Multiplicative updates for nonnegative quadratic programming
Multiplicative updates for nonnegative quadratic programming
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DOI：
10.1162/neco.2007.19.8.2004
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发表时间：
2007-08-01
影响因子：
2.9
通讯作者：
Lee, Daniel D.
中科院分区：
文献类型：
--
作者：
Sha, Fei;Lin, Yuanqing;Lee, Daniel D.
神经计算和统计学习中的许多问题都涉及到带非负约束的优化问题。在这篇文章中，我们研究了二次规划中的凸问题，其中最优化被限制在非负正交中的一个轴化区域。对于这些问题，我们推导出乘性更新，在每次迭代中提高目标函数的值，并单调收敛到全局最小值。更新具有简单的封闭形式，不涉及任何必须调整以确保收敛的启发式或自由参数。尽管它们很简单，但它们在形式上与机器学习中使用的其他乘性更新有着惊人的不同。我们给出了这些更新收敛的完整证明，并描述了它们在信号处理和模式识别问题中的应用。
Many problems in neural computation and statistical learning involve optimizations with nonnegativity constraints. In this article, we study convex problems in quadratic programming where the optimization is confined to an axis-atigned region in the nonnegative orthant. For these problems, we derive multiplicative updates that improve the value of the objective function at each iteration and converge monotonically to the global minimum. The updates have a simple closed form and do not involve any heuristics or free parameters that must be tuned to ensure convergence. Despite their simplicity, they differ strikingly in form from other multiplicative updates used in machine learning. We provide complete proofs of convergence for these updates and describe their application to problems in signal processing and pattern recognition.