Package 'rSFA' reference manual

Title:	Slow Feature Analysis
Description:	Slow Feature Analysis (SFA), ported to R based on 'matlab' implementations of SFA: 'SFA toolkit' 1.0 by Pietro Berkes and 'SFA toolkit' 2.8 by Wolfgang Konen.
Authors:	Wolfgang Konen <[email protected]>, Martin Zaefferer, Patrick Koch; Bug hunting and testing by Ayodele Fasika, Ashwin Kumar, Prawyn Jebakumar
Maintainer:	Martin Zaefferer <[email protected]>
License:	GPL (>= 2)
Version:	1.5
Built:	2024-11-01 06:48:17 UTC
Source:	CRAN

Slow Feature Analysis

Description

Slow Feature Analysis

Details

Package:	rSFA
Type:	Package
Version:	1.5
Date:	29.03.2022
Maintainer:	Martin Zaefferer [email protected]
License:	GPL (>= 2)
LazyLoad:	yes

Slow Feature Analysis (SFA), ported to R based on the matlab implementations SFA toolkit 1.0 by Pietro Berkes and SFA toolkit 2.8 by Wolfgang Konen.

Author(s)

Wolfgang Konen [email protected], Martin Zaefferer, Patrick Koch; Bug hunting and testing by Ayodele Fasika, Ashwin Kumar, Prawyn Jebakumar

Add noisy copies for parametric bootstrap

Description

Given training data X with true labels REALCLASS, add new records to X and REALCLASS, which are noisy copies of the training data.

Usage

addNoisyCopies(realclass, x, pars)
addNoisyCopies(realclass, x, pars)

Arguments

`realclass`	true class of training data (can be vector, numerics, integers, factors)
`x`	a matrix containing the training data
`pars`	list of parameters: `pars$ncopies`: Number of new records to add `pars$ncsort`: Defines if training data should be sorted by class. Default is FALSE `pars$ncsigma`: The noise in each column of x has the std.dev. pars$ncsigma(standard deviation of column). Default Value: 0.8 `pars$ncmethod`: =1: each 'old' record from X in turn is the centroid for a new pattern; =2: the centroid is the average of all records from the same class, the std.dev. is the same for all classes; =3: centroid as in '2', the std.dev. is the std.dev. of all records from the same class (recommended*)

Value

list res
- res contains two list entries: realclass and x (including added copies)

References

sfaPBootstrap

Computes the eta value of a signal (slowness)

Description

Computes the eta value of a signal (slowness)

Usage

etaval(x, T = length(x))
etaval(x, T = length(x))

Arguments

`x`	The columns of signal correspond to different input components. Must be normalized (zero mean, unit variance)
`T`	Time interval

Value

returns the eta value of the signal in a time interval T time units long.

Classifier for SFA demos

Description

Train or apply a Gaussian classifier..

Usage

gaussClassifier(gauss, y, realC, method = "train")
gaussClassifier(gauss, y, realC, method = "train")

Arguments

`gauss`	List created by gaussCreate. Contains also the elements: aligned =0: do not align the Gaussian classifiers with axes, use full covariance matrix =1 (default): set the off-diagonals in covariance matrix to 0, i.e. the Gaussian classifier is forced to be aligned with the axes. This is more robust in the case where the data deviate largely from a multivariate normal distribution. epsD [defaults to 0.04] replace diagonal elements of COV smaller than epsD with epsD to avoid too small Gaussians
`y`	K x M matrix where K is the total number of patterns and M is the number of variables used for classification. I.e. each row of y contains the data for one pattern.
`realC`	1 x K matrix with NCLASS distinct real class labels needed only for method='train'. In case of method="apply" realC is not used and can have any value
`method`	either "train" (default) or "apply"

Value

list gauss containing

`gauss$predC`	1 x K matrix: the predicted class
`gauss$prob`	K x NCLASS matrix: prob(k,n) is the estimated probability that pattern k belongs to class m

Create an Gaussian classifier object

Description

Create an Gaussian classifier object

Usage

gaussCreate(nclass, dimY)
gaussCreate(nclass, dimY)

Arguments

`nclass`	number of classes
`dimY`	dimension

Value

list of defaults for gauss classifier

The SFA1 algorithm, linear SFA.

