├── LICENSE ├── README.md ├── demo ├── demo_classif.m ├── demo_unmix.m └── visu_classif.m ├── unmix ├── README.md ├── USGS_1995_Library.mat ├── demo1_sparse_TV.m ├── prune_library.m ├── soft.m ├── sort_library_by_angle.m ├── sunsal.m └── sunsal_tv.m └── utils ├── get_reg_prox.m ├── gist_chinge.m ├── gist_hinge2.m ├── gist_least.m ├── gist_logreg.m ├── gist_opt.m ├── initoptions.m ├── l2_unmix.m ├── l2_unmix_simplex.m └── l2simplex.m /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | {project} Copyright (C) {year} {fullname} 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | Non-convex optimization Toolbox 2 | =============================== 3 | 4 | 5 | This matlab toolbox propose a generic solver for proximal gradient descent in the convex or non-convex case. It is a complete reimplementation of the GIST algorithm proposed in [1] with new regularization terms such as the lp pseudo-norm with p=1/2. 6 | 7 | When using this toolbox in your research works please cite the paper [Non-convex regularization in remote sensing](http://remi.flamary.com/biblio/tuia2016nonconvex.pdf): 8 | ``` 9 | D. Tuia, R. Flamary and M. Barlaud, "Non-convex regularization in remote sensing", 10 | IEEE transactions Transactions on Geoscience and Remote Sensing, (to appear) 2016. 11 | ``` 12 | 13 | The code solve optimization problems of the form: 14 | 15 | min_x f(x)+lambda g(x) 16 | 17 | We provide solvers for solving the following data fitting terms f(x) problems: 18 | - Least square (linear regression) 19 | - Linear SVM with quadratic Hinge loss 20 | - Linear logistic regression 21 | - Calibrated Hinge loss 22 | 23 | The regularization terms g(x) that have been implemented include: 24 | - Lasso (l1) 25 | - Ridge (squared l2) 26 | - Log sum penalty (LSP) ([2],prox in [1]) 27 | - lp regularization with p=1/2 (prox in [3]) 28 | - Group lasso (l1-l2) 29 | - Minimax concave penalty (MCP) 30 | - Indicator function on convex (projection) 31 | - Indicator function on simplex (projection) 32 | 33 | New regularization terms can be easily implemented as discussed in section 3. 34 | 35 | # Start using the toolbox 36 | 37 | ## Installation 38 | 39 | All the functions in the toolbox a given in the folder /utils. 40 | 41 | The unmix folder contains code and data downloaded from the website of [ Jose M. Bioucas Dias](http://www.lx.it.pt/~bioucas/publications.html). 42 | 43 | In order to use the function we recommend to execute the following command 44 | 45 | ```Matlab 46 | addpath(genpath('.')) 47 | ``` 48 | 49 | if you are not working in the root folder of the toolbox or replacing '.' by the location of the folder on your machine. 50 | 51 | 52 | ## Entry points 53 | 54 | We recommend to look at the following files to see how to use the toolbox: 55 | * demo/demo_classif.m : contains an example of 4 class linear classification problem and show how to learn different classifiers. 56 | * demo/demo_unmix.m : show an example of linear unmixing with positivity constraint and non-convex regularization. 57 | * demo/visu_classif.m : reproduce the example figure in the paper. 58 | 59 | # Solving your own optimization problem 60 | 61 | ## New regularization terms 62 | 63 | All the regularization terms (and theri proximal operators) are defined in the function [utils/get_reg_prox.m](utils/get_reg_prox.m). 64 | 65 | If you want to add a regularization term (or a projection), you only need to add a case to the switch beginning [line 37](utils/get_reg_prox.m#L37) and define two functions: 66 | - g(x) : R^d->R, loss function for the regularization term 67 | - prox_g(x,lambda) : R^d->R^d, proximal operator of lambda*g(x) 68 | 69 | For a simple example look at the implementations of the Lasso loss ([line 124](utils/get_reg_prox.m#L124)) soft thresholding ([Line 128](utils/get_reg_prox.m#L128)) and loss implementations. 70 | 71 | note that in order to limit the number of files, the loss and proximal operators functions are all implemented as subfunctions of file [utils/get_reg_prox.m](utils/get_reg_prox.m). 72 | 73 | 74 | ## Data fitting term 75 | 76 | You can easily change the data fitting term by providing a new loss and gradient functions to the optimization function [utils/gist_opt.m](utils/gist_opt.m). 77 | 78 | A good starting point is by looking at the least square implementation in [utils/gist_least.m](utils/gist_least.m). Changing the data fitting term correspond to only code the loss function at [Line 63](utils/gist_least.m#L63) and the corresponding gradient function at [Line 59](utils/gist_least.m#L59). 79 | 80 | 81 | 82 | 83 | 84 | # Contact and contributors 85 | 86 | * [Rémi Flamary](http://remi.flamary.com/) 87 | * [Devis Tuia](https://sites.google.com/site/devistuia/) 88 | 89 | ## Aknowledgements 90 | 91 | We want to thank [ Jose M. Bioucas Dias](http://www.lx.it.pt/~bioucas/publications.html) for providing the unmixing dataset and functions on his website. 92 | 93 | # References 94 | 95 | [1] Gong, P., Zhang, C., Lu, Z., Huang, J., & Ye, J. (2013, June). A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems. In ICML (2) (pp. 37-45). 96 | 97 | [2] Candes, E. J., Wakin, M. B., & Boyd, S. P. (2008). Enhancing sparsity by reweighted ? 1 minimization. Journal of Fourier analysis and applications, 14(5-6), 877-905. 98 | 99 | [3] Xu, Z., Chang, X., Xu, F., & Zhang, H. (2012). L1/2 regularization: A thresholding representation theory and a fast solver. IEEE Transactions on neural networks and learning systems, 23(7), 1013-1027. 100 | 101 | 102 | 103 | Copyright 2016 104 | -------------------------------------------------------------------------------- /demo/demo_classif.m: -------------------------------------------------------------------------------- 1 | % This file show how to use the toolbox to estimate linear classifier with 2 | % different regularization scheme. 