Recurrence-based time series analysis by means of complex network methods (1010.6032v1)

Abstract: Complex networks are an important paradigm of modern complex systems sciences which allows quantitatively assessing the structural properties of systems composed of different interacting entities. During the last years, intensive efforts have been spent on applying network-based concepts also for the analysis of dynamically relevant higher-order statistical properties of time series. Notably, many corresponding approaches are closely related with the concept of recurrence in phase space. In this paper, we review recent methodological advances in time series analysis based on complex networks, with a special emphasis on methods founded on recurrence plots. The potentials and limitations of the individual methods are discussed and illustrated for paradigmatic examples of dynamical systems as well as for real-world time series. Complex network measures are shown to provide information about structural features of dynamical systems that are complementary to those characterized by other methods of time series analysis and, hence, substantially enrich the knowledge gathered from other existing (linear as well as nonlinear) approaches.

• The paper pioneers a method that transforms recurrence plots into complex networks to extract detailed insights from time series data.
• It leverages network measures like degree centrality, clustering coefficients, and motif distributions to differentiate between periodic and chaotic dynamics.
• The approach is practically applied to classify dynamical systems and detect transitions in examples such as clarinet tones and geological climate records.

Recurrence-Based Time Series Analysis Using Complex Network Methods

The paper "Recurrence-Based Time Series Analysis by Means of Complex Network Methods" introduces a novel approach to time series analysis by reinterpreting the concept of recurrence plots within the framework of complex networks. This work bridges two established areas in complex systems science: the recurrence plot analysis used in nonlinear dynamics and the analysis of complex networks, a tool for understanding interconnected systems.

The fundamental innovation of this paper is the transformation of recurrence plots into complex networks. By treating recurrence plots as adjacency matrices, the authors explore the structural and geometric properties of dynamical systems through the lens of graph theory. The key idea is to use network-theoretic measures, such as degree centrality, clustering coefficients, and motif distributions, to extract insights about the underlying dynamics of the system that are not easily accessible through traditional time series analysis.

Methodological Insights

The authors provide a comprehensive overview of three primary methodologies for constructing complex networks from time series:

1. Proximity Networks: These networks use the closeness of trajectory segments as a criterion for connectivity, resulting in representations such as cycle networks and correlation networks.
2. Visibility Graphs: This method translates the time series into networks by establishing links based on geometric visibility between data points, presenting a novel way to capture temporal patterns.
3. Transition Networks: Here, state transitions are mapped directly into network edges, offering a straightforward interpretation of dynamical transitions.

Among these, recurrence networks derived from recurrence plots offer a particularly compelling approach. By encoding recurrence relations as edges in a network, these networks capture the local and global geometric information of the attractor in phase space.

Numerical Results and Claims

The paper highlights several significant results:

• Robust Classification and Detection Capabilities: Through network measures, the authors demonstrate a robust capability to distinguish between periodic and chaotic regimes, detect dynamical transitions, and identify invariant structures.
• Practical Applications: The paper showcases two applications: the classification of dynamical systems and the identification of dynamical transitions, with compelling examples including clarinet tones and geological climate records.
• Complementary to Traditional Methods: Recurrence networks are shown to characterize distinct properties of complex systems compared to traditional recurrence quantification analysis (RQA), capturing geometric aspects that RQA may not.

Implications and Future Perspectives

This research opens up several avenues for further investigation. The potential applicability of recurrence networks spans domains such as ecology, finance, and climate science, where understanding complex dynamics is crucial. The connection between network-based analysis and nonlinear time series methods could lead to new hybrid techniques that leverage the strengths of both approaches.

Future work may explore the scalability of these methods to high-dimensional datasets and examine the impact of different network construction parameters across diverse applications. Additionally, tuning the methodology for specific domains, particularly for handling real-world data imperfections like noise and missing values, remains an important task.

In summary, this paper represents a significant methodological advancement in the analysis of complex systems. By merging recurrence plots with complex network analysis, it provides a new, complementary toolset for dissecting the intricacies of time series data, offering insights that could enhance the comprehension and modeling of complex dynamical systems across various scientific fields.