Non-Convex Optimization on Stiefel Manifold and Applications to Machine Learning
Non-Convex Optimization on Stiefel Manifold and Applications to Machine Learning
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Stiefel 流形的非凸优化及其在机器学习中的应用
DOI：
10.1007/978-3-642-34475-6_14
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
Takafumi Kanamori and Akiko Takeda
中科院分区：
文献类型：
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作者：
Sakuma;Y. and Inoie A;Takafumi Kanamori and Akiko Takeda
我们研究了机器学习和统计学中出现的非凸优化问题。近年来，凸性成为开发高性能学习算法的一个重要特征。另一方面，机器学习也需要非凸优化。本文特别研究了Stiefel流形上的非凸优化问题。Stiefel流形由矩形矩阵组成，机器学习中的许多重要问题都可以用这个框架来表示。比较了几种适用于机器学习算法的非线性优化方法。
We study non-convex optimization problems which appear in machine learning and statistics. Recently, convexity became an important feature to develop high-performance learning algorithms. On the other hand, non-convex optimization is also required in machine learning. In this paper, especially we deal with non-convex optimization problems on the Stiefel manifold. The Stiefel manifold consists of rectangular matrices, and many important problems in machine learning can be expressed in this framework. We compare some non-linear optimization methods which are applicable to machine learning algorithms.