3 | % note that all classifiers naturally handle multiclass data 4 | % 5 | % The dataset contains only 2 discriminant dimensions and 8 noisy 6 | % dimension. 7 | % The timated classifier should select automatically the two first 8 | % dimension when sparsity is promoted. 9 | 10 | clear all 11 | close all 12 | addpath(genpath('.')) 13 | 14 | 15 | %% generate dataset 16 | 17 | 18 | mclass=[1 1; -1 1; 1 -1; -1 -1]; 19 | 20 | nbperclass=1000; 21 | 22 | 23 | % generating good features and labels 24 | x=[]; 25 | y=[]; 26 | sigma=.5; 27 | for i=1:size(mclass,1); 28 | 29 | x=[x; ones(nbperclass,1)*mclass(i,:)+sigma*randn(nbperclass,size(mclass,2))]; 30 | y=[y;i*ones(nbperclass,1)]; 31 | end 32 | 33 | 34 | % adding random features 35 | nbnoise=8; 36 | x=[x sigma*randn(size(x,1),nbnoise)]; 37 | 38 | % models should have only the two first components active 39 | 40 | %% visu data on 2 diuscriminant components 41 | 42 | figure(1) 43 | 44 | plot(x(y==1,1),x(y==1,2),'+') 45 | hold on 46 | plot(x(y==2,1),x(y==2,2),'x') 47 | plot(x(y==3,1),x(y==3,2),'o') 48 | plot(x(y==4,1),x(y==4,2),'s') 49 | hold off 50 | 51 | %% SVM with l2 regularization 52 | 53 | % options for solver 54 | options.verbose=1; 55 | options.lambda=1e-3 ;% regul parameter 56 | options.theta=.01; % parameter for lsp 57 | options.p=.5; % parameter for lp 58 | options.reg='l2'; % l2 l1 lp, lsp are possible options 59 | 60 | tic 61 | [svml2]=gist_hinge2(x,y,options); % hinge squared svn 62 | %[svm,LOG]=gist_chinge(x,y,options) % calibrated hinge 63 | %[svm,LOG]=gist_logreg(x,y,options) % logistic regression 64 | toc 65 | 66 | % classifier linear parameter 67 | wl2=svml2.w % normal vector to hyperlpaln 68 | w0l2=svml2.w0; % svm bias 69 | 70 | %% SVM with lp regularization 71 | 72 | % options for solver 73 | options.verbose=1; 74 | options.lambda=1e-2 ;% regul parameter 75 | options.theta=.01; % parameter for lsp 76 | options.p=.5; % parameter for lp 77 | options.reg='lp'; % l2 l1 lp, lsp are possible options 78 | 79 | tic 80 | [svmlp]=gist_hinge2(x,y,options); % hinge squared svn 81 | %[svm,LOG]=gist_chinge(x,y,options) % calibrated hinge 82 | %[svm,LOG]=gist_logreg(x,y,options) % logistic regression 83 | toc 84 | 85 | % classifier linear parameter 86 | wlp=svmlp.w % normal vector to hyperlpaln 87 | w0lp=svmlp.w0; % svm bias 88 | 89 | 90 | 91 | %% visu separation 92 | % plot classification regions in 2D (discriminant features) 93 | 94 | nbgrid=100; 95 | [Xgrid,Ygrid]=meshgrid(linspace(-3,3,nbgrid),linspace(-3,3,nbgrid)); 96 | 97 | xtest=[Xgrid(:) Ygrid(:)]; 98 | 99 | ypred=xtest*wlp(1:2,:)+ones(nbgrid*nbgrid,1)*w0lp; 100 | 101 | [temp,ypred_c]=min(ypred,[],2); 102 | 103 | Ypred=reshape(ypred_c,[nbgrid nbgrid]); 104 | 105 | figure(2) 106 | 107 | imagesc(linspace(-3,3,nbgrid),linspace(-3,3,nbgrid),Ypred) 108 | 109 | hold on 110 | plot(x(y==1,1),x(y==1,2),'+') 111 | plot(x(y==2,1),x(y==2,2),'x') 112 | plot(x(y==3,1),x(y==3,2),'o') 113 | plot(x(y==4,1),x(y==4,2),'s') 114 | hold off 115 | 116 | 117 | -------------------------------------------------------------------------------- /demo/demo_unmix.m: -------------------------------------------------------------------------------- 1 | % This file show how to use the toolbox to estimate linear mixture with 2 | % different regularization scheme. 3 | % 4 | % The dataset contains only 3 active components 5 | % We compare l2 unmixing with positivity constraints, l1 and lp 6 | % regularization 7 | 8 | clear all 9 | close all 10 | addpath(genpath('.')) 11 | 12 | 13 | %% generate data 14 | seed=0 15 | rng(seed) 16 | 17 | load USGS_1995_Library.mat 18 | 19 | D=datalib(:,4:end); 20 | 21 | anglemin=20; 22 | D = prune_library(D,anglemin); 23 | 24 | 25 | wl=datalib(:,1); 26 | 27 | 28 | d=size(D,2); 29 | n=size(D,1); 30 | 31 | 32 | alpha_t=zeros(d,1); 33 | 34 | 35 | nbactive=3; 36 | 37 | perm=randperm(d); 38 | alpha_t(perm(1:nbactive))=rand(nbactive,1); 39 | %wtrue=wtrue./sum(wtrue) 40 | 41 | sigma=1e-1; 42 | 43 | y=D*alpha_t+sigma*randn(n,1); 44 | ytrue=D*alpha_t; 45 | 46 | %% 47 | figure(1) 48 | subplot(2,1,1) 49 | 50 | plot(wl,D) 51 | 52 | xlabel('Wavelength in microns') 53 | 54 | subplot(2,1,2) 55 | 56 | plot(wl,[ytrue y]) 57 | 58 | xlabel('Wavelength in microns') 59 | 60 | %% l2 unmix 61 | lambda=1e-2; 62 | 63 | alpha_l2=l2_unmix(y,D,lambda) 64 | err_l2=sum(abs(alpha_l2-alpha_t).^2) 65 | 66 | 67 | %% l1 unmixing 68 | 69 | options.verbose=0; % do not print 70 | options.lambda=1e-3;% regul parameter 71 | options.reg='l1' % regularization 72 | options.bias=0; % forc no bias estimation 73 | options.pos=1; % fore positivity 74 | options.stopvarx=1e-6; % convergence conditions 75 | options.stopvarj=1e-6;% convergence conditions 76 | options.nbitermax=1e4;% convergence conditions 77 | 78 | tic 79 | [svm_l1,LOG]=gist_least(D,y,options); 80 | toc 81 | 82 | alpha_l1=svm_l1.w 83 | 84 | 85 | 86 | err_l2 87 | err_l1=sum(abs(alpha_l1-alpha_t).^2)/2 88 | 89 | %% lp unmixing 90 | 91 | options.verbose=0; 92 | options.lambda=5e-2% regul parameter 93 | options.p=.5; % value for p 94 | options.reg='lp' 95 | options.bias=0; % force no bias estimation 96 | options.pos=1; % force positivity 97 | options.stopvarx=1e-6; % convergence conditions 98 | options.stopvarj=1e-6;% convergence conditions 99 | options.nbitermax=1e4;% convergence conditions 100 | 101 | tic 102 | [svm_lp,LOG]=gist_least(D,y,options); 103 | toc 104 | 105 | alpha_lp=svm_lp.w 106 | 107 | 108 | % display errors 109 | err_l2 110 | err_l1 111 | err_lp=sum(abs(alpha_lp-alpha_t).