极小最小二乘问题在神经网络中的应用

为了解决在神经网络的前馈算法中矩阵的极小最小二乘的失效问题,在Matlab和C 的平台上研究并比较了奇异值分解(SVD)、超松弛迭代(SSOR)和共轭梯度法(CG)几种算法在解上千阶矩阵最小二乘问题的优劣。SSOR算法在百阶的条件下,具有实用性;CG算法和SVD算法在千阶的条件下,可以取得比较好的收敛速度和比较高的精度。这两种算法还可以继续完善。CG算法可加预处理方法使其更加稳定,收敛更快。该文研究表明SVD和CG算法可以有效的解决经典算法如QR算法在大中规模矩阵条件下,解最小二乘问题失效的问题。

Least square problems in artificial neural networks

Singular value decomposition (SVD), symmetric successive over relaxation (SSOR) and conjugate gradient (CG) methods were evaluated using Matlab and C to solve the least square problem in the artificial neural network feed-forward algorithm. If the order of the matrix is less than 1 000, the SSOR method can provide acceptable results. Otherwise, the CG and SVD methods should be applied for reasonable accuracy and speed. Modified CG and SVD methods provide even better stability, speed, and accuracy. In general, the SVD and CG algorithms are recommended for large least square problems.