
 Description:
Kernel Adaptive Filtering Toolbox
A Matlab benchmarking toolbox for kernel adaptive filtering.
This toolbox focuses on online and adaptive algorithms that use kernel methods to perform nonlinear regression. It includes algorithms, demos and tools to compare their performance.
Maintainer: Steven Van Vaerenbergh (steven at gtas dot dicom dot unican dot es)
Contributors:
 Miguel LazaroGredilla
 Sohan Seth
 Masahiro Yukawa
Official web: https://sourceforge.net/projects/kafbox
This toolbox is a collaborative effort: every developer wishing to contribute code or suggestions can do so. More info below.
Directories included in the toolbox
data/
 data setsdemo/
 demos and test fileslib/
 algorithm libraries and utilitiesSetup
Run install.m
Octave / Matlab pre2008a
This toolbox uses the
classdef
command which is not supported in Matlab pre2008a and not yet in Octave. The older 0.x versions of this toolbox do not useclassdef
and can therefore be used with all versions of Matlab and Octave. http://sourceforge.net/projects/kafbox/files/Usage
Each kernel adaptive filtering algorithm is implemented as a Matlab class. To use one, first define its options:
options = struct('nu',1E4,'kerneltype','gauss','kernelpar',32);
Next, create an instance of the filter:
kaf = aldkrls(options);
One iteration of training is performed by feeding one inputoutput data pair to the filter:
kaf = kaf.train(x,y);
The outputs for one or more test inputs are evaluated as follows:
Y_test = kaf.evaluate(X_test);
Example: timeseries prediction
Code from
demo/demo_prediction.m
% Demo: 1step ahead prediction on Lorenz attractor timeseries data [X,Y] = kafbox_data(struct('file','lorenz.dat','embedding',6)); % make a kernel adaptive filter object of class aldkrls with options: % ALD threshold 1E4, Gaussian kernel, and kernel width 32 kaf = aldkrls(struct('nu',1E4,'kerneltype','gauss','kernelpar',32)); %% RUN ALGORITHM N = size(X,1); Y_est = zeros(N,1); for i=1:N, if ~mod(i,floor(N/10)), fprintf('.'); end % progress indicator, 10 dots Y_est(i) = kaf.evaluate(X(i,:)); % predict the next output kaf = kaf.train(X(i,:),Y(i)); % train with one inputoutput pair end fprintf('\n'); SE = (YY_est).^2; % test error %% OUTPUT fprintf('MSE after first 1000 samples: %.2fdB\n\n',10*log10(mean(SE(1001:end))));
Result:
MSE after first 1000 samples: 40.17dB
Included algorithms
 Approximate Linear Dependency Kernel Recursive LeastSquares (ALDKRLS), as proposed in Y. Engel, S. Mannor, and R. Meir. "The kernel recursive leastsquares algorithm", IEEE Transactions on Signal Processing, volume 52, no. 8, pages 22752285, 2004.
 SlidingWindow Kernel Recursive LeastSquares (SWKRLS), as proposed in S. Van Vaerenbergh, J. Via, and I. Santamaria. "A slidingwindow kernel RLS algorithm and its application to nonlinear channel identification", 2006 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), Toulouse, France, 2006.
 Naive Online Regularized Risk Minimization Algorithm (NORMA), as proposed in J. Kivinen, A. Smola and C. Williamson. "Online Learning with Kernels", IEEE Transactions on Signal Processing, volume 52, no. 8, pages 21652176, 2004.
 Kernel LeastMeanSquare (KLMS), as proposed in W. Liu, P.P. Pokharel, and J.C. Principe, "The Kernel LeastMeanSquare Algorithm," IEEE Transactions on Signal Processing, vol.56, no.2, pp.543554, Feb. 2008.
 FixedBudget Kernel Recursive LeastSquares (FBKRLS), as proposed in S. Van Vaerenbergh, I. Santamaria, W. Liu and J. C. Principe, "FixedBudget Kernel Recursive LeastSquares", 2010 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010), Dallas, Texas, U.S.A., March 2010.