Description

Y = sfa1(X) performs linear 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 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 nr. i at time t.

Usage

sfa1(x)
sfa1(x)

Arguments

`x`	Input data, each column a different variable

Value

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

Create structured list for linear SFA

Description

Create structured list for linear SFA

Usage

sfa1Create(sfaRange, axType = "ORD1", regCt = 0)
sfa1Create(sfaRange, axType = "ORD1", regCt = 0)

Arguments

`sfaRange`	number of slowly-varying functions to be kept
`axType`	is the type of derivative approximation to be used, see `sfaTimediff`
`regCt`	regularization constant, currently not used

Value

list sfaList contains all arguments passed into sfa1create plus

deg

This list will be expanded by other SFA functions with further SFa results

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.

Usage

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

Arguments

`x`	input data
`method`	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`

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

Create structured list for expanded SFA

Description

'Expanded' SFA means that the input data are expanded into a higher-dimensional space with the function sfaExpandFun. See sfaExpand for the default expansion function.

Usage

sfa2Create(
  ppRange,
  sfaRange,
  ppType = "SFA1",
  axType = "ORD1",
  regCt = 0,
  opts = NULL,
  xpDimFun = xpDim,
  sfaExpandFun = sfaExpand
)
sfa2Create(
  ppRange,
  sfaRange,
  ppType = "SFA1",
  axType = "ORD1",
  regCt = 0,
  opts = NULL,
  xpDimFun = xpDim,
  sfaExpandFun = sfaExpand
)

Arguments

`ppRange`	umber of dimensions to be kept after preprocessing step - or - a two-number vector with lower and upper dimension number
`sfaRange`	umber of slowly-varying functions to be kept
`ppType`	preprocessing type: ="PCA", "PCA2" (principal component analysis) or ="SFA1" (linear sfa)
`axType`	is the type of derivative approximation to be used, see `sfaTimediff`
`regCt`	regularization constant, currently not used
`opts`	optional list of additional options
`xpDimFun`	Function to calculate dimension of expanded data
`sfaExpandFun`	Function to expand data

Value

list sfaList contains all arguments passed into sfa2create plus

`xpRange`	evaluates to `xpDimFun(ppRange)`
`deg`	2

This list will be expanded by other SFA functions with further SFa results

Predict Class for SFA classification

Description

Create a SFA classification mode, predict & evaluate on new data (xtst,realc_tst).
Author of orig. matlab version: Wolfgang Konen, May 2009 - Jan 2010
See also [Berkes05] Pietro Berkes: Pattern recognition with Slow Feature Analysis. Cognitive Sciences EPrint Archive (CogPrint) 4104, http://cogprints.org/4104/ (2005)

Usage

sfaClassify(x, realclass, xtst = 0, realcTst = 0, opts)
sfaClassify(x, realclass, xtst = 0, realcTst = 0, opts)

Arguments

`x`	NREC x IDIM, training input data
`realclass`	1 x NREC, training class labels
`xtst`	NTST x IDIM, test input data
`realcTst`	1 x NTST, test class labels
`opts`	list with several parameter settings: gaussdim ... Filename [ = s,g,x] from where to load the models (see `sfaClassify`)

Value

list res containing

`res$errtrn`	1 x 2 matrix: error rate with / w/o SFA on training set
`res$errtst`	1 x 2 matrix: error rate with / w/o SFA on test set
`res$y`	output from SFA when applied to training data
`res$ytst`	output from SFA when applied to test data
`res$predT`	predictions with SFA + GaussClassifier on test set
`res$predX`	predictions w/o SFA (only GaussClassifier) on test set (only if opts.xFilename exists)

Predict Class for SFA classification

Description

Use a SFA classification model (stored in opts$*Filename), predict & evaluate on new data (xtst,realc_tst).
Author of orig. matlab version: Wolfgang Konen, Jan 2011-Mar 2011.
See also [Berkes05] Pietro Berkes: Pattern recognition with Slow Feature Analysis. Cognitive Sciences EPrint Archive (CogPrint) 4104, http://cogprints.org/4104/ (2005)

