Last data update: 2014.03.03

R: Average Mutual Information (AMI)
 mutualInformation R Documentation

## Average Mutual Information (AMI)

### Description

Functions for estimating the Average Mutual Information (AMI) of a time series.

### Usage

mutualInformation(time.series, lag.max = NULL, n.partitions = NULL,
units = c("Nats", "Bits", "Bans"), do.plot = TRUE, ...)

## S3 method for class 'mutualInf'
plot(x, main = "Average Mutual Information (AMI)",
xlab = "Time lag", ylab = NULL, type = "h", ...)

## S3 method for class 'mutualInf'
as.numeric(x, ...)

## S3 method for class 'mutualInf'
x[i]

## S3 method for class 'mutualInf'
x[[i]]

### Arguments

 time.series The observed time series. lag.max Largest lag at which to calculate the AMI. n.partitions Number of bins used to compute the probability distribution of the time series. units The units for the mutual information. Allowed units are "Nats", "Bits" or "Bans" (somethings called Hartleys). Default is "Nats". do.plot Logical value. If TRUE, the AMI is plotted ... Further arguments for the plotting function. x A mutualInf object. main Title for the plot. xlab Title for the x axis. ylab Title for the y axis. type Type of plot to be drawn. i Indices specifying elements to extract.

### Details

The Average Mutual Information (AMI) measures how much one random variable tells us about another. In the context of time series analysis, AMI helps to quantify the amount of knowledge gained about the value of x(t+tau) when observing x(t).

To measure the AMI iof a time series, we create a histogram of the data using bins. Let Pi the probability that the signal has a value inside the ith bin, and let Pij(tau) be the probability that x(t) is in bin i ans x(t+tau) is in bin j. Then, AMI for time delay tau is defined as

AMI(tau) = sum( Pij log( Pij / (Pi*Pj) ) )

Depending on the base of the logarithm used to define AMI, the AMI is measured in bits (base 2, also called shannons), nats (base e) or bans (base 10, also called hartleys).

### Value

A mutualInf object that consist of a list containing all the relevant information of the AMI computation: time.lag, mutual.information, units and n.partitions.

### Author(s)

Constantino A. Garcia

### References

H. Kantz and T. Schreiber: Nonlinear Time series Analysis (Cambridge university press) H. Abarbanel: Analysis of observed chaotic data (Springer, 1996).