Core Concepts
Integration of machine learning with recurrence measures for classifying dynamical states in time series data.
Abstract
The study combines machine learning algorithms with nonlinear time series analysis, focusing on classifying dynamical states like periodic, chaotic, hyperchaotic, or noisy. Three algorithms - Logistic Regression, Random Forest, and Support Vector Machine are implemented. Features extracted from recurrence quantification analysis and recurrence networks play a crucial role in classification. The study explores the significance of input features and demonstrates successful prediction of dynamical states in variable stars.
- Introduction to Time Series Analysis
- Nonlinear time series analysis offers insights into complex systems.
- Linear models are inadequate for capturing dynamic interactions.
- Application of Recurrence Measures
- Recurrence plots and networks reveal temporal dependencies.
- Techniques explore patterns within time series data.
- Machine Learning Algorithms
- Logistic Regression, Random Forest, and Support Vector Machine used for classification.
- Supervised methods automate complex manual processes.
- Performance Analysis
- RF algorithm exhibits higher accuracy in classifying multiple dynamical states.
- SVM shows tolerance to noise contamination up to 5% in data.
- Feature Importance
- Features quantifying density of recurrence points are crucial for accurate classification.
- Real Data Application
- Successful prediction of dynamical states in variable stars using trained algorithms.
- Extension to Discrete Systems
- Classification of dynamical states from discrete systems using machine learning techniques.
Stats
We implement three machine learning algorithms: Logistic Regression, Random Forest, and Support Vector Machine for this study.
The classifiers perform well on average with Random Forest exhibiting higher accuracy than Support Vector Machine and Logistic Regression.
Random forest and support vector machine classifiers can tolerate noise contamination in data up to 5%.