^2)/2 112 | 113 | 114 | %% show reconsruction 115 | 116 | 117 | figure(2) 118 | imagesc([alpha_t alpha_l2 alpha_l1 alpha_lp]') 119 | set(gca,'Ytick',[1 2 3 4]) 120 | set(gca,'YtickLabel',{'Ground truth','l2 unmix','l1 unmix','lp unmix'}) 121 | colorbar() 122 | 123 | 124 | 125 | -------------------------------------------------------------------------------- /demo/visu_classif.m: -------------------------------------------------------------------------------- 1 | % test gist 2 | 3 | clear all 4 | close all 5 | addpath(genpath('.')) 6 | 7 | 8 | %% generate dataset 9 | 10 | 11 | nbperclass=100; 12 | 13 | 14 | % generating good features and labels 15 | x=[]; 16 | y=[]; 17 | sigma=1; 18 | m1=[1, .5]; 19 | m2=-m1; 20 | x=[ones(nbperclass,1)*m1+sigma*randn(nbperclass,2);ones(nbperclass,1)*m2+sigma*randn(nbperclass,2)]; 21 | y=[ones(nbperclass,1);-ones(nbperclass,1)]; 22 | 23 | 24 | % adding random features 25 | nbnoise=18; 26 | x=[x sigma*randn(size(x,1),nbnoise)]; 27 | 28 | %% visu data 29 | 30 | figure(1) 31 | 32 | plot(x(y==1,1),x(y==1,2),'+') 33 | hold on 34 | plot(x(y==-1,1),x(y==-1,2),'xr') 35 | hold off 36 | 37 | 38 | %% bayes decision 39 | 40 | wb=(m1-m2) 41 | 42 | fb=@(x,y) x*wb(1)+y*wb(2); 43 | 44 | 45 | figure(1) 46 | 47 | plot(x(y==1,1),x(y==1,2),'+') 48 | hold on 49 | plot(x(y==-1,1),x(y==-1,2),'xr') 50 | h=ezplot(fb); 51 | set(h, 'Color','b') 52 | hold off 53 | %title('test') 54 | legend('Class 1','Class -1','Bayes decision') 55 | 56 | 57 | 58 | %% svm l1 59 | 60 | options.verbose=1; 61 | options.lambda=1e-1 62 | options.theta=.01; 63 | options.p=.5; 64 | options.reg='l1' 65 | 66 | tic 67 | [svml1,LOG]=gist_hinge2(x,y,options) 68 | %[svm,LOG]=gist_chinge(x,y,options) 69 | %[svml1,LOG]=gist_logreg(x,y,options) 70 | toc 71 | 72 | wl1=svml1.w(:,1); 73 | 74 | fl1=@(x,y) x*wl1(1)+y*wl1(2); 75 | 76 | figure(1) 77 | 78 | plot(x(y==1,1),x(y==1,2),'+') 79 | hold on 80 | plot(x(y==-1,1),x(y==-1,2),'xr') 81 | h=ezplot(fb); 82 | set(h, 'Color','b') 83 | h=ezplot(fl1); 84 | set(h, 'Color','r') 85 | hold off 86 | %title('test') 87 | legend('Class 1','Class -1','Bayes decision','l1 reg.') 88 | 89 | %% LSP 90 | 91 | options.verbose=1; 92 | options.lambda=2e-3 93 | options.theta=.001; 94 | options.p=.5; 95 | options.reg='lsp' 96 | 97 | tic 98 | [svmlsp,LOG]=gist_hinge2(x,y,options) 99 | %[svm,LOG]=gist_chinge(x,y,options) 100 | %[svmlsp,LOG]=gist_logreg(x,y,options) 101 | toc 102 | 103 | wlsp=svmlsp.w(:,1); 104 | 105 | flsp=@(x,y) x*wlsp(1)+y*wlsp(2); 106 | figure(1) 107 | 108 | plot(x(y==1,1),x(y==1,2),'+') 109 | hold on 110 | plot(x(y==-1,1),x(y==-1,2),'xr') 111 | h=ezplot(fb); 112 | set(h, 'Color','b') 113 | h=ezplot(fl1); 114 | set(h, 'Color','r') 115 | h=ezplot(flsp); 116 | set(h, 'Color',[0 .7 0]) 117 | hold off 118 | %title('test') 119 | legend('Class 1','Class -1','Bayes decision','l1 reg.','lsp reg.') 120 | 121 | 122 | %% lp 123 | 124 | options.verbose=1; 125 | options.lambda=6e-2 126 | options.theta=.1; 127 | options.p=.5; 128 | options.reg='lp' 129 | 130 | tic 131 | [svmlp,LOG]=gist_hinge2(x,y,options) 132 | %[svm,LOG]=gist_chinge(x,y,options) 133 | %[svmlsp,LOG]=gist_logreg(x,y,options) 134 | toc 135 | 136 | limx=[-4,4] 137 | 138 | wlp=svmlp.w(:,1); 139 | 140 | flp=@(x,y) x*wlp(1)+y*wlp(2); 141 | figure(1) 142 | 143 | plot(x(y==1,1),x(y==1,2),'+') 144 | hold on 145 | plot(x(y==-1,1),x(y==-1,2),'xr') 146 | h=ezplot(fb,limx); 147 | set(h, 'Color','b') 148 | h=ezplot(fl1,limx); 149 | set(h, 'Color','r') 150 | h=ezplot(flsp,limx); 151 | set(h, 'Color',[0 .7 0],'LineStyle','-.') 152 | h=ezplot(flp,limx); 153 | set(h, 'Color',[0 .7 .7],'LineStyle','--') 154 | hold off 155 | title('') 156 | legend('Class 1','Class -1','Bayes decision','l1 reg.','lsp reg.','lp reg.') 157 | 158 | print('-depsc','toybias.eps') -------------------------------------------------------------------------------- /unmix/README.md: -------------------------------------------------------------------------------- 1 | 2 | Source of this folder: 3 | 4 | This folder contains code and data downloaded from the website of [ Jose M. Bioucas Dias](http://www.lx.it.pt/~bioucas/publications.html). 5 | -------------------------------------------------------------------------------- /unmix/USGS_1995_Library.mat: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rflamary/nonconvex-optimization/4f09aa52f0147c6516c8d5a7d808c5faf14f85db/unmix/USGS_1995_Library.mat -------------------------------------------------------------------------------- /unmix/demo1_sparse_TV.m: -------------------------------------------------------------------------------- 1 | %% demo_sunsal_TV 2 | % 3 | % This demo illustrates the sunsal_TV sparse regression algorithm 4 | % introduced in the paper 5 | % 6 | % M.-D. Iordache, J. Bioucas-Dias, and A. Plaza, "Total variation spatial 7 | % regularization for sparse hyperspectral unmixing", IEEE Transactions on 8 | % Geoscience and Remote Sensing, vol. PP, no. 99, pp. 1-19, 2012. 9 | % 10 | % which solves the optimization problem 11 | % 12 | % min 0.5*||AX-Y||^2_F + lambda_1 ||X||_{1,1} + lambda_tv TV(X) 13 | % X>=0 14 | % 15 | % 16 | % Demo parameters: 17 | % p = 5 % number of endmembers 18 | % SNR = 40 dB 19 | % size(A) = [220, 240] % size of the library 20 | % min angle(a_i, a_j) = 4.44 degs % minimum angle between any two 21 | % % elements of A 22 | % 23 | % Notes: 24 | % 25 | % You may change the demo parameters, namely SNR, the noise correlation, 26 | % the size of dictionary A by changing min_angle, and the true endmember 27 | % matrix M, which, in any case, must contain p=5 columns. 28 | % 29 | % Please keep in mind the following: 30 | % 31 | % a) sunsal adapts automatically the ADMM parameter for 32 | % convergence speed 33 | % 34 | % b) sunsal_tv deoes not adapts automatically the ADMM parameter. 35 | % So the inputted parameter mu has a critical impact on the 36 | % convergence speed 37 | % 38 | % c) the regularization parameters were hand tuned for optimal 39 | % performance. 