CalculateInfDim {RHRV}

Information dimension of the RR time series

Description

Information dimension of the RR time series

Usage

CalculateInfDim(HRVData,
  indexNonLinearAnalysis = length(HRVData$NonLinearAnalysis),
  minEmbeddingDim = NULL, maxEmbeddingDim = NULL, timeLag = NULL,
  minFixedMass = 1e-04, maxFixedMass = 0.005, numberFixedMassPoints = 50,
  radius = 1, increasingRadiusFactor = 1.05, numberPoints = 500,
  theilerWindow = 100, doPlot = TRUE)

EstimateInfDim(HRVData,
  indexNonLinearAnalysis = length(HRVData$NonLinearAnalysis),
  regressionRange = NULL, useEmbeddings = NULL, doPlot = TRUE)

PlotInfDim(HRVData,
  indexNonLinearAnalysis = length(HRVData$NonLinearAnalysis), ...)

Arguments

HRVData

Data structure that stores the beats register and information related to it

indexNonLinearAnalysis

Reference to the data structure that will contain the nonlinear analysis.

minEmbeddingDim

Integer denoting the minimum dimension in which we shall embed the time series.

maxEmbeddingDim

Integer denoting the maximum dimension in which we shall embed the time series. Thus, we shall estimate the correlation dimension between minEmbeddingDim and maxEmbeddingDim.

timeLag

Integer denoting the number of time steps that will be use to construct the Takens' vectors.

minFixedMass

Minimum percentage of the total points that the algorithm shall use for the estimation.

maxFixedMass

Maximum percentage of the total points that the algorithm shall use for the estimation.

numberFixedMassPoints

The number of different fixed mass fractions between minFixedMass and maxFixedMass that the algorithm will use for estimation.

radius

Initial radius for searching neighbour points in the phase space. Ideally, it should be small enough so that the fixed mass contained in this radius is slightly greater than the minFixedMass. However, whereas the radius is not too large (so that the performance decreases) the choice is not critical.

increasingRadiusFactor

Numeric value. If no enough neighbours are found within radius, the radius is increased by a factor increasingRadiusFactor until succesful. Default: 1.05.

numberPoints

Number of reference points that the routine will try to use, saving computation time.

theilerWindow

Integer denoting the Theiler window: Two Takens' vectors must be separated by more than theilerWindow time steps in order to be considered neighbours. By using a Theiler window, we exclude temporally correlated vectors from our estimations.

doPlot

Logical value. If TRUE (default), a plot of the correlation sum with q=1 is shown

regressionRange

Vector with 2 components denoting the range where the function will perform linear regression

useEmbeddings

A numeric vector specifying which embedding dimensions should the algorithm use to compute the information dimension.

...

Additional plot parameters.

Details

The information dimension is a particular case of the generalized correlation dimension when setting the order q = 1. It is possible to demonstrate that the information dimension D_1 may be defined as: D_1=lim_{r \rightarrow 0} <\log p(r)>/\log(r). Here, p(r) is the probability of finding a neighbour in a neighbourhood of size r and <> is the mean value. Thus, the information dimension specifies how the average Shannon information scales with the radius r.

In order to estimate D_1, the algorithm looks for the scaling behaviour of the average radius that contains a given portion (a "fixed-mass") of the total points in the phase space. By performing a linear regression of \log(p)\;Vs.\;\log(<r>) (being p the fixed-mass of the total points), an estimate of D_1 is obtained. The user should run the method for different embedding dimensions for checking if D_1 saturates.

The calculations for the information dimension are heavier than those needed for the correlation dimension.

Value

The CalculateCorrDim returns the HRVData structure containing a infDim object storing the results of the correlation sum (see infDim) of the RR time series.

The EstimateInfDim function estimates the information dimension of the RR time series by averaging the slopes of the correlation sums with q=1. The slopes are determined by performing a linear regression over the radius' range specified in regressionRange.If doPlot is TRUE, a graphic of the regression over the data is shown. The results are returned into the HRVData structure, under the NonLinearAnalysis list.

PlotInfDim shows a graphics of the correlation sum with q=1.

Note

In order to run EstimateInfDim, it is necessary to have performed the correlation sum before with ComputeInfDim.

References

H. Kantz and T. Schreiber: Nonlinear Time series Analysis (Cambridge university press)

See Also

CalculateCorrDim.