Correlation Dimension of a Time Series

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Correlation Dimension of a Time Series
Madhulika Pannuri Intelligent Electronic
Systems Human and Systems Engineering Department
of Electrical and Computer Engineering
http//www.cavs.msstate.edu/hse/ies/publications/s
eminars/msstate/2006/dimension_estimation/
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Correlation Dimension from Correlation Integral
Correlation Integral It is a measure of the
spatial organization of chaotic
attractor. Where n is the total number of
points in the time series. Using Heaviside
function For a limited range of , it can be
found that That is correlation integral is
proportional to some power (D) of the epsilon. D
is called the correlation dimension of the
attractor.
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• Correlation dimension estimation

Read in the time series
Construct RPS using SVD Embedding to a much
Higher dimension
Compute the correlation integral for Rps.
Compute the correlation dimension with
appropriate differentiation
See Takens theorem and algorithm by Grassberger
and Procaccia.
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• Some results on Lorentz

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• Correlation Dimension

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• Currently working on

Correlation dimension on phonemes. The dimension
for some phonemes. Need to further run
experiments with the other implementations. Runnin
g experiments for Correlation dimension for
various speakers on sustained phones. Optimum
tau Next Task Complete experiments ASAP for
Interspeech. Further run several experiments on
sustained phones. Dimension estimates at
different SNRs. Reconstruct the phase space
using the time delay and correlation dimension
estimation.