libsvm 을 사용하자

LibSVM

libsvm-3.14.zip

RBF kernel을 사용할 때 한가지 tip은 

svm_type = ['-t 2 -h 0 -g ' num2str(1/xmax/xmax) '-q']; % <= RBF 커널

다음과 같이 하는 것이다. 즉 rbf kernel function의 파라미터를 1/max/max 로 할 경우 input을 normalize할 필요가 없다. 

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xmax, ymax가 10일 때 

  

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xmax, ymax가 1일 때 

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xmax, ymax 에 따른 RBF kernel 결과 변화 

 모두 동일한 파라미터를 사용했다. input space에 kernel svm이 민감함을 알 수 있다. 

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코드

%% Libsvm

clc;

clear all;

close all;

addpath('../../Solvers/libsvm-3.14');

%% 그림 그릴지 여부 

plot_train  = 0;

kernel_type = 2; % 0: linear // 2: RBF

%% Training data를 만든다. 

rng(20);

xmax = 1; ymax = xmax;

nr_class = 5; 

class_mean = zeros(nr_class, 2);

for i = 1:nr_class

    class_mean(i, :) = [xmax*rand ymax*rand];

end

nr_data_per_class = 20;

train_input = zeros(nr_class*nr_data_per_class, 2);

train_label = zeros(nr_class*nr_data_per_class, 1);

for i = 1:nr_class

    for j = 1:nr_data_per_class

        idx = j + nr_data_per_class*(i-1);

        train_input(idx, :) = class_mean(i, :) + xmax/10*randn(1, 2);

        train_label(idx, :) = i;

    end

end

% 그려본다. 

if plot_train

    colors = varyColor(nr_class);

    figure(1); hold on; 

    for i = 1:nr_class

        for j = 1:nr_data_per_class

            idx = j + nr_data_per_class*(i-1);

            plot(train_input(idx, 1), train_input(idx, 2), 'o' ...

                , 'Color', colors(i, :) ...

                , 'MarkerFaceColor', colors(i, :));

        end

    end

    hold off; axis equal; axis([0 xmax 0 ymax]);

end

%% SVM을 학습한다. 

% -s svm_type : set type of SVM (default 0)

%     0 -- C-SVC      (multi-class classification)

%     1 -- nu-SVC     (multi-class classification)

%     2 -- one-class SVM

%     3 -- epsilon-SVR    (regression)

%     4 -- nu-SVR     (regression)

% -t kernel_type : set type of kernel function (default 2)

%     0 -- linear: u'*v

%     1 -- polynomial: (gamma*u'*v + coef0)^degree

%     2 -- radial basis function: exp(-gamma*|u-v|^2)

%     3 -- sigmoid: tanh(gamma*u'*v + coef0)

%     4 -- precomputed kernel (kernel values in training_set_file)

% -d degree : set degree in kernel function (default 3)

% -g gamma : set gamma in kernel function (default 1/num_features)

% -r coef0 : set coef0 in kernel function (default 0)

% -c cost : set the parameter C of C-SVC, epsilon-SVR, and nu-SVR (default 1)

% -n nu : set the parameter nu of nu-SVC, one-class SVM, and nu-SVR (default 0.5)

% -p epsilon : set the epsilon in loss function of epsilon-SVR (default 0.1)

% -m cachesize : set cache memory size in MB (default 100)

% -e epsilon : set tolerance of termination criterion (default 0.001)

% -h shrinking : whether to use the shrinking heuristics, 0 or 1 (default 1)

% -b probability_estimates : whether to train a SVC or SVR model for probability estimates, 0 or 1 (default 0)

% -wi weight : set the parameter C of class i to weight*C, for C-SVC (default 1)

% -v n: n-fold cross validation mode

% -q : quiet mode (no outputs)

% kernel_type = 2; % 0: linear // 2: RBF

svm_type = ['-t ' num2str(kernel_type) ' -h 0 -g ' num2str(1/xmax/xmax) '-q']; % <= RBF 커널

model = svmtrain( train_label, train_input, svm_type);

%% SVM을 테스트 한다. 

stage.xmin = 0;

stage.xmax = xmax;

stage.ymin = 0;

stage.ymax = ymax;

stage.xres = 40;

stage.yres = 40;

stage.xgrid = linspace(stage.xmin, stage.xmax, stage.xres);

stage.ygrid = linspace(stage.ymin, stage.ymax, stage.yres);

[mesh_X, mesh_Y] = meshgrid(stage.xgrid, stage.ygrid); 

stage.points = [mesh_X(:) mesh_Y(:)]; 

stage.nr_points = length(stage.points); 

field.zdata = zeros(stage.yres, stage.xres);

for xi = 1:stage.xres

    for yi = 1:stage.yres

        x = stage.xgrid(xi);

        y = stage.ygrid(yi);

        predict_label = svmpredict( 1, [x y], model); 

        field.zdata(yi, xi) = predict_label;

    end

end

% 그림을 그린다. 

colors = varyColor(nr_class);

fig = figure('Position', [400 300 500 500]); 

subaxes(fig, 1, 1, 1); hold on;

pcolor(stage.xgrid, stage.ygrid, field.zdata); % colorbar;

% shading interp; % lighting phong; 

for i = 1:nr_class

    for j = 1:nr_data_per_class

        idx = j + nr_data_per_class*(i-1);

        plot(train_input(idx, 1), train_input(idx, 2), 'o' ...

            , 'Color', 'k' ...

            , 'MarkerFaceColor', colors(i, :) ...

            , 'MarkerSize', 11 );

    end

end

hold off; axis equal; axis([0 xmax 0 ymax]);

if kernel_type == 0

    title('Linear SVM Result' ...

        , 'FontSize', 15);

elseif kernel_type == 2

    title('Kernel (RBF) SVM Result' ...

        , 'FontSize', 15);

else

    title('SVM Result' ...

        , 'FontSize', 15);

end