Dynamics reconstruction and classification via Koopman features

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 compel...

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Bibliographic Details
Published in:Data mining and knowledge discovery Vol. 33; no. 6; pp. 1710 - 1735
Main Authors: Zhang, Wei, Yu, Yao-Chi, Li, Jr-Shin
Format: Journal Article
Language:English
Published: New York Springer US 01.11.2019
Springer Nature B.V
Subjects:
Analytics
Artificial Intelligence
Bioinformatics
Chemistry and Earth Sciences
Classification
Computer Science
Data mining
Data Mining and Knowledge Discovery
Dynamic characteristics
Dynamic systems theory
Dynamical systems
Feature extraction
Information retrieval
Information Storage and Retrieval
Linear systems
Machine learning
Nonlinear systems
Pattern recognition
Physics
Seizures
Statistics for Engineering
Support vector machines
System theory
Dimensionality reduction
Koopman operators
Dynamic data mining
Healthcare
Time-series classification
Bioinformatics
Spectral methods
Data-driven methods
ISSN:1384-5810, 1573-756X
Online Access:Get full text
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Summary: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.
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ISSN:1384-5810
1573-756X
DOI:10.1007/s10618-019-00639-x