Correlations in Complex Systems

Yulmetyev, Renat M.; Hänggi, Peter

doi:10.1007/978-0-387-30440-3_105

Cited by 3 publications

(2 citation statements)

References 94 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In some literature this quantity is known as the correlation [4], we cautiously use the term covariance here to distinguish it from the statistical correlation ,…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The derivation of mutual information and covariance function using centered random variables

Razak¹

2014

AIP Conference Proceedings

View full text Add to dashboard Cite

Information theoretic measures such as Mutual Information are often said to be able to measure nonlinear dependencies whereas covariance (and correlation) are able to measure only linear dependencies. We aim to illustrate this claim using centered random variables. The set of centered random variable is mapped from . For , we derive the relationship between the Mutual Information function, , and the covariance function, , and show that . Furthermore we show that when , the nonlinearities are captured by Mutual Information by highlighting a case where .

show abstract

“…In some literature this quantity is known as the correlation [4], we cautiously use the term covariance here to distinguish it from the statistical correlation ,…”

Section: Introductionmentioning

confidence: 99%

“…and thus can be substituted into the Mutual Information formula in equation (4) to get (X, Y) (X, Y)…”

mentioning

confidence: 99%

The derivation of mutual information and covariance function using centered random variables

Razak¹

2014

AIP Conference Proceedings

View full text Add to dashboard Cite

show abstract

Discrimination and Characterization of Parkinsonian Rest Tremors by Analyzing Long-Term Correlations and Multifractal Signatures

Livi

Sadeghian

2016

IEEE Trans. Biomed. Eng.

View full text Add to dashboard Cite

In this paper, we analyze 48 signals of rest tremor velocity related to 12 distinct subjects affected by Parkinson's disease. The subjects belong to two different groups, high-and low-amplitude rest tremors, with four and eight subjects, respectively. Each subject has been tested in four settings given by combining the use of deep brain stimulation and L-DOPA medication. We develop two main feature-based representations of such signals, which are obtained by considering (i) the long-term correlations and multifractal properties, and (ii) the power spectra. Such feature-based representations are initially utilized for the purpose of characterizing the subjects under different settings. Our results show that the effect of medication is clearly recognizable. In addition, when medication is used, we observe a change in the related signals from anti-correlated to long-term, positively correlated. In agreement with previous studies, we observe that deep brain stimulation does not significantly characterize neither of the two groups regardless of the adopted representation. On the other hand, the medication effect yields statistically significant differences in both high-and low-amplitude tremor groups. We successively test several different instances of the two featurebased representations of the signals in the setting of supervised classification and (nonlinear) feature transformation. We consider three different classification problems, involving the recognition of (i) the presence of medication, (ii) the use of deep brain stimulation, and (iii) the membership to the high-and low-amplitude tremor groups. Classification results show that the use of medication can be discriminated with higher accuracy, considering many of the feature-based representations. Notably, we show that the best results are obtained with a parsimonious, two-dimensional representation encoding the long-term correlations and multifractal character of the signals.

show abstract

Mutual information based measures on complex interdependent networks of neuro data sets

Razak¹

2013

View full text Add to dashboard Cite

Correlations in Complex Systems

Abstract: Correlations in Complex SystemsPlease note that the pagination is not final; in the print version an entry will in general not start on a new page.Editor's or typesetter's annotations (will be removed before the final T E X run)

Cited by 3 publications

References 94 publications

The derivation of mutual information and covariance function using centered random variables

The derivation of mutual information and covariance function using centered random variables

Discrimination and Characterization of Parkinsonian Rest Tremors by Analyzing Long-Term Correlations and Multifractal Signatures

Mutual information based measures on complex interdependent networks of neuro data sets

Contact Info

Product

Resources

About