Changes sfa-tk.V2

Author:            Wolfgang Konen, wolfgang.konen@fh-koeln.de

Created:          Nov’2009

Last modified: Nov’2009

This document is a summary of changes in sfa-tk.V2 as compared to sfa-tk.V1.0.1:

• lcov_pca2.m: same interface as lcov_pca.m but better numerical stability in the case where the covariance matrix object becomes singular.
• sfa_step.m: new parameters method and dbg, handed over to sfa2_step.m. Added default settings for method and dbg, depending on step.
• sfa2_step.m:
1. In step ‘sfa’: method=’GEN_EIG’ is the original [Berkes03]-code; method=’SVD_SFA’ is the new [Konen09b]-method using lcov_pca2.m, along the lines of [WisSej02]. If dbg>0, then both branches are executed and their results are compared with sfa2_dbg.m. If method=’SVD_SFA’, the matrices DSF and SF are reduced to those dimensions with eigenvalue  ¹ 0 in D.
2. Added check and warning w.r.t. ill-conditionedness of matrix B for method=’GEN_EIG’. Always print rank(B).
3. In step ‘expansion’: method=’TIMESERIES’ is the original Berkes-code where the goal is to minimize the time difference signal. The method=’CLASSIF’ is new for classification purposes, along the lines of [Berkes05]. Each data chunk is assumed to be a set of patterns for the same class, and the goal is to minimize the pairwise pattern difference for all pairs existing in this chunk of data. (I.e. if the data of a certain class label are presented in several chunks, then only the pairs among each chunk are formed. Therefore it is recommended to add each class label in one chunk, if possible.)
4. in step ‘preprocessing -> expansion’: New branch for SFA_STRUCTS{hdl}.pp_type=’PCA2’: similar to ‘PCA’, but use lcov_pca2.m instead of lcov_pca.m for whitening of input data and throw away those dimensions with eigenvalue close to zero.
• sfa2_dbg.m: called from sfa2_step.m if dbg>0 and method=’SVD_SFA’. Is only needed for debugging purposes.
1. Several checks are performed on the results from ’GEN_EIG’ and ’SVD_SFA’. See rich documented source code for further details.
2. The part with OLD_VERSION==1 is only for debugging comparisions, it contains the old, no longer recommended version of ‘SVD_SFA’. Note that in case OLD_VERSION==1 the call to step ‘sfa’ in sfa_step.m (or sfa2_step.m) has to be
   sfa_step(hdl, x, 'sfa', method); instead of 
   sfa_step(hdl, [], 'sfa', method); and the data in x have to contain all training data in one chunk
• sfa2.m:
1. additional check with matrix Cslow, which prints a warning, if some of the slow (training) signals have variance <>1.
2. added parameter method (=’GEN_EIG’,’SVD_SFA’) to the input of sfa2.
3. added parameter pp_type (=’PCA’,’PCA2’ ,’PCAVAR’) to the input of sfa2.
• gaussCreate.m: create an Gaussian classifier object
• gaussClassifier.m: train or apply a Gaussian classifier HDL, which has been created before with gaussCreate.m.
  Remark: if the data entered during training are not normally distributed, the inversion of the full covariance matrix can become numerically difficult. It is the recommended to call gaussClassifier.m with aligned=1 which zeros the off-diagonal elements of the covariance matrix (and aligns the Gaussian ellipsoid with the coordinate axes). This is always numerically robust.
• gauss_clearall.m: clear all Gaussian classifier objects.
• drive1.m: demo for driving force experiments [Konen09a, Wis03c]. Additional parameter noiseperc allows to inject noise into the time series.
• class_demo1.m: demo for classification experiments à la [Berkes05] on synthetic data.
• class_demo2.m: demo for classification experiments à la [Berkes05] on real data (UCI repository or gesture data).
• class_CVdemo2.m: demo for classification experimentsà la [Berkes05] with cross validataion on real data (UCI repository or gesture data).

Literature

• [Wis03c] Wiskott, L. (12. December 2003). Estimating driving forces of nonstationary time series with slow feature analysis. arXiv.org e-Print archive, http://arxiv.org/abs/cond-mat/0312317.
• [Berkes05] Pietro Berkes: Pattern recognition with Slow Feature Analysis. Cognitive Sciences EPrint Archive (CogPrint) 4104, http://cogprints.org/4104/ (2005).
• [Berkes03] Berkes, P.  SFA-TK: Slow Feature Analysis Toolkit for Matlab (v.1.0.1). http://itb.biologie.hu-berlin.de/~berkes/software/sfa-tk/sfa-tk.shtml or http://people.brandeis.edu/~berkes/software/sfa-tk/index.html.
• [Konen09a] Konen, W. (2009).  How slow is slow? SFA detects signals that are slower than the driving force. arXiv.org e-Print archive, http://arXiv.org, in preparation.
• [Konen09b] Konen, W. (2009). On the numeric stability of the SFA implementation sfa-tk. arXiv.org e-Print archive, http://arXiv.org, in preparation.