Analysis of Observed Chaotic Data

Abarbanel, Henry D. I.

doi:10.1007/978-1-4612-0763-4

Cited by 1,323 publications

(1,017 citation statements)

References 55 publications

Supporting

Mentioning

974

Contrasting

Unclassified

Order By: Relevance

“…Finite time Lyapunov exponents (FTL) have been introduced to quantify dynamical instabilities over a finite interval of time [22,23,24,25]. They depend on time and on the initial conditions of the dynamical system.…”

Section: Quantitative Measures To Characterize Transient Dynamicsmentioning

confidence: 99%

Thresholds in transient dynamics of signal transduction pathways

Rateitschak¹

2010

Journal of Theoretical Biology

View full text Add to dashboard Cite

Section: Quantitative Measures To Characterize Transient Dynamicsmentioning

confidence: 99%

Thresholds in transient dynamics of signal transduction pathways

Rateitschak¹

2010

Journal of Theoretical Biology

View full text Add to dashboard Cite

“…Chaotic systems are very sensitive to initial conditions, and often appear to be random processes, even though they are deterministic. Because of the highly sensitive nature of some chaotic measures to noise [7], the presence of nonlinear and chaotic characteristics in speech is not easily confirmed. Different studies have produced varying conclusions about the question of chaotic components in speech, but the postulate that nonlinear components are present appears more solid [5].…”

Section: Nonlinear Analysis Of Speech Signalsmentioning

confidence: 99%

“…These parameters will be discussed in further detail in chapter 3. As stated previously, this RPS can be used to estimate the dynamical invariants [7] of the system. This work uses the shape or density of the RPS as a basis for modeling and classification of speech phonemes.…”

Section: Dynamical Systemsmentioning

confidence: 99%

“…These methods involve first minimum of auto-mutual information and first zero of autocorrelation for lag identification, and global false nearest neighbors for dimension determination [7]. For the decision of time lag and embedding dimension in this thesis, the auto-mutual information and global false nearest neighbors methods are used, respectively.…”

Section: Rps Parametersmentioning

confidence: 99%

See 1 more Smart Citation

Sub-banded reconstructed phase spaces for speech recognition

Indrebo

Povinelli

Johnson

2006

Speech Communication

View full text Add to dashboard Cite

ii Preface A novel method for classification of speech phonemes, based on the combination of dynamical systems theory and filter banks, is introduced. The benefit of this approach is seen in its ability to model nonlinear characteristics of speech, something that traditional methods cannot do. The modeling tool that provides this capability is the reconstructed phase space. This space carries all the dynamical information present in the signal's underlying system. The reconstructed phase spaces used for modeling and classification of the phonemes are built using frequency sub-banded signals that are generated using a set of band-pass filters. This approach is motivated by empirical evidence that suggests humans process and recognize speech in sub-bands. Modeling and classification is performed on the sub-banded reconstructed phase spaces using Gaussian Mixture Models, and the results of the classifications for each sub-band are combined to form an overall classification. Several methods for the combination of the sub-band classifications are examined, and it is found that an un-weighted linear combination produces classification accuracies that are significantly higher than those of a classification system using reconstructed phase spaces of unfiltered signals. Results also demonstrate that the proposed phoneme classification system is competitive with state-of-the-art approaches.iii

show abstract

“…(Typically, the Whitney Embedding Theorem states that any smooth dynamical system of dimension D may be faithfully reconstructed in a space of 2D +1.) To measure the fraction of self-crossings as a function of embedding dimension, we use the concept of false nearest neighbors (Abarbanel, 1996). A false nearest neighbor test was performed on the all data, and converged to a dimension of 5.…”

Section: Local Expansion Ratesmentioning

confidence: 99%