R: The SFA2 algorithm, SFA with degree 2 expansion.
sfa2
R Documentation
The SFA2 algorithm, SFA with 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 in a column and each data (time) point in a
row, i.e. X(t,i) is the value of variable 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.
eigenvector calculation method: ="SVDSFA" for singular value decomposition (recommended) or
="GENEIG" for generalized eigenvalues (unstable!). GENEIG is not implemented in the current version, since
R lacks an easy option to calculate generalized eigenvalues.
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 SFA information, among them are
y
a matrix containing the output Y (as described above)
-
all input parameters to sfa2Create
-
all elements of sfaList as specified in sfa2Step
See Also
sfa2Stepsfa2CreatesfaExecutesfa1
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
providing 
.