Usage

sfaClassPredict(xtst, realcTst, opts)
sfaClassPredict(xtst, realcTst, opts)

Arguments

xtst

NTST x IDIM, test input data

realcTst

1 x NTST, test class labels

opts

list with several parameter settings:

gaussdim
...
*Filename: [* = s,g,x] from where to load the models (see sfaClassify)

Value

list res containing

`res$errtst`	1 x 2 matrix: error rate with / w/o SFA on test set
`res$ytst`	output from SFA when applied to test data
`res$predT`	predictions with SFA + GaussClassifier on test set
`res$predX`	predictions w/o SFA (only GaussClassifier) on test set (only if opts.xFilename exists)

Execute learned function for input data

Description

After completion of the learning phase (step="sfa") this function can be used to apply the learned function to the input data.
The execution is completed in 4 steps:
1. projection on the input principal components (dimensionality reduction)
2. expansion (if necessary)
3. projection on the whitened (expanded) space
4. projection on the slow functions

Usage

sfaExecute(sfaList, DATA, prj = NULL, ncomp = NULL)
sfaExecute(sfaList, DATA, prj = NULL, ncomp = NULL)

Arguments

`sfaList`	A list that contains all information about the handled sfa-structure
`DATA`	Input data, each column a different variable
`prj`	If not NULL, the preprocessing step 1 is skipped for SFA2
`ncomp`	number of learned functions to be used

Value

matrix DATA containing the calculated output

Degree 2 Expansion

Description

Expand a signal in the space of polynomials of degree 2. This is the default expansion function used by rSFA.

Usage

sfaExpand(sfaList, DATA)
sfaExpand(sfaList, DATA)

Arguments

`sfaList`	A list that contains all information about the handled sfa-structure
`DATA`	Input data, each column a different variable

Value

expanded matrix DATA

Perform non-linear regression

Description

Given the data in arg, expand them nonlinearly in the same way as it was done in the SFA-object sfaList (expanded dimension M) and search the vector RCOEF of M constant coefficients, such that the sum of squared residuals between a given function in time FUNC and the function
R(t) = (v(t) - v0)' * RCOEF, t=1,...,T,
is minimal

Usage

sfaNlRegress(sfaList, arg, func)
sfaNlRegress(sfaList, arg, func)

Arguments

`sfaList`	A list that contains all information about the handled sfa-structure
`arg`	Input data, each column a different variable
`func`	(T x 1) the function to be fitted nonlinearly

Value

returns a list res with elements

`res$R`	(T x 1) the function fitted by NL-regression
`res$rcoef`	(M x 1) the coefficients for the NL-expanded dimensions

Parametric Bootstrap

Description

If training set too small, augment it with parametric bootstrap

Usage

sfaPBootstrap(realclass, x, sfaList)
sfaPBootstrap(realclass, x, sfaList)

Arguments

`realclass`	true class of training data (can be vector, numerics, integers, factors)
`x`	matrix containing the training data
`sfaList`	list with several parameter settings, e.g. as created by `sfa2Create` `sfaList$xpDimFun` (=xpDim by default) calculated dimension of expaned SFA space `sfaList$deg` degree of expansion (should not be 1, not implemented) `sfaList$ppRange` ppRange for SFA algorithm `sfaList$nclass` number of unique classes `sfaList$doPB` do (1) or do no (0) param. bootstrap.

Value

a list list containing:

`x`	training set extended to minimu number of recors1.5*(xpdim+nclass), if necessary
`realclass`	training class labels, extended analogously

Update a step of the SFA algorithm.