 Kernel Recursive LeastSquares Tracker (KRLST), as proposed in S. Van Vaerenbergh, M. LazaroGredilla, and I. Santamaria, "Kernel Recursive LeastSquares Tracker for TimeVarying Regression," Neural Networks and Learning Systems, IEEE Transactions on , vol.23, no.8, pp.13131326, Aug. 2012.
 Quantized Kernel Least Mean Squares (QKLMS), as proposed in Chen B., Zhao S., Zhu P., Principe J.C. "Quantized Kernel Least Mean Square Algorithm," IEEE Transactions on Neural Networks and Learning Systems, vol.23, no.1, Jan. 2012, pages 2232.
 Random Fourier Fourier Feature Kernel Least Mean Squares (RFFKLMS), as proposed in Abhishek Singh, Narendra Ahuja and Pierre Moulin, "Online Learning With Kernels: Overcoming The Growing Sum Problem", 2012 IEEE International Workshop on Machine Learning For Signal Processing.
 Extended Kernel Recursive Least Squares (EXKRLS), as proposed in W. Liu and I. Park and Y. Wang and J.C. Principe, "Extended kernel recursive least squares algorithm", IEEE Transactions on Signal Processing, volume 57, number 10, pp. 38013814, oct. 2009.
 GaussianProcess based estimation of the parameters of KRLST, as proposed in Steven Van Vaerenbergh, Ignacio Santamaria, and Miguel LazaroGredilla, "Estimation of the forgetting factor in kernel recursive least squares," 2012 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2012.
 Kernel Affine Projection algorithm with Coherence Criterion, as proposed in C. Richard, J.C.M. Bermudez, P. Honeine, "Online Prediction of Time Series Data With Kernels," IEEE Transactions on Signal Processing, vol.57, no.3, pp.1058,1067, March 2009.
 Kernel Normalized LeastMeanSquare algorithm with Coherence Criterion, as proposed in C. Richard, J.C.M. Bermudez, P. Honeine, "Online Prediction of Time Series Data With Kernels," IEEE Transactions on Signal Processing, vol.57, no.3, pp.1058,1067, March 2009.
 Recursive LeastSquares algorithm with exponential weighting (RLS), as described in S. Haykin, "Adaptive Filtering Theory (3rd Ed.)", Prentice Hall, Chapter 13.
 Multikernel Normalized Least Mean Square algorithm with Coherencebased Sparsification (MKNLMSCS), as proposed in M. Yukawa, "Multikernel Adaptive Filtering", IEEE Transactions on Signal Processing, vol.60, no.9, pp.46724682, Sept. 2012.
 Parallel HYperslab Projection along Affine SubSpace (PHYPASS) algorithm, as described in M. Takizawa and M. Yukawa, "An Efficient DataReusing Kernel Adaptive Filtering Algorithm Based on Parallel Hyperslab Projection Along Affine Subspace," 2013 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp.35573561, May 2013.
How to contribute code to the toolbox
Option 1: email it to me (steven@gtas.dicom.unican.es)
Option 2: Fork the toolbox on GitHub, push your change to a named branch, then send me a pull request.
License
This source code is released under the FreeBSD License.
 Changes to previous version:
Initial Announcement on mloss.org.
 BibTeX Entry: Download
 URL: Project Homepage
 Supported Operating Systems: Platform Independent
 Data Formats: Any Format Supported By Matlab
 Tags: Regression, Online Learning, Kernel Methods, Gaussian Processes
 Archive: download here
Other available revisons

Version Changelog Date 1.4 
Improvements and demo script for profiler

Initial version of documentation

Several new algorithms
May 26, 2014, 18:24:23 1.3 Inclusion of Gaussian process based parameter estimation, and several new regression algorithms.
October 21, 2013, 18:15:23 1.2 Initial Announcement on mloss.org.
September 2, 2013, 20:22:31 
Improvements and demo script for profiler
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