In RobertGM111/Tangle: Calcuates Tangle of a Time Series

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.path = "man/figures/README-",
  out.width = "100%"
)
library(nonlinearTseries)

Tangle

Tangle is a means of quantifying complexity in relatively short time series data.

Installation

You can install a development version of Tangle from github with:

library(devtools)
install_github("RobertGM111/Tangle")
library(Tangle)

Visual

Tangle algorithm in process: (a) 0 iterations, (b) 500 iterations, and (c) 10,000 iterations.

par(mai=c(.1,.1,.2,.1))
par(mfrow=c(1,3))

#XP <- read.csv("~/Documents/APS2016/XP.csv")
XP <- lorenz(time = seq(0,100,.01), do.plot = FALSE)
# tau.ami = timeLag(XP$x, technique = "ami",
#                   lag.max = 100, do.plot = FALSE)
# emb.dim = estimateEmbeddingDim(XP$x, time.lag = tau.ami,
#                                max.embedding.dim = 15,do.plot = FALSE)
tak = cbind(XP$x,XP$y,XP$z)
plot(x=NULL, y=NULL, type="n", xlab=NA, ylab=NA,
     xlim=c(-3, 3), ylim=c(-3, 3),frame=FALSE,main="a",
     xaxt='n', yaxt='n')
lines(scale(XP$x), scale(XP$z), col=rgb(0,0,0,.8),lwd=1)

XP <- lorenz(time = seq(0,100,.05), do.plot = FALSE)
# tau.ami = timeLag(XP$x, technique = "ami",
#                   lag.max = 100, do.plot = FALSE)
# emb.dim = estimateEmbeddingDim(XP$x, time.lag = tau.ami,
#                                max.embedding.dim = 15,do.plot = FALSE)
tak = cbind(XP$x,XP$y,XP$z)

N<-nrow(tak)# Number of samples
S<-diag(N) # Generate "upshift" matrix
S<-S[,c(dim(S)[2],(1:(dim(S)[2]-1)))]
W<-((diag(N)+S)/2)# Generate Updating matrix

for (i in 1:500){
  tak <- W%*%tak
  tak <- scale(tak)
}

plot(x=NULL, y=NULL, type="n", xlab=NA, ylab=NA,
     xlim=c(-3, 3), ylim=c(-3, 3),frame=FALSE,main="b",
     xaxt='n', yaxt='n')
lines(scale(tak[,1]), scale(tak[,3]), col=rgb(0,0,0,.8),lwd=1)

for (i in 1:10000){
  tak <- W%*%tak
  tak <- scale(tak)
}
plot(x=NULL, y=NULL, type="n", xlab=NA, ylab=NA,
     xlim=c(-3, 3), ylim=c(-3, 3),frame=FALSE,main="c",
     xaxt='n', yaxt='n')
lines(scale(tak[,1]), scale(tak[,3]), col=rgb(0,0,0,.8),lwd=1)

Example

Example use of tangle on a simulated time series

# Generate data from Lorenz attractor
library(nonlinearTseries)
lorTS <- lorenz(do.plot = FALSE)$x

# Downsample for example speed
samps <- seq(1, length(lorTS), length.out = 500)
lorTS <- lorTS[samps]

# Estimate tau
lorTau <- timeLag(lorTS)

# Calculate Tangle
tangle(lorTS, tau = lorTau)