数据进行建模。在所提出的结构中，为了处理符号区间数据，对RBFN中所需的高斯函数进行了修改，以考虑区间距离度量，并且RBFN的突触权重被线性区间回归权重所取代。在这些线性区间回归权重中，考虑了区间值数据的下限和上限以及区间值数据的中心和范围。此外，在所提出的方法中，提出了两个学习机制阶段。在阶段1中，通过区间竞争凝聚聚类算法获得所提出结构的初始结构（即隐藏节点的数量和径向基函数的可调参数）。在阶段2中，应用一种梯度下降类学习算法来微调径向基函数的参数和线性区间回归权重的系数。进行了各种实验，并将蒙特卡罗实验框架内的均方根误差的平均行为和相关系数的平方作为性能指标。结果清楚地表明了所提出结构的有效性。