40 | % 41 | % Author: Jose Bioucas Dias, August 2012 42 | 43 | close all 44 | clear all 45 | 46 | %% 47 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 48 | % Generate data 49 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 50 | % number of end members 51 | p = 5; % fixed for this demo 52 | 53 | %SNR in dB 54 | SNR = 40; 55 | % noise bandwidth in pixels of the noise low pass filter (Gaussian) 56 | bandwidth = 1000; % 10000 == iid noise 57 | %bandwidth = 5*pi/224; % colored noise 58 | 59 | 60 | % define random states 61 | rand('state',10); 62 | randn('state',10); 63 | 64 | 65 | %% 66 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 67 | % gererate fractional abundances 68 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 69 | 70 | % pure pixels 71 | x1 = eye(p); 72 | 73 | % mixtures with two materials 74 | x2 = x1 + circshift(eye(p),[1 0]); 75 | 76 | % mixtures with three materials 77 | x3 = x2 + circshift(eye(p),[2 0]); 78 | 79 | % mixtures with four materials 80 | x4 = x3 + circshift(eye(p),[3 0]); 81 | 82 | % mixtures with four materials 83 | x5 = x4 + circshift(eye(p),[4 0]); 84 | 85 | 86 | % normalize 87 | x2 = x2/2; 88 | x3 = x3/3; 89 | x4 = x4/4; 90 | x5 = x5/5; 91 | 92 | 93 | % background (random mixture) 94 | %x6 = dirichlet(ones(p,1),1)'; 95 | x6 = [0.1149 0.0741 0.2003 0.2055, 0.4051]'; % as in the paper 96 | 97 | % build a matrix 98 | xt = [x1 x2 x3 x4 x5 x6]; 99 | 100 | 101 | % build image of indices to xt 102 | imp = zeros(3); 103 | imp(2,2)=1; 104 | 105 | imind = [imp*1 imp*2 imp* 3 imp*4 imp*5; 106 | imp*6 imp*7 imp* 8 imp*9 imp*10; 107 | imp*11 imp*12 imp*13 imp*14 imp*15; 108 | imp*16 imp*17 imp* 18 imp*19 imp*20; 109 | imp*21 imp*22 imp* 23 imp*24 imp*25]; 110 | 111 | imind = kron(imind,ones(5)); 112 | 113 | % set backround index 114 | imind(imind == 0) = 26; 115 | 116 | % generare frectional abundances for all pixels 117 | [nl,nc] = size(imind); 118 | np = nl*nc; % number of pixels 119 | for i=1:np 120 | X(:,i) = xt(:,imind(i)); 121 | end 122 | 123 | Xim = reshape(X',nl,nc,p); 124 | 125 | % image endmember 1 126 | figure(1) 127 | imagesc(Xim(:,:,5)) 128 | title('Frational abundance of endmember 5') 129 | 130 | %% 131 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 132 | % buid the dictionary 133 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 134 | load USGS_1995_Library.mat 135 | % order bands by increasing wavelength 136 | [dummy index] = sort(datalib(:,1)); 137 | A = datalib(index,4:end); 138 | 139 | % prune the library 140 | % min angle (in degres) between any two signatures 141 | % the larger min_angle the easier is the sparse regression problem 142 | min_angle = 4.44; 143 | A = prune_library(A,min_angle); % 240 signature 144 | 145 | % order the columns of A by decreasing angles 146 | [A, index, angles] = sort_library_by_angle(A); 147 | 148 | 149 | %% select p endmembers from A 150 | % 151 | 152 | % angles (a_1,a_j) \simeq min_angle) 153 | supp = 1:p; 154 | M = A(:,supp); 155 | [L,p] = size(M); % L = number of bands; p = number of material 156 | 157 | 158 | %% 159 | %--------------------------------- 160 | % generate the observed data X 161 | %--------------------------------- 162 | 163 | % set noise standard deviation 164 | sigma = sqrt(sum(sum((M*X).^2))/np/L/10^(SNR/10)); 165 | % generate Gaussian iid noise 166 | noise = sigma*randn(L,np); 167 | 168 | 169 | % make noise correlated by low pass filtering 170 | % low pass filter (Gaussian) 171 | filter_coef = exp(-(0:L-1).^2/2/bandwidth.^2)'; 172 | scale = sqrt(L/sum(filter_coef.^2)); 173 | filter_coef = scale*filter_coef; 174 | noise = idct(dct(noise).*repmat(filter_coef,1,np)); 175 | 176 | % observed spectral vector 177 | Y = M*X + noise; 178 | 179 | 180 | % create true X wrt the library A 181 | n = size(A,2); 182 | N = nl*nc; 183 | XT = zeros(n,N); 184 | XT(supp,:) = X; 185 | 186 | 187 | %% estimate noise and filter it out 188 | % [w,Rw] = estNoise(Y); 189 | % 190 | % % determine signal subspace 191 | % [kp,Ek] = hysime(Y,w,Rw); 192 | % 193 | % % remove noise 194 | % Y = Y-w; 195 | % 196 | % % project observed data on the signal subspace 197 | % Y = Ek*Ek'*Y; 198 | % 199 | % clear w; 200 | 201 | 202 | %% 203 | %-------------------------------------------------------------------------- 204 | % SUNSAL and SUNSAL_TV solutions 205 | %-------------------------------------------------------------------------- 206 | 207 | % constrained least squares CLS 208 | lambda = 0; 209 | [X_hat_cls] = sunsal(A,Y,'lambda',lambda,'ADDONE','no','POSITIVITY','yes', ... 210 | 'TOL',1e-4, 'AL_iters',2000,'verbose','yes'); 211 | 212 | SRE_cls = 20*log10(norm(XT,'fro')/norm(X_hat_cls-XT,'fro')); 213 | 214 | 215 | % constrained least squares l2-l1 216 | lambda = 1e-2; 217 | [X_hat_l1] = sunsal(A,Y,'lambda',lambda,'ADDONE','no','POSITIVITY','yes', ... 218 | 'TOL',1e-4, 'AL_iters',2000,'verbose','yes'); 219 | 220 | SRE_l1 = 20*log10(norm(XT,'fro')/norm(X_hat_l1-XT,'fro')); 221 | 222 | 223 | % constrained least squares l2-l1-TV (nonisotropic) 224 | lambda = 1e-3; 225 | lambda_TV = 3e-3; 226 | [X_hat_tv_ni,res,rmse_ni] = sunsal_tv(A,Y,'MU',0.05,'POSITIVITY','yes','ADDONE','no', ... 227 | 'LAMBDA_1',lambda,'LAMBDA_TV', lambda_TV, 'TV_TYPE','niso',... 228 | 'IM_SIZE',[75,75],'AL_ITERS',200, 'TRUE_X', XT, 'VERBOSE','yes'); 229 | 230 | SRE_tv_ni = 20*log10(norm(XT,'fro')/norm(X_hat_tv_ni-XT,'fro')); 231 | 232 | % constrained least squares l2-l1-TV (isotropic) 233 | lambda = 1e-3; 234 | lambda_TV = 3e-3; 235 | [X_hat_tv_i,res,rmse_i] = sunsal_tv(A,Y,'MU',0.05,'POSITIVITY','yes','ADDONE','no', ... 236 | 'LAMBDA_1',lambda,'LAMBDA_TV', lambda_TV, 'TV_TYPE','iso',... 