线性三层降秩神经网络的广义逆矩阵训练算法

Generalized Matrix Inversion Training Algorithm for Linear Three-layer Reduced-rank Neural Networks

先得到计算矩阵的广义逆的一种有效算法,即正交反向传播(OBP)算法,利用OBP 算法,经有限次迭代即可以得到矩阵广义逆的精确解。然后利用OBP 算法来讨论线性三层降秩网络的训练问题,经过有限次迭代就可得到网络的误差函数的全局最优解,且不存在任何收敛性问题。

We first get an effective algorithm for generalized inversion of a matrix,i.e. OBP algorithm. The exact generalized inversion of a matrix is obtained after finite steps by using OBP algorithm. Then we investigate the training problem of the linear three-layer reduced-rank neural networks by using OBP algorithm .The global optimal solutions for the error function of the networks can be obtained after finite iterations.