平均递归量化分析--省略递归阈值选择的方法
Averaged Recurrence Quantification Analysis -- Method omitting the recurrence threshold choice
摘要：
递归量化分析（RQA）是一种成熟的非线性数据分析方法。在这项工作中，我们提出了一个新的策略，几乎无参数的RQA。该方法最后通过计算一系列阈值（实际上是复发率）的RQA措施来省略阈值参数的选择。具体来说，我们测试的RQA措施确定性的能力，排序数据的信噪比。我们考虑一个周期信号，简单的混沌逻辑斯谛方程和Lorenz系统在测试数据集上具有不同的，甚至很小的信噪比长度$10^2, 10^3, 10^4,$和$10^5$。为了使计算成为可能，开发了一种新的有效算法，用于简化图形处理单元（GPU）上的数值运算。
英文摘要：
Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal to noise ratios of lengths $10^2, 10^3, 10^4,$ and $10^5$. To make the calculations possible a new effective algorithm was developed for streamlining of the numerical operations on Graphics Processing Unit (GPU).
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