关于正交变换在前馈网络设计与分析中的应用。
On the application of orthogonal transformation for the design and analysis of feedforward networks.
作者信息
Kanjilal P P, Banerjee D N
机构信息
Dept. of Electron. and Electr. Commun. Eng., Indian Inst. of Technol., Kharagpur.
出版信息
IEEE Trans Neural Netw. 1995;6(5):1061-70. doi: 10.1109/72.410351.
Orthogonal transformation, which can lead to compaction of information, has been used in two ways to optimize on the size of feedforward networks: 1) through the selection of optimum set of time-domain inputs, and the optimum set of links and nodes within a neural network (NN); and 2) through the orthogonalization of the data to be used in NN's, in case of processes with periodicity. The proposed methods are efficient and are also extremely robust numerically. The singular value decomposition (SVD) and QR with column pivoting factorization (QRcp) are the transformations used. SVD mainly serves as the null space detector; QRcp coupled with SVD is used for subset selection, which is one of the main operations on which the design of the optimal network is based. SVD has also been used to devise a new approach for the assessment of the convergence of the NN's, which is an alternative to the conventional output error analysis.
正交变换可导致信息压缩，已被用于两种方式来优化前馈网络的规模：1）通过选择最佳的时域输入集，以及神经网络（NN）内的最佳链接和节点集；2）对于具有周期性的过程，通过对NN中使用的数据进行正交化。所提出的方法是有效的，并且在数值上也极其稳健。使用的变换是奇异值分解（SVD）和带列主元分解的QR（QRcp）。SVD主要用作零空间检测器；QRcp与SVD相结合用于子集选择，这是最优网络设计所基于的主要操作之一。SVD还被用于设计一种评估NN收敛性的新方法，这是传统输出误差分析的一种替代方法。
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