We study a general nonconvex formulation for low-rank minimization problems. We use recent results on non-Euclidean first-order methods to provide efficient and scalable algorithms. Our approach uses the geometry induced by the Bregman divergence of well-chosen kernel functions; for unconstrained problems, we introduce a novel family of Gram quartic kernels that improve numerical performance. Numerical experiments on Euclidean distance matrix completion and symmetric nonnegative matrix factorization show that our algorithms scale well and reach state-of-the-art performance when compared to specialized methods.

中文翻译：

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低秩最小化的四阶一阶方法

我们研究低阶最小化问题的一般非凸公式。我们使用非欧几里德一阶方法的最新结果来提供高效且可扩展的算法。我们的方法使用了由精选内核函数的Bregman散度引起的几何形状。对于不受约束的问题，我们介绍了一种新型的Gram四次核，可以改善数值性能。欧氏距离矩阵完成和对称非负矩阵分解的数值实验表明，与专用方法相比，我们的算法可很好地缩放并达到最新的性能。