237 | 'IM_SIZE',[75,75],'AL_ITERS',200, 'TRUE_X', XT, 'VERBOSE','yes'); 238 | 239 | SRE_tv_i = 20*log10(norm(XT,'fro')/norm(X_hat_tv_i-XT,'fro')); 240 | 241 | 242 | %% 243 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 244 | % print results 245 | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 246 | 247 | fprintf('\n\n SIGNAL-TO-RECONSTRUCTION ERRORS (SRE)\n\n') 248 | 249 | fprintf('SRE-cls = %2.3f\nSRE-l1 = %2.3f\nSRE_tv-ni = %2.3f\nSRE-tv-i = %2.3f\n\n', ... 250 | SRE_cls, SRE_l1,SRE_tv_ni, SRE_tv_i) 251 | 252 | 253 | % endmember no. 1 (cls) 254 | X_hat_cls_im = reshape(X_hat_cls', nl,nc,n); 255 | figure(2) 256 | imagesc(X_hat_cls_im(:,:,supp(5))) 257 | title('CLS - Frational abundance of endmember 5') 258 | 259 | 260 | % endmember no. 1 (l2-l1) 261 | X_hat_l1_im = reshape(X_hat_l1', nl,nc,n); 262 | figure(3) 263 | imagesc(X_hat_l1_im(:,:,supp(5))) 264 | title('SUnSAL - Frational abundance of endmember 5') 265 | 266 | 267 | % endmember no. 1 (tv_ni) 268 | X_hat_tv_ni_im = reshape(X_hat_tv_ni', nl,nc,n); 269 | figure(4) 270 | imagesc(X_hat_tv_ni_im(:,:,supp(5))) 271 | title('SUnSAL-TV (NISO) - Frational abundance of endmember 5') 272 | 273 | 274 | % endmember no. 1 (tv_ni) 275 | X_hat_tv_i_im = reshape(X_hat_tv_i', nl,nc,n); 276 | figure(5) 277 | imagesc(X_hat_tv_i_im(:,:,supp(5))) 278 | title('SUnSAL-TV (ISO) - Frational abundance of endmember 5') 279 | 280 | 281 | 282 | scrsz = get(0,'ScreenSize'); 283 | figure('Position',[1 1 scrsz(3)/2 scrsz(4)/2]) 284 | 285 | subplot(151) 286 | imagesc(XT(:,1:100)) 287 | title('spectral vectors (1;100)') 288 | 289 | subplot(152) 290 | imagesc(X_hat_cls(:,1:100)) 291 | axis off 292 | title('CLS') 293 | 294 | subplot(153) 295 | imagesc(X_hat_l1(:,1:100)) 296 | axis off 297 | title('SUnSAL') 298 | 299 | subplot(154) 300 | imagesc(X_hat_tv_ni(:,1:100)) 301 | axis off 302 | title('SUnSAL-TV-NISO') 303 | 304 | subplot(155) 305 | imagesc(X_hat_tv_i(:,1:100)) 306 | axis off 307 | title('SUnSAL-TV-ISO') 308 | 309 | 310 | 311 | -------------------------------------------------------------------------------- /unmix/prune_library.m: -------------------------------------------------------------------------------- 1 | function B = prune_library(A,min_angle) 2 | % B = prune_library(A,min_angle) 3 | % 4 | % remove columns from A such that the minimum angle between the columns 5 | % of B in no smaller than max_angle 6 | % 7 | % Author: Jose Bioucas Dias. June, 2011 8 | % 9 | 10 | [L,m] = size(A); % L = number of bands; m = number of materilas 11 | 12 | %normalize A 13 | nA = sqrt(sum(A.^2)); 14 | A_norm = A./repmat(nA,L,1); 15 | 16 | % compute angles 17 | angles = abs(acos(A_norm'*A_norm))*180/pi; 18 | 19 | 20 | % discard vectors with angles less than min_angle 21 | index = 1; 22 | for i=1:m 23 | if angles(i,i) ~= inf 24 | B(:,index) = A(:,i); 25 | angles(:,angles(i,:) < min_angle ) = inf; 26 | index = index + 1; 27 | end 28 | 29 | end 30 | 31 | 32 | 33 | 34 | 35 | -------------------------------------------------------------------------------- /unmix/soft.m: -------------------------------------------------------------------------------- 1 | function y = soft(x,T) 2 | 3 | T = T + eps; 4 | y = max(abs(x) - T, 0); 5 | y = y./(y+T) .* x; 6 | 7 | -------------------------------------------------------------------------------- /unmix/sort_library_by_angle.m: -------------------------------------------------------------------------------- 1 | function [B,index,angles] = sort_library_by_angle(A) 2 | % [B,index,angles] = sort_library_by_angle(A) 3 | % 4 | % B = A(index,:) where index in the column index of A ordered by inreasing 5 | % minimum angle with every other colum 6 | % 7 | % 8 | % % Author: Jose Bioucas Dias. June, 2011 9 | 10 | BIG = 1e10; 11 | 12 | [L,m] = size(A); % L = number of bands; m = number of materilas 13 | 14 | %normalize A 15 | nA = sqrt(sum(A.^2)); 16 | A_norm = A./repmat(nA,L,1); 17 | 18 | % compute angles 19 | angles = abs(acos(A_norm'*A_norm))*180/pi; 20 | angles = angles + BIG*diag(ones(1,m)); 21 | 22 | % compute min angles between a given column and every other column 23 | [min_angles index_rows] = min(angles); 24 | % sort columns by increasing angles 25 | [angles, index] = sort(min_angles); 26 | 27 | B = A(:,index); 28 | 29 | 30 | 31 | 32 | 33 | -------------------------------------------------------------------------------- /unmix/sunsal.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rflamary/nonconvex-optimization/4f09aa52f0147c6516c8d5a7d808c5faf14f85db/unmix/sunsal.m -------------------------------------------------------------------------------- /unmix/sunsal_tv.m: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/rflamary/nonconvex-optimization/4f09aa52f0147c6516c8d5a7d808c5faf14f85db/unmix/sunsal_tv.m -------------------------------------------------------------------------------- /utils/get_reg_prox.m: -------------------------------------------------------------------------------- 1 | function [g,prox_g]=get_reg_prox(reg,params) 2 | % return reg function and corresponding proximal operator 3 | % 4 | % the regularization functions are of the form: 5 | % g(x)=\sum_k h(x_k) 6 | % 7 | % reg: regularization term 8 | % - 'l2' : squared l2 ,orme (ridge regularization) 9 | % h(u)=u^2 10 | % - '0' : no reglarization 11 | % h(u)=0 12 | % - 'set' : indicator function of a set C=[C(1) C(2)] 13 | % h(u)= 0 if C(1)<= u <= C(2), Inf otherwise 14 | % params.C : 1D set (default=[0 1]) 15 | % - 'l1' : lasso l1 regularization 16 | % h(u)=|u| 17 | % - 'l1l2' : group lasso on the columns of x 18 | % h(u)=||u||_2 19 | % - 'lsp' : log sum penalty 20 | % h(u)=log(1+|u|/theta) 21 | % params.theta: lsp param (default=1) 22 | % - 'mcp' : minimax concave penalty 23 | % Zhang, C. H. (2010). Nearly unbiased variable selection under minimax concave penalty. The Annals of statistics, 894-942. 