毕业设计+课设-内核自适应滤波的Matlab基准工具箱.zip

matlab算法，工具源码 Kernel Adaptive Filtering Toolbox === A Matlab benchmarking toolbox for kernel adaptive filtering. Kernel adaptive filters are online machine learning algorithms based on kernel methods. Typical applications include time-series prediction, nonlinear adaptive filtering, tracking and online learning for nonlinear regression. This toolbox includes algorithms, demos, and tools to compare their performance. <p align="center"> <img src="doc/kaf_diagram.png" width="60%"> <div align="center"><i>Nonlinear system identification using kernel adaptive filtering.</i></div> </p> Maintainer: [Steven Van Vaerenbergh](http://gtas.unican.es/people/steven), University of Cantabria, Spain. Contributors: - [Miguel Lazaro-Gredilla](http://www.tsc.uc3m.es/~miguel), Universidad Carlos III de Madrid, Spain. - [Sohan Seth](http://www.sohanseth.com/), University of Edinburgh, UK. - [Masahiro Yukawa](http://www.ykw.elec.keio.ac.jp/yukawa/), Keio University, Japan. - [Masa-aki Takizawa](http://www.ykw.elec.keio.ac.jp/member.html), Keio University, Japan. - [Osamu Toda](http://www.ykw.elec.keio.ac.jp/member.html), Keio University, Japan. - [Motoya Ohnishi](http://www.ykw.elec.keio.ac.jp/member.html), Keio University, Japan. - [Dominik Rzepka](http://home.agh.edu.pl/~drzepka/), AGH University of Science and Technology, Poland. - [Pantelis Bouboulis](http://bouboulis.mysch.gr/), University of Athens, Greece. - [Stephan Rhode](https://www.fast.kit.edu/lff/1011_3295.php), Karlsruher Institut f&uuml;r Technologie, Germany. Official web: https://github.com/steven2358/kafbox/ This toolbox is a collaborative effort: every developer wishing to contribute code or suggestions can do so. More info below. Sample run --- Figure generated by `demo/demo_sample_run.m`. <p align="center"> <img src="demo/fig/kafbox_sample_run.gif" width="75%"> <div align="center"><i>Online learning of a 1D nonlinear regression by a kernel adaptive filter on a fixed budget.</i></div> </p> Directories included in the toolbox --- `data/` - data sets `demo/` - demos and test files `doc/` - documentation `lib/` - algorithm libraries and utilities Setup --- 1. Run `install.m` to add the toolbox folders to the path. 2. Type `savepath` to save the changes to the path. Octave / Matlab pre-2008a ------------------------- This toolbox uses the `classdef` command which is not supported in Matlab pre-2008a and not yet in Octave. The older 0.x versions of this toolbox do not use `classdef` 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: ```matlab options = struct('nu',1E-4,'kerneltype','gauss','kernelpar',32); ``` Next, create an instance of the filter. E.g., for an instance of the original KRLS algorithm run: ```matlab kaf = krls(options); ``` One iteration of training is performed by feeding one input-output data pair to the filter: ```matlab kaf.train(x,y); ``` The outputs for one or more test inputs are evaluated as follows: ```matlab Y_test = kaf.evaluate(X_test); ``` Example: time-series prediction --- Code from `demo/demo_prediction.m` ```matlab % Demo: 1-step ahead prediction on Lorenz attractor time-series data [X,Y] = kafbox_data(struct('file','lorenz.dat','embedding',6)); % make a kernel adaptive filter object of class krls with options: % ALD threshold 1E-4, Gaussian kernel, and kernel width 32 kaf = krls(struct('nu',1E-4,'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.train(X(i,:),Y(i)); % train with one input-output pair end fprintf('\n'); SE = (Y-Y_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 Citing KAFBOX --- If you use this toolbox in your research please cite ["A Comparative Study of Kernel Adaptive Filtering Algorithms"](http://gtas.unican.es/pub/356): @inproceedings{vanvaerenbergh2013comparative, author = {Van Vaerenbergh, Steven and Santamar{\'i}a, Ignacio}, booktitle = {2013 IEEE Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE)}, title = {A Comparative Study of Kernel Adaptive Filtering Algorithms}, doi = {10.1109/DSP-SPE.2013.6642587}, pages = {181--186}, year = {2013}, month = aug, note = {Software available at \url{https://github.com/steven2358/kafbox/}} } Included algorithms --- - Kernel Recursive Least-Squares (KRLS) algorithm with approximate linear dependency criterion, as proposed in Y. Engel, S. Mannor, and R. Meir. "The kernel recursive least-squares algorithm", IEEE Transactions on Signal Processing, volume 52, no. 8, pages 2275-2285, 2004. - Sliding-Window Kernel Recursive Least-Squares (SW-KRLS), as proposed in S. Van Vaerenbergh, J. Via, and I. Santamaria. "A sliding-window 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 2165-2176, 2004. - Kernel Least-Mean-Square (KLMS), as proposed in W. Liu, P.P. Pokharel, and J.C. Principe, "The Kernel Least-Mean-Square Algorithm," IEEE Transactions on Signal Processing, vol.56, no.2, pp.543-554, Feb. 2008. - Fixed-Budget Kernel Recursive Least-Squares (FB-KRLS), as proposed in S. Van Vaerenbergh, I. Santamaria, W. Liu and J. C. Principe, "Fixed-Budget Kernel Recursive Least-Squares", 2010 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 2010), Dallas, Texas, U.S.A., March 2010. - Kernel Recursive Least-Squares Tracker (KRLS-T), as proposed in S. Van Vaerenbergh, M. Lazaro-Gredilla, and I. Santamaria, "Kernel Recursive Least-Squares Tracker for Time-Varying Regression," IEEE Transactions on Neural Networks and Learning Systems, vol.23, no.8, pp.1313-1326, 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 22-32. - Random Fourier Feature Kernel Least Mean Square (RFF-KLMS) algorithm, 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 (MLSP), Sept. 2012. - Extended Kernel Recursive Least Squares (EX-KRLS), 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. 3801-3814, oct. 2009. - Gaussian-Process based estimation of the parameters of KRLS-T, as proposed in Steven Van Vaerenbergh, Ignacio Santamaria, and Miguel Lazaro-Gredilla, "Estimation of the forgetting factor in kernel recursive least squares," 2012 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), Sept. 2012. - Kernel Affine Projection (KAP) 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 Least-Mean-Square (KNLMS) algorithm with Coherence Criterion, as proposed in C. Richard, J.C.M. Bermudez, P. Honeine, "Online Prediction of Time Series Data With K