Gupta Soumyajit, Bajaj Chandrajit
Dept. of Computer Science, University of Texas at Austin, Austin, TX, USA.
Dept. of Computer Science and Oden Institute, University of Texas, Austin, Austin, TX, USA.
Proc IEEE Int Conf Big Data. 2019 Dec;2019:74-83. doi: 10.1109/BigData47090.2019.9006512. Epub 2020 Feb 24.
The Rayleigh quotient optimization is the maximization of a rational function, or a max-min problem, with simultaneous maximization of the numerator function and minimization of the denominator function. Here, we describe a low-rank, streaming solution for Rayleigh quotient optimization applicable for big-data scenarios where the data matrix is too large to be fully loaded into main memory. We apply this for a maximization of the Signal to Noise ratio of big-data, of very large static and dynamic data. Our implementation is shown to achieve faster processing time compared to a standard data read into memory. We demonstrate the trade-offs with synthetic and real data, on different scales to validate the approach in terms of accuracy, speed and storage.
瑞利商优化是一个有理函数的最大化问题，即一个最大-最小问题，同时要使分子函数最大化且分母函数最小化。在此，我们描述一种适用于大数据场景的低秩、流式瑞利商优化解决方案，在这些场景中数据矩阵太大而无法完全加载到主内存中。我们将此应用于最大化大数据（非常大的静态和动态数据）的信噪比。与读入内存的标准数据相比，我们的实现显示出能实现更快的处理时间。我们在不同规模上用合成数据和真实数据展示了权衡，以在准确性、速度和存储方面验证该方法。