24 | % - 'lp' : lp pseudo-norm (implemented only for p=1/2) 25 | % h(u)=|u|^p 26 | % params.p: (default=1/2) 27 | % - 'l0' : l0 pseudo norm 28 | % h(u)=0 if u=0 1 otherwise 29 | % - 'simplex' : simplex indicator function (for projected gradient) 30 | 31 | if nargin<2 32 | param=struct; 33 | end 34 | 35 | params=initoptions(mfilename,params,'params'); 36 | 37 | switch reg 38 | 39 | case 'l2' 40 | 41 | g=@reg_l2; 42 | prox_g=@prox_l2; 43 | 44 | case '0' 45 | 46 | g=@(x) 0; 47 | prox_g=@(x,lambda) x; 48 | 49 | 50 | case 'set' 51 | 52 | g=@(x) reg_set(x,params.C); 53 | prox_g=@(x,lambda) prox_set(x,lambda,params.C); 54 | 55 | case 'l1' 56 | 57 | g=@reg_l1; 58 | prox_g=@prox_l1; 59 | 60 | case 'l1l2' 61 | 62 | g=@reg_l1l2; 63 | prox_g=@prox_l1l2; 64 | 65 | 66 | case 'lsp' 67 | 68 | g=@(x) reg_lsp(x,params.theta); 69 | prox_g=@(x,lambda) prox_lsp(x,lambda,params.theta); 70 | 71 | case 'mcp' 72 | 73 | g=@(x) reg_mcp(x,1,params.theta); 74 | prox_g=@(x,lambda) prox_mcp(x,lambda,params.theta); 75 | 76 | case 'lp' 77 | 78 | g=@(x) reg_lp(x,params.p); 79 | prox_g=@(x,lambda) prox_lp(x,lambda,params.p); 80 | 81 | case 'l0' 82 | 83 | g=@(x) reg_l0(x); 84 | prox_g=@(x,lambda) prox_l0(x,lambda); 85 | 86 | case 'simplex' 87 | 88 | g=@(x) reg_simplex(x); 89 | prox_g=@(x,lambda) prox_simplex(x,lambda); 90 | 91 | 92 | otherwise 93 | 94 | error('unknown reg term') 95 | 96 | end 97 | 98 | 99 | 100 | end 101 | 102 | 103 | function res=reg_set(x,C) 104 | res=sum((xC(2))); 105 | if res>0 106 | res=1e3; 107 | end 108 | end 109 | 110 | function res=prox_set(x,lambda,C) 111 | res=max(min(x,C(2)),C(1)); 112 | end 113 | 114 | 115 | 116 | function res=reg_l2(x) 117 | res=norm(x(1:end,:),'fro')^2/2; 118 | end 119 | 120 | function res=prox_l2(x,lambda) 121 | res=x/(1+lambda); 122 | end 123 | 124 | function res=reg_l1(x) 125 | res=sum(sum(abs(x(1:end,:)))); 126 | end 127 | 128 | function res=prox_l1(x,lambda) 129 | res=sign(x).*max(abs(x)-lambda,0); 130 | end 131 | 132 | function res=reg_l1l2(x) 133 | res=sum(sqrt(sum(abs(x(1:end-1,:)).^2,2))); 134 | end 135 | 136 | function res=prox_l1l2(x,lambda) 137 | res=x; 138 | for i=1:size(x,1) 139 | res(i,:)=x(i,:).*max(0,1-lambda/norm(x(i,:))); 140 | end 141 | end 142 | 143 | function res=reg_lsp(x,theta) 144 | res=sum(sum(log(1+abs(x(1:end,:))/theta))); 145 | end 146 | 147 | function res=prox_lsp(x,lambda,theta) 148 | z = abs(x) - theta; 149 | v = z.*z - 4.0*(lambda - abs(x)*theta); 150 | 151 | 152 | sqrtv = sqrt(v); 153 | xtemp1 = max(0,0.5*(z + sqrtv)); 154 | xtemp2 = max(0,0.5*(z - sqrtv)); 155 | 156 | ytemp0 = 0.5*x.*x; 157 | ytemp1= 0.5*(xtemp1 - abs(x)).*(xtemp1 - abs(x)) + lambda*log(1.0 + xtemp1/theta); 158 | ytemp2 = 0.5*(xtemp2 - abs(x)).*(xtemp2 - abs(x)) + lambda*log(1.0 + xtemp2/theta); 159 | 160 | sel1=(ytemp10).*xtemp; 166 | end 167 | 168 | function res=reg_mcp(x,lambda,theta) 169 | indUnb = (abs(x(1:end-1,:))>theta*lambda) ; 170 | indBia = (abs(x(1:end-1,:))<=theta*lambda).*(abs(x(1:end-1,:))>0) ; 171 | res=sum(sum((x(1:end,:)-x(1:end,:).^2/(2*theta*lambda)).*indBia + theta*lambda/2*indUnb)); 172 | end 173 | 174 | function res=prox_mcp(x,lambda,theta) 175 | res=zeros(size(x)); 176 | indUnb = (abs(x(1:end,:))>theta*lambda) ; 177 | indBia = (abs(x(1:end,:))<=theta*lambda).*(abs(x(1:end,:))>0) ; 178 | res(1:end,:)=x(1:end,:).*indUnb + theta/(theta-1)*(x(1:end,:)-lambda*sign(x(1:end-1,:))).*indBia; 179 | end 180 | 181 | function res=reg_lp(x,p) 182 | res=sum(sum(abs(x(1:end,:)).^p)); 183 | end 184 | 185 | function res=prox_lp(x,lambda,p) 186 | res=zeros(size(x)); 187 | switch p 188 | case .5 189 | ind = (abs(x)>(.75*lambda^(2/3))) ; 190 | res(ind) = 2/3*x(ind).*(1+cos(2*pi/3-2/3*acos(lambda/8*(abs(x(ind))/3).^(-3/2)))) ; 191 | end 192 | end 193 | 194 | function res=reg_l0(x) 195 | res=sum(sum(abs(x(1:end,:)))>0); 196 | end 197 | 198 | function res=prox_l0(x,lambda) 199 | thr=sqrt(2*lambda); 200 | res=x.*(abs(x)>thr); 201 | end 202 | 203 | 204 | function res=reg_simplex(x) 205 | res=0; 206 | end 207 | 208 | function res=prox_simplex(x,lambda) 209 | res=projectSimplex(x(1:end-1)); 210 | res(end+1)=0; 211 | end 212 | 213 | 214 | function [w] = projectSimplex(v) 215 | % Computest the minimum L2-distance projection of vector v onto the probability simplex 216 | nVars = length(v); 217 | mu = sort(v,'descend'); 218 | sm = 0; 219 | for j = 1:nVars 220 | sm = sm+mu(j); 221 | if mu(j) - (1/j)*(sm-1) > 0 222 | row = j; 223 | sm_row = sm; 224 | end 225 | end 226 | theta = (1/row)*(sm_row-1); 227 | w = max(v-theta,0); 228 | end 229 | -------------------------------------------------------------------------------- /utils/gist_chinge.m: -------------------------------------------------------------------------------- 1 | function [svm,LOG]=gist_chinge(X,y,options) 2 | % GIST solver for the problem 3 | % 4 | % min_x |y-Xw|^2/n+\lambda*g(x) 5 | % 6 | % options: 7 | % options.lambda : reg term (default=1) 8 | % options.eps : l2 reg term for bounded fun (default=1e-8) 9 | % options.reg: reg term (l1,lsp,l2) (default='l2') 10 | % options.bias: learn bias (default=1) 11 | 12 | options=initoptions(mfilename,options); 13 | 14 | [g,prox_g]=get_reg_prox(options.reg,options); 15 | 16 | if options.bias 17 | X0=[X ones(size(X,1),1)]; 18 | g=@(x) g(x(1:end-1,:)); 19 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g); 20 | else 21 | X0=X; 22 | end 23 | 24 | vals=unique(y); 25 | nbclass=length(vals); 26 | 27 | y0=-ones(size(X,1),nbclass); 28 | 29 | for i=1:nbclass 30 | y0(y==vals(i),i)=1; 31 | end 32 | 33 | 34 | f=@(x) cost(x,X0,y0); 35 | df=@(x) grad(x,X0,y0); 36 | 37 | W0=zeros(size(X0,2),nbclass); 38 | 39 | 40 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options); 41 | 42 | if options.bias 43 | svm.w=W(1:end-1,:); 44 | svm.w0=W(end,:); 45 | else 46 | svm.w=W; 47 | svm.w0=0; 48 | end 49 | 50 | svm.W=W; 51 | 52 | svm.multiclass=1; 53 | svm.nbclass=length(vals); 54 | svm.vals=vals; 55 | 56 | 57 | end 58 | 59 | function df=grad(w,X,y) 60 | yp=y.