论文标题
有效且稳定的算法将Greville的方法扩展到基于Cholesky逆因化的分区矩阵
Efficient and Stable Algorithms to Extend Greville's Method to Partitioned Matrices Based on Inverse Cholesky Factorization
论文作者
论文摘要
Greville的方法已用于（广泛的学习系统）BLS中，可以提出一个有效而有效的增量学习系统，而无需从一开始就重新培训整个网络。对于第二部分由P列组成的列分区矩阵，Greville的方法需要P迭代才能从第一部分的伪内部计算整个矩阵的伪源。 BLS中的增量算法扩展了Greville的方法，以从第一部分的伪源来计算整个矩阵的伪源，仅通过1个迭代来忽略了一些可能的情况，并且需要进一步提高效率和数值稳定性。在本文中，我们提出了一种来自Greville方法的有效且数值的稳定算法，以通过仅考虑1个迭代的情况，计算第一部分的伪内部矩阵的伪内质体，并且考虑了所有可能的情况，并且最近提出的近方cholesky centressky cressization可以应用计算复杂性。最后，我们为BLS中的列分区矩阵提供了整个算法。另一方面，我们还为BLS中的行分区矩阵提供了建议的算法。
Greville's method has been utilized in (Broad Learn-ing System) BLS to propose an effective and efficient incremental learning system without retraining the whole network from the beginning. For a column-partitioned matrix where the second part consists of p columns, Greville's method requires p iterations to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part. The incremental algorithms in BLS extend Greville's method to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part by just 1 iteration, which have neglected some possible cases, and need further improvements in efficiency and numerical stability. In this paper, we propose an efficient and numerical stable algorithm from Greville's method, to compute the pseudoinverse of the whole matrix from the pseudoinverse of the first part by just 1 iteration, where all possible cases are considered, and the recently proposed inverse Cholesky factorization can be applied to further reduce the computational complexity. Finally, we give the whole algorithm for column-partitioned matrices in BLS. On the other hand, we also give the proposed algorithm for row-partitioned matrices in BLS.
