Asymptotic optimality of competitive associative nets for their learning in function approximation
Asymptotic optimality of competitive associative nets for their learning in function approximation
复制标题
竞争关联网络在函数逼近中学习的渐近最优性
DOI：
10.1109/iconip.2002.1202222
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
S. Kurogi
中科院分区：
文献类型：
--
作者：
S. Kurogi
竞争联想网络称为CAN2涉及竞争和联想计划的学习，以实现分段线性逼近的非线性函数。虽然网络的学习方案已被证明是有效的，在许多应用中，如函数逼近，控制，降雨量估计，竞争学习基本上有局部极小值问题。为了克服这些问题，我们在这里引入渐近的情况下，其中的单元数是非常大的，然后推导出一个渐近最优性的条件，最小化的均方误差（MSE）的近似。接下来，我们将该条件嵌入到增量学习算法中，其中该条件用于决定学习过程是否停留在局部最小值，并重新初始化全局最优的单元。通过对多个基准函数进行数值实验，我们验证了采用本算法的CAN 2比使用学习或优化技术广泛使用的方案（BPN（反向传播网络）、RBFN（径向基函数））实现了更小的MSE。网络）和SVR（支持向量回归）。
The competitive associative nets called CAN2 involve competitive and associative schemes for learning to achieve piecewise linear approximation of nonlinear functions. Although the learning schemes of the nets have been shown effective in many applications such as function approximation, control, and rainfall estimation, the competitive learning basically has local minima problems. To overcome the problems, we here introduce asymptotic situation, where the number of units are very large, and then derive a condition of asymptotic optimality for minimizing the mean square error (MSE) of approximation. We next embed the condition into the incremental learning algorithm, where the condition is used for deciding whether the learning process is stuck at a local minimum or not, and reinitializing a unit for global optimum. By means of numerical experiments with a number of benchmark functions, we have verified the CAN2 with the present algorithm achieves smaller MSE than the widely used schemes using learning or optimization techniques as follows: the BPN (backpropagation net), the RBFN (radial basis function net) and the SVR (support vector regression).