*(X*w); 61 | P=1-(1+max(0,yp))./(2+abs(yp)); 62 | df=-(X)'*(y.*P)/size(X,1); 63 | end 64 | 65 | function f=cost(w,X,y) 66 | yp=y.*(X*w); 67 | f=sum(sum(max(0,-yp)-log(2+abs(yp))))/size(X,1); 68 | end 69 | 70 | function res=prox_bias(x,lambda,prox) 71 | res=prox(x,lambda); 72 | res(end,:)=x(end,1); 73 | end -------------------------------------------------------------------------------- /utils/gist_hinge2.m: -------------------------------------------------------------------------------- 1 | function [svm,LOG]=gist_hinge2(X,y,options) 2 | % GIST solver for the problem 3 | % 4 | % min_x |y-Xw|^2/n+\lambda*g(x) 5 | % 6 | % options: 7 | % options.lambda : reg term (default=1) 8 | % options.eps : l2 reg term for bounded fun (default=1e-8) 9 | % options.reg: reg term (l1,lsp,l2) (default='l2') 10 | % options.bias: learn bias (default=1) 11 | 12 | options=initoptions(mfilename,options); 13 | 14 | [g,prox_g]=get_reg_prox(options.reg,options); 15 | 16 | if options.bias 17 | X0=[X ones(size(X,1),1)]; 18 | g=@(x) g(x(1:end-1,:)); 19 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g); 20 | else 21 | X0=X; 22 | end 23 | 24 | vals=unique(y); 25 | nbclass=length(vals); 26 | 27 | y0=-ones(size(X,1),nbclass); 28 | 29 | for i=1:nbclass 30 | y0(y==vals(i),i)=1; 31 | end 32 | 33 | 34 | f=@(x) cost(x,X0,y0); 35 | df=@(x) grad(x,X0,y0); 36 | 37 | W0=zeros(size(X0,2),nbclass); 38 | 39 | 40 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options); 41 | 42 | if options.bias 43 | svm.w=W(1:end-1,:); 44 | svm.w0=W(end,:); 45 | else 46 | svm.w=W; 47 | svm.w0=0; 48 | end 49 | 50 | svm.W=W; 51 | 52 | svm.multiclass=1; 53 | svm.nbclass=length(vals); 54 | svm.vals=vals; 55 | 56 | 57 | end 58 | 59 | function df=grad(w,X,y) 60 | T=max(1-y.*(X*w),0); 61 | df=-X'*(T.*y)/size(X,1); 62 | end 63 | 64 | function f=cost(w,X,y) 65 | T=max(1-y.*(X*w),0); 66 | f=sum(sum(T.^2))/size(X,1)/2; 67 | end 68 | 69 | function res=prox_bias(x,lambda,prox) 70 | res=prox(x,lambda); 71 | res(end,:)=x(end,1); 72 | end 73 | -------------------------------------------------------------------------------- /utils/gist_least.m: -------------------------------------------------------------------------------- 1 | % function [w,w0,LOG]=gist_least(X,y,options) 2 | function [svm,LOG]=gist_least(X,y,options) 3 | % GIST solver for the problem 4 | % 5 | % min_x |y-Xw|^2/n+\lambda*g(x) 6 | % 7 | % options: 8 | % options.lambda : reg term (default=1) 9 | % options.reg: reg term (l1,lsp,l2) (default='l2') 10 | % options.bias : estimate a bias (default=1) 11 | % options.pos : force positive 0 (default=0) 12 | % options.W0 : force positive 0 (default=[]) 13 | 14 | options=initoptions(mfilename,options); 15 | 16 | 17 | % get proximal operator and reg function 18 | [g,prox_g]=get_reg_prox(options.reg,options); 19 | 20 | % generate matrix with without bias 21 | if options.bias 22 | X0=[X ones(size(X,1),1)]; 23 | g=@(x) g(x(1:end-1,:)); 24 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g); 25 | else 26 | X0=X; 27 | end 28 | 29 | % add positivity constraints 30 | if options.pos 31 | prox_g=@(x,lambda) prox_g(max(x,0),lambda); 32 | end 33 | 34 | if isempty(options.W0) 35 | W0=zeros(size(X0,2),size(y,2)); % Starting point a parametrer ? 36 | W0(end)=0; 37 | else 38 | W0=options.W0; 39 | end 40 | 41 | f=@(x) cost(x,X0,y); 42 | df=@(x) grad(x,X0,y); 43 | 44 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options); 45 | 46 | if options.bias 47 | svm.w=W(1:end-1,:); 48 | svm.w0=W(end,:); 49 | else 50 | svm.w=W; 51 | svm.w0=0; 52 | end 53 | 54 | svm.W=W; 55 | 56 | 57 | end 58 | 59 | function df=grad(w,X,y) 60 | df=-X'*(y-X*w);%/size(X,1); 61 | end 62 | 63 | function f=cost(w,X,y) 64 | f=norm(y-X*w,'fro')^2/2;%/size(X,1)/2; 65 | end 66 | 67 | function res=prox_bias(x,lambda,prox) 68 | res=prox(x,lambda); 69 | res(end,:)=x(end,1); 70 | end -------------------------------------------------------------------------------- /utils/gist_logreg.m: -------------------------------------------------------------------------------- 1 | function [svm,LOG]=gist_logreg(X,y,options) 2 | % GIST solver for the problem 3 | % 4 | % min_x |y-Xw|^2/n+\lambda*g(x) 5 | % 6 | % options: 7 | % options.lambda : reg term (default=1) 8 | % options.eps : l2 reg term for bounded fun (default=1e-8) 9 | % options.reg: reg term (l1,lsp,l2) (default='l2') 10 | % options.bias: learn bias (default=1) 11 | 12 | options=initoptions(mfilename,options); 13 | 14 | [g,prox_g]=get_reg_prox(options.reg,options); 15 | 16 | if options.bias 17 | X0=[X ones(size(X,1),1)]; 18 | g=@(x) g(x(1:end-1,:)); 19 | prox_g=@(x,lambda) prox_bias(x,lambda,prox_g); 20 | else 21 | X0=X; 22 | end 23 | 24 | vals=unique(y); 25 | nbclass=length(vals); 26 | 27 | y0=zeros(size(X,1),nbclass); 28 | 29 | for i=1:nbclass 30 | y0(y==vals(i),i)=1; 31 | end 32 | 33 | y0=logical(y0); 34 | 35 | f=@(x) cost(x,X0,y0); 36 | df=@(x) grad(x,X0,y0); 37 | 38 | W0=zeros(size(X0,2),nbclass); 39 | 40 | 41 | [W,LOG]=gist_opt(f,df,g,prox_g,W0,options); 42 | 43 | if options.bias 44 | svm.w=W(1:end-1,:); 45 | svm.w0=W(end,:); 46 | else 47 | svm.w=W; 48 | svm.w0=0; 49 | end 50 | 51 | svm.W=W; 52 | 53 | svm.multiclass=1; 54 | svm.nbclass=length(vals); 55 | svm.vals=vals; 56 | 57 | 58 | end 59 | 60 | function df=grad(w,X,y) 61 | [R]=lr_mc_residue(w,X,y); 62 | df=X'*R/size(X,1); 63 | end 64 | 65 | function f=cost(w,X,y) 66 | t=size(y,2); 67 | M=X*w; 68 | py=M(y); 69 | E=exp(M-py*ones(1,t)); 70 | f=sum(log(sum(E,2)))/size(X,1); 71 | end 72 | 73 | function [R]=lr_mc_residue(w,X,y) 74 | t=size(y,2); 75 | M=X*w; 76 | py=M(y); 77 | 78 | E=exp(M-py*ones(1,t)); 79 | 80 | SE=sum(E,2)*ones(1,t); 81 | 82 | R=(E-y.