rSFA (version 1.00)

sfa2: The SFA2 algorithm, degree 2 expansion.

Description

Y = sfa2(X) performs expanded Slow Feature Analysis on the input data X and returns the output signals Y ordered by increasing temporal variation, i.e. the first signal Y[,1] is the slowest varying one, Y[,2] the next slowest varying one and so on. The input data have to be organized with each variable on a column and each data point on a row, i.e. X(t,i) is the value of variable nr. i at time t. By Default an expansion to the space of 2nd degree polynomials is done, this can be changed by using different functions for xpDimFun and sfaExpandFun.

Usage

sfa2(x, method = "SVDSFA", ppType = "PCA",
    xpDimFun = xpDim, sfaExpandFun = sfaExpand)

Arguments

x

Input data

method

="SVDSFA" for singular value decomposition (recommended) or ="GENEIG" for generalized eigenvalues (unstable!) GENEIG is not implemented in the current version, since R lacks the option to calculate generalized eigenvalues easily.

ppType

preprocessing type: ="PCA" (principal component analysis) or ="SFA1" (linear sfa)

xpDimFun

Function to calculate dimension of expanded data

sfaExpandFun

Function to expand data

Value

• list sfaList with all learned information, where sfaList$y contains the Y outputs

References

sfaStep sfa1Create sfaExecute

Examples

## prepare input data for simple demo
t=seq.int(from=0,by=0.011,to=2*pi)
x1=sin(t)+cos(11*t)^2
x2=cos(11*t)
x=data.frame(x1,x2)
## perform sfa2 algorithm with data
res = sfa2(x)
## plot slowest varying function of result
plot(t, res$y[,1],type="l",main="output of the slowest varying function")
## see http://www.scholarpedia.org/article/Slow_feature_analysis#The_algorithm
## for detailed description of this example