一种主奇异三元组提取的快速神经网络算法

A Fast Neural Network Algorithm for Principal Singular Triplet Extraction

摘要:

为了对两路高维数据流的互协方差矩阵进行在线奇异值分解，提出了一种快速稳定的主奇异三元组提取神经网络算法。首先，提出了一个新颖信息准则，并且基于该准则推导出了一个动态系统。然后，基于该动态系统，推导出了一种快速稳定的在线神经网络算法。该算法可以提取两路高维数据流的互协方差矩阵的左右主奇异向量。另外，算法中奇异向量的长度会收敛到一个与相应主奇异值相关的值，因而该主奇异值也可以被估计出来。相比于传统算法，该算法可以提取该矩阵的主奇异三元组而非仅仅是主奇异向量。与已有算法相比，该算法具有较低计算复杂度、较高收敛速度和稳定性。

Abstract:

A fast and stable neural network algorithm for principal singular triplet (PST) extraction is proposed to perform the online singular value decomposition (SVD) of the cross-covariance matrix of two high-dimensional data streams. A novel information criterion is firstly proposed and then based on which a dynamical system is derived. Thereafter, an online fast and stable neural network algorithm is developed from the dynamical system. The proposed algorithm can extract the left and right principal singular vectors of the cross-covariance matrix of two high-dimensional data streams. Moreover, the length of each singular vector will converge to a value that is correlated to the corresponding principal singular value. Therefore the singular value can also be estimated from the length of the singular vector. Compared with the conventional algorithms, the proposed algorithm can extract the PST of the cross-covariance matrix, but not only the singular vectors. Furthermore, the proposed algorithm is low in computation complexity, high in convergence speed and good in stability.