Multiview representation learning is very popular for latent factor analysis. It naturally arises in many data analysis, machine learning, and information retrieval applications to model dependent structures between a pair of data matrices. For computational convenience, existing approaches usually formulate the multiview representation learning as convex optimization problems, where global optima can be obtained by certain algorithms in polynomial time. However, many evidences have corroborated that heuristic nonconvex approaches also have good empirical computational performance and convergence to the global optima, although there is a lack of theoretical justification. Such a gap between theory and practice motivates us to study a nonconvex formulation for multiview representation learning, which can be efficiently solved by two stochastic gradient descent (SGD) methods. Theoretically, by analyzing the dynamics of the algorithms based on diffusion processes, we establish global rates of convergence to the global optima with high probability. Numerical experiments are provided to support our theory.

非凸多视角表示学习问题最近在机器学习领域中备受关注，本文提出一种由简单随机梯度下降算法有效求解的非凸公式，并且通过扩散近似建立起渐近全局收敛速率的理论证明。

放弃凸性以获得更高效可伸缩的在线多视角学习