Harezlak Katarzyna, Kasprowski Pawel
Institute of Informatics, Silesian University of Technology, 44-100 Gliwice, Poland.
Entropy (Basel). 2018 Jan 7;20(1):32. doi: 10.3390/e20010032.
Most naturally-occurring physical phenomena are examples of nonlinear dynamic systems, the functioning of which attracts many researchers seeking to unveil their nature. The research presented in this paper is aimed at exploring eye movement dynamic features in terms of the existence of chaotic nature. Nonlinear time series analysis methods were used for this purpose. Two time series features were studied: fractal dimension and entropy, by utilising the embedding theory. The methods were applied to the data collected during the experiment with "jumping point" stimulus. Eye movements were registered by means of the Jazz-novo eye tracker. One thousand three hundred and ninety two (1392) time series were defined, based on the horizontal velocity of eye movements registered during imposed, prolonged fixations. In order to conduct detailed analysis of the signal and identify differences contributing to the observed patterns of behaviour in time scale, fractal dimension and entropy were evaluated in various time series intervals. The influence of the noise contained in the data and the impact of the utilized filter on the obtained results were also studied. The low pass filter was used for the purpose of noise reduction with a 50 Hz cut-off frequency, estimated by means of the Fourier transform and all concerned methods were applied to time series before and after noise reduction. These studies provided some premises, which allow perceiving eye movements as observed chaotic data: characteristic of a space-time separation plot, low and non-integer time series dimension, and the time series entropy characteristic for chaotic systems.
大多数自然发生的物理现象都是非线性动力系统的例子，其运行吸引了许多试图揭示其本质的研究人员。本文提出的研究旨在从混沌性质的存在方面探索眼动的动态特征。为此使用了非线性时间序列分析方法。利用嵌入理论研究了两个时间序列特征：分形维数和熵。这些方法应用于“跳点”刺激实验期间收集的数据。眼动通过Jazz-novo眼动仪进行记录。基于在施加的长时间注视期间记录的眼动水平速度，定义了1392个时间序列。为了对信号进行详细分析并识别在时间尺度上对观察到的行为模式有贡献的差异，在不同的时间序列间隔中评估了分形维数和熵。还研究了数据中包含的噪声的影响以及所使用的滤波器对所得结果的影响。使用低通滤波器以50Hz的截止频率进行降噪，通过傅里叶变换进行估计，并且所有相关方法都应用于降噪前后的时间序列。这些研究提供了一些前提，使得可以将眼动视为观察到的混沌数据：时空分离图的特征、低且非整数的时间序列维数以及混沌系统的时间序列熵特征。