*SE)./SE; 83 | end 84 | 85 | function res=prox_bias(x,lambda,prox) 86 | res=prox(x,lambda); 87 | res(end,:)=x(end,1); 88 | end 89 | -------------------------------------------------------------------------------- /utils/gist_opt.m: -------------------------------------------------------------------------------- 1 | function [x,LOG]=gist_opt(f,df,g,prox_g,x0,options) 2 | % GIST solver for the problem 3 | % 4 | % min_x f(x)+\lambda g(x) 5 | % 6 | % f : cost function 7 | % df : gradien of the cost function 8 | % g : reg function 9 | % prox_g: proximal function 10 | % x0 : starting point 11 | % 12 | % options: 13 | % options.lambda : reg term (default=1e0) 14 | % options.eta: backward param for linesearch (default=2) 15 | % options.t0 : initial step (default=1) 16 | % options.sigma : line search param (default=1e-5) 17 | % options.m : line serarch param 2 (default=5) 18 | % options.nbitermax: max number iterations (default=1000) 19 | % options.stopvarx: stop threshold variation w (default=1e-5) 20 | % options.stopvarj: stop threshold variation cost (default=1e-5) 21 | % options.nbinneritermax: max number iterations (default=20) 22 | % options.verbose: print infos (default=0) 23 | 24 | 25 | options=initoptions(mfilename,options); 26 | 27 | x=x0; 28 | 29 | grad=df(x); 30 | 31 | loss=f(x)+options.lambda*g(x); 32 | 33 | t=options.t0; 34 | 35 | 36 | if options.verbose 37 | fprintf('|%5s|%13s|%13s|%13s|\n-------------------------------------------------\n','Iter','Loss','Dloss','Step') 38 | fprintf('|%5d|%+8e|%+8e|%+8e|\n',0,loss(end),0,1/t) 39 | end 40 | 41 | loop=1; 42 | it=1; 43 | test = 0 ; 44 | 45 | while loop 46 | 47 | x_1=x; 48 | grad_1=grad; 49 | 50 | grad=df(x); 51 | 52 | x=prox_g(x_1-grad/t,options.lambda/t); 53 | 54 | loss=[loss;f(x)+options.lambda*g(x)]; 55 | 56 | it2=1; 57 | ifin = length(loss) ; 58 | thr_back=max(loss(max(ifin-options.m,1):ifin-1)-options.sigma/2*t*norm(x-x_1,'fro')^2); 59 | while loss(end)>thr_back && it2 < options.nbinneritermax 60 | t=t*options.eta; 61 | x=prox_g(x_1-grad/t,options.lambda/t); 62 | loss(end)=f(x)+options.lambda*g(x); 63 | ifin = length(loss) ; 64 | thr_back=max(loss(max(ifin-options.m,1):ifin-1)-options.sigma/2*t*norm(x-x_1,'fro')^2); 65 | it2=it2+1; 66 | end 67 | 68 | xbb=x-x_1; 69 | ybb=grad-grad_1; 70 | % if it>=1 && norm(xbb,'fro')>1e-12 && norm(ybb,'fro')>1e-12 71 | if it>=1 && norm(xbb,'fro')/size(xbb,1)>1e-12 && norm(ybb,'fro')/size(ybb,1)>1e-12 72 | t=abs(sum(sum((xbb.*ybb)))/sum(sum(xbb.*xbb))); 73 | t = min(max(t,1e-20),1e20); 74 | end 75 | 76 | if options.verbose 77 | if mod(it,20)==0 78 | fprintf('|%5s|%13s|%13s|%13s|\n-------------------------------------------------\n','Iter','Loss','Dloss','Step') 79 | end 80 | fprintf('|%5d|%+8e|%+8e|%+8e|\n',it,loss(end),(loss(end)-loss(end-1))/abs(loss(end-1)),1/t) 81 | end 82 | 83 | % if norm(x-x_1)/norm(x)=options.nbitermax 101 | loop=0; 102 | if options.verbose 103 | disp('max number iteration reached') 104 | end 105 | end 106 | 107 | if test>=3 108 | loop=0; 109 | if options.verbose 110 | disp('3 criteres de cv atteints') 111 | end 112 | end 113 | 114 | it=it+1; 115 | 116 | 117 | 118 | end 119 | 120 | 121 | LOG.loss=loss ; -------------------------------------------------------------------------------- /utils/initoptions.m: -------------------------------------------------------------------------------- 1 | function options=initoptions(fname,options,optname) 2 | % options=initoptions(fname,options) 3 | % function that automatically load default options from comments 4 | % in a matlab function 5 | % example of options parameters 6 | % 7 | % options parameters: 8 | % options.test1 Crappy value to set (default=10) 9 | % options.test2 Crappy value to also set (default='testdestring') 10 | 11 | if nargin<2 12 | options=struct(); 13 | end 14 | 15 | 16 | if nargin<3 17 | optname='options'; 18 | end 19 | 20 | 21 | pattern_opt=[optname '\.(\w+)' ]; 22 | pattern_val=['\(default=(.+)\)' ]; 23 | 24 | fileID = fopen([fname '.m'],'r'); 25 | 26 | tline = fgetl(fileID); 27 | while ischar(tline) 28 | if ~isempty(tline) 29 | if tline(1)=='%' 30 | opt=regexp(tline,pattern_opt,'tokens'); 31 | if ~isempty(opt) 32 | val=regexp(tline,pattern_val,'tokens'); 33 | if ~isempty(val) 34 | tsk=['temp=' val{1}{1} ';']; 35 | eval(tsk); 36 | if ~isfield(options,opt{1}{1}) 37 | options.(opt{1}{1}) =temp; 38 | end 39 | end 40 | end 41 | 42 | end 43 | end 44 | tline = fgetl(fileID); 45 | end 46 | 47 | fclose(fileID); 48 | -------------------------------------------------------------------------------- /utils/l2_unmix.m: -------------------------------------------------------------------------------- 1 | function x=l2_unmix(y,D,lambda) 2 | 3 | H=D'*D+lambda*eye(size(D,2)); 4 | f=-y'*D; 5 | opts1= optimset('display','off'); 6 | 7 | x = quadprog(H,f,[],[],[],[],zeros(size(D,2),1),[],[],opts1); -------------------------------------------------------------------------------- /utils/l2_unmix_simplex.m: -------------------------------------------------------------------------------- 1 | function x=l2_unmix(y,D,lambda) 2 | 3 | H=D'*D+lambda*eye(size(D,2)); 4 | f=-y'*D; 5 | A=ones(1,size(D,2)); 6 | b=1; 7 | x = quadprog(H,f,[],[],A,b,zeros(size(D,2),1)); -------------------------------------------------------------------------------- /utils/l2simplex.m: -------------------------------------------------------------------------------- 1 | function res=l2simplex(x,lambda) 2 | if lambda>=1 3 | res=zeros(size(x)); 4 | ind=find(x==max(x)); 5 | res(ind(1))=1; 6 | else 7 | res=projectSimplex(x/(1-lambda)); 8 | end 9 | end --------------------------------------------------------------------------------