自监督学习子空间模式识别方法的统计特性分析

An Analysis of the Statistical Properties on the Self-Supervised Learning Subspaces for Pattern Recognition

本文研究了神经网络无导师自监督学习子空间模式识别方法的收敛性问题，证明了学习子空间法的变换矩阵收敛于模式的自相关矩阵估计；证明了一类Ｋｏｈｏｎｅｎ自监督学习子空间方法的收敛性；给出了子空间旋转变化所引起的子空间特征谱分布的近似表达式，同时给出了子空间扰动的上界定理。

The convergence of Learning Subspace Methods(LSM) for pattern recognition is studied. The transformed matrices of learning subspaces are proved to converge to the estimation of pattern autocorrelation matrix,thus the convergence of Kohonen's self-supervised LSMs is proved. At the same time, the approximate expression of the eigen spectrum caused by LSM's rotation and the upper bound disturbed theorem of Learning Subspace are presented.