Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method

Chen, Zai Yu; Yao, Bao Heng; Guo, Mei Na

doi:10.1051/matecconf/20166304027

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…In summary, this method is simple and demands no parameters to compute, which satisfies R1 and R2. However, despite SVF shows consistent results for different dimensions, as recently reinforced by a modified version [Chen et al, 2016], it may not properly work for attractors whose genii (number of voids in the manifold) is greater than 1, thus it does not fully meet R3. Gautama et al [2003] realized that a deterministic attractor should have a well-formed structure and, therefore, low entropy.…”

Section: Related Workmentioning

confidence: 93%

Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling

Pagliosa¹,

Telea²,

Mello³

2020

Preprint

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The reconstruction of phase spaces is an essential step to analyze time series according to Dynamical System concepts. A regression performed on such spaces unveils the relationships among system states from which we can derive their generating rules, that is, the most probable set of functions responsible for generating observations along time. In this sense, most approaches rely on Takens' embedding theorem to unfold the phase space, which requires the embedding dimension and the time delay. Moreover, although several methods have been proposed to empirically estimate those parameters, they still face limitations due to their lack of consistency and robustness, which has motivated this paper. As an alternative, we here propose an artificial neural network with a forgetting mechanism to implicitly learn the phase spaces properties, whatever they are. Such network trains on forecasting errors and, after converging, its architecture is used to estimate the embedding parameters. Experimental results confirm that our approach is either as competitive as or better than most state-of-the-art strategies while revealing the temporal relationship among time-series observations.

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Section: Related Workmentioning

confidence: 93%

Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling

Pagliosa¹,

Telea²,

Mello³

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Methods to estimate the optimal time delay (Section 4.2.1) can be mainly grouped in two categories: the ones that use series correlation (FRASER; SWINNEY, 1986;ALBANO et al, 1987;PASSAMANTE;FARRELL, 1991;MA;HAN, 2006), and the ones based on the phase-space expansion (KEMBER;FOWLER, 1993;ROSENSTEIN;COLLINS;LUCA, 1994;GUO, 2016). Despite their differences, such methods do not attempt to estimate in the process, usually performing computations on the time series itself (which, roughly speaking, is the same as using an embedding dimension = 1) or on some predefined .…”

Section: Assuming Independence Of Embedding Parametersmentioning

confidence: 99%

“…Similarly, Chen, Yao and Guo (2016) proposed Singular Entropy (SE), a modified version of SVF. They based their algorithm on the same principle of equality as SVF, but used the ratio of the entropy of eigenvalues instead…”

Section: Ie In Function Of the Singular Valuesmentioning

confidence: 99%

Exploring chaotic time series and phase spaces

Pagliosa¹

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Technology advances have allowed and inspired the study of data produced along time from applications such as health treatment, biology, sentiment analysis, and entertainment. Those types of data, typically referred to as time series or data streams, have motivated several studies mainly in the area of Machine Learning and Statistics to infer models for performing prediction and classification. However, several studies either employ batchdriven strategies to address temporal data or do not consider chaotic observations, thus missing recurrent patterns and other temporal dependencies especially in real-world data. In that scenario, we consider Dynamical Systems and Chaos Theory tools to improve datastream modeling and forecasting by investigating time-series phase spaces, reconstructed according to Takens' embedding theorem. This theorem relies on two essential embedding parameters, known as embedding dimension and time delay , which are complex to be estimated for real-world scenarios. Such difficulty derives from inconsistencies related to phase space partitioning, computation of probabilities, the curse of dimensionality, and noise. Moreover, an optimal phase space may be represented by attractors with different structures for different systems, which also aggregates to the problem.

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Algorithm Robustness Analysis for the Choice of Optimal Time Delay of Phase Space Reconstruction Based on Singular Entropy Method

Cited by 2 publications

References 12 publications

Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling

Supporting Optimal Phase Space Reconstructions Using Neural Network Architecture for Time Series Modeling

Exploring chaotic time series and phase spaces

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