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May, 2023
矩阵分解的交替梯度下降收敛
Convergence of Alternating Gradient Descent for Matrix Factorization
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Rachel Ward, Tamara G. Kolda
TL;DR
本文研究了交替梯度下降算法应用于非对称矩阵分解目标函数的收敛性分析,证明了在充分迭代步数内,随机初始化下可以收敛到较优解,此结果可以为更广泛的非凸低秩矩阵分解问题的收敛分析提供帮助,并在实验中得到了验证。
Abstract
We consider
alternating gradient descent
(AGD) with fixed step size $\eta > 0$, applied to the
asymmetric matrix factorization
objective. We show that, for a rank-$r$ matrix $\mathbf{A} \in \mathbb{R}^{m \times n
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