Description

sfaStep() updates the current step of the SFA algorithm. Depending on sfaList$deg it calls either sfa1Step or sfa2Step to do the main work. See further documentation there

Usage

sfaStep(sfaList, arg, step = NULL, method = NULL)
sfaStep(sfaList, arg, step = NULL, method = NULL)

Arguments

`sfaList`	A list that contains all information about the handled sfa-structure
`arg`	Input data, each column a different variable
`step`	Specifies the current SFA step. Must be given in the right sequence: for SFA1 objects: "preprocessing", "sfa" for SFA2 objects: "preprocessing", "expansion", "sfa" Each time a new step is invoked, the previous one is closed, which might take some time.
`method`	Method to be used: For `sfaList$step="expansion"` the choices are "TIMESERIES" or "CLASSIF". For `sfaList$step="sfa"` (`sfa2Step` only) the choices are "SVDSFA" (recommended) or "GENEIG" (unstable).

Value

list sfaList taken from the input, with new information added to this list. See sfa1Step or sfa2Step for details.

Examples

   ## Suppose you have divided your training data into two chunks,
   ## DATA1 and DATA2. Let the number of input dimensions be N. To apply
   ## SFA on them write:
   ## Not run:  
   sfaList = sfa2Create(N,xpDim(N))
   sfaList = sfaStep(sfaList, DATA1, "preprocessing")
   sfaList = sfaStep(sfaList, DATA2)
   sfaList = sfaStep(sfaList, DATA1, "expansion")
   sfaList = sfaStep(sfaList, DATA2)
   sfaList = sfaStep(sfaList, NULL, "sfa")
   output1 = sfaExecute(sfaList, DATA1)
   output2 = sfaExecute(sfaList, DATA2)
   
## End(Not run)

## Suppose you have divided your training data into two chunks,
   ## DATA1 and DATA2. Let the number of input dimensions be N. To apply
   ## SFA on them write:
   ## Not run:  
   sfaList = sfa2Create(N,xpDim(N))
   sfaList = sfaStep(sfaList, DATA1, "preprocessing")
   sfaList = sfaStep(sfaList, DATA2)
   sfaList = sfaStep(sfaList, DATA1, "expansion")
   sfaList = sfaStep(sfaList, DATA2)
   sfaList = sfaStep(sfaList, NULL, "sfa")
   output1 = sfaExecute(sfaList, DATA1)
   output2 = sfaExecute(sfaList, DATA2)
   
## End(Not run)

Calculates the first derivative of signal data

Description

Calculates the first derivative of signal data

Usage

sfaTimediff(DATA, axType = "ORD1")
sfaTimediff(DATA, axType = "ORD1")

Arguments

`DATA`	The matrix of signals for which the derivative is calculated (one column per signal)
`axType`	Type of interpolation: "ORD1" (default) first order, "SCD" second ,"TRD" third, "ORD3a" cubic polynom

Value

matrix DATA
- DATA contains the derivative signals, with the same structure as the input data.

Note

setting axType to invalid values will lead to first order interpolation.

Degree 2 Dimension Calculation

Description

Compute the dimension of a vector expanded in the space of polynomials of 2nd degree.

Usage

xpDim(n)
xpDim(n)

Arguments

`n`	Dimension of input vector

Value

Dimension of expanded vector

Package 'rSFA'

Help Index

Slow Feature Analysis

Description

Details

Author(s)

Add noisy copies for parametric bootstrap

Description

Usage

Arguments

Value

References

Computes the eta value of a signal (slowness)

Description

Usage

Arguments

Value

Classifier for SFA demos

Description

Usage

Arguments

Value

See Also

Create an Gaussian classifier object

Description

Usage

Arguments

Value

See Also

The SFA1 algorithm, linear SFA.

Description

Usage

Arguments

Value

See Also

Create structured list for linear SFA

Description

Usage

Arguments

Value

See Also

The SFA2 algorithm, SFA with degree 2 expansion.

Description

Usage

Arguments

Value

See Also

Examples

Create structured list for expanded SFA

Description

Usage

Arguments

Value

See Also

Predict Class for SFA classification

Description

Usage

Arguments

Value

See Also

Predict Class for SFA classification

Description

Usage

Arguments

Value

See Also

Execute learned function for input data

Description

Usage

Arguments

Value

See Also

Degree 2 Expansion

Description

Usage

Arguments

Value

See Also

Perform non-linear regression

Description