Dynamics reconstruction and classification via Koopman features
Dynamics reconstruction and classification via Koopman features
复制标题
通过 Koopman 特征进行动力学重建和分类
DOI：
10.1007/s10618-019-00639-x
复制
发表时间：
2019
影响因子：
4.8
通讯作者：
Li, Jr-Shin
中科院分区：
文献类型：
--
作者：
Zhang, Wei;Yu, Yao-Chi;Li, Jr-Shin
大型复杂数据集的知识发现和信息提取在统计学、生物学、医学等领域引起了极大的关注。来自机器学习、数据挖掘和神经计算的工具已经被广泛探索和利用来完成这些引人注目的数据分析任务。然而，对于呈现主动动态特征的时间序列数据，许多最先进的技术在捕捉这些数据中继承的时间结构方面可能表现不佳。本文将Koopman算子和线性动力系统理论与支持向量机相结合，提出了一种新的动态数据挖掘框架，用于构建低维线性模型，逼近由未知非线性动力系统产生的高维时间序列数据的非线性流动。然后，该框架立即实现对复杂时间序列数据的模式识别，例如分类，以通过使用由简化的线性系统生成的轨迹来区分它们的动态行为。此外，我们通过生物信息学和医疗保健中的时间序列分类问题，包括认知分类和基于fMRI和EEG数据的癫痫检测，验证了该框架的适用性和有效性。开发的Koopman动态学习框架为有效的动态数据挖掘奠定了坚实的基础，并为提取非线性动态系统的动态和重要的时间结构提供了一种数学上合理的方法。
Knowledge discovery and information extraction of large and complex datasets has attracted great attention in wide-ranging areas from statistics and biology to medicine. Tools from machine learning, data mining, and neurocomputing have been extensively explored and utilized to accomplish such compelling data analytics tasks. However, for time-series data presenting active dynamic characteristics, many of the state-of-the-art techniques may not perform well in capturing the inherited temporal structures in these data. In this paper, integrating the Koopman operator and linear dynamical systems theory with support vector machines, we develop a novel dynamic data mining framework to construct low-dimensional linear models that approximate the nonlinear flow of high-dimensional time-series data generated by unknown nonlinear dynamical systems. This framework then immediately enables pattern recognition, e.g., classification, of complex time-series data to distinguish their dynamic behaviors by using the trajectories generated by the reduced linear systems. Moreover, we demonstrate the applicability and efficiency of this framework through the problems of time-series classification in bioinformatics and healthcare, including cognitive classification and seizure detection with fMRI and EEG data, respectively. The developed Koopman dynamic learning framework then lays a solid foundation for effective dynamic data mining and promises a mathematically justified method for extracting the dynamics and significant temporal structures of nonlinear dynamical systems.
使用受限玻尔兹曼机检测致癫痫病变的非参数方法
DOI：
--
发表时间：
2016
期刊：
Knowledge Discovery and Data Mining
影响因子：
--
作者：
Yijun Zhao;Bilal Ahmed;T. Thesen;K. Blackmon;Jennifer G. Dy;C. Brodley;R. Kuzniecky;O. Devinsky
通讯作者：
O. Devinsky