Libsvm自定义核函数【转】

1. 使用libsvm工具箱时，可以指定使用工具箱自带的一些核函数（-t参数），主要有：

-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)

2. 有时我们需要使用自己的核函数，这时候可以用 -t 4参数来实现：

-t kernel_type : set type of kernel function (default 2)
4 -- precomputed kernel (kernel values in training_instance_matrix)

使用-t 4参数时，再有了核函数后，需要给出核矩阵，关于核函数以及核函数构造相关的知识，大家可以看看相关书籍，在此不特别深入说明。

比如线性核函数 是 K(x,x‘) = (x * x‘)，设训练集是train_data，设训练集有150个样本 , 测试集是test_data，设测试集有120个样本
则 训练集的核矩阵是 ktrain1 = train_data*train_data‘
测试集的核矩阵是 ktest1 = test_data*train_data‘
想要使用-t 4参数还需要把样本的序列号放在核矩阵前面 ，形成一个新的矩阵，然后使用svmtrain建立支持向量机，再使用svmpredict进行预测即可。形式与使用其他-t参数少有不同，如下：

ktrain1 = train_data*train_data‘;
Ktrain1 = [(1:150)‘,ktrain1];

model_precomputed1 = svmtrain(train_label, Ktrain1, ‘-t 4‘);  % 注意此处的 输入 Ktrain1

ktest1 = test_data*train_data‘;
Ktest1 = [(1:120)‘, ktest1];

[predict_label_P1, accuracy_P1, dec_values_P1] = svmpredict(test_label,Ktest1,model_precomputed1); % 注意此处输入Ktest1</pre>

下面是一个整体的小例子，大家可以看一下：

%% Use_precomputed_kernelForLibsvm_example
% faruto
% last modified by 2011.04.20
%%
tic;
clear;
clc;
close all;
format compact;
%%
load heart_scale.mat;
% Split Data
train_data = heart_scale_inst(1:150,:);
train_label = heart_scale_label(1:150,:);
test_data = heart_scale_inst(151:270,:);
test_label = heart_scale_label(151:270,:);

%% Linear Kernel
model_linear = svmtrain(train_label, train_data, ‘-t 0‘);
[predict_label_L, accuracy_L, dec_values_L] = svmpredict(test_label, test_data, model_linear);

%% Precomputed Kernel One
% 使用的核函数 K(x,x‘) = (x * x‘)
% 核矩阵
ktrain1 = train_data*train_data‘;
Ktrain1 = [(1:150)‘,ktrain1];
model_precomputed1 = svmtrain(train_label, Ktrain1, ‘-t 4‘);
ktest1 = test_data*train_data‘;
Ktest1 = [(1:120)‘, ktest1];
[predict_label_P1, accuracy_P1, dec_values_P1] = svmpredict(test_label, Ktest1, model_precomputed1);

%% Precomputed Kernel Two
% 使用的核函数 K(x,x‘) = ||x|| * ||x‘||
% 核矩阵
ktrain2 = ones(150,150);
for i = 1:150
 for j = 1:150
 ktrain2(i,j) = sum(train_data(i,:).^2)^0.5 * sum(train_data(j,:).^2)^0.5;
 end
end
Ktrain2 = [(1:150)‘,ktrain2];
model_precomputed2 = svmtrain(train_label, Ktrain2, ‘-t 4‘);

ktest2 = ones(120,150);
for i = 1:120
 for j = 1:150
 ktest2(i,j) = sum(test_data(i,:).^2)^0.5 * sum(train_data(j,:).^2)^0.5;
 end
end
Ktest2 = [(1:120)‘, ktest2];
[predict_label_P2, accuracy_P2, dec_values_P2] = svmpredict(test_label, Ktest2, model_precomputed2);
%% Precomputed Kernel Three
% 使用的核函数 K(x,x‘) = (x * x‘) / ||x|| * ||x‘||
% 核矩阵
ktrain3 = ones(150,150);
for i = 1:150
 for j = 1:150
 ktrain3(i,j) = ...
 train_data(i,:)*train_data(j,:)‘/(sum(train_data(i,:).^2)^0.5 * sum(train_data(j,:).^2)^0.5);
 end
end
Ktrain3 = [(1:150)‘,ktrain3];
model_precomputed3 = svmtrain(train_label, Ktrain3, ‘-t 4‘);

ktest3 = ones(120,150);
for i = 1:120
 for j = 1:150
 ktest3(i,j) = ...
 test_data(i,:)*train_data(j,:)‘/(sum(test_data(i,:).^2)^0.5 * sum(train_data(j,:).^2)^0.5);
 end
end
Ktest3 = [(1:120)‘, ktest3];
[predict_label_P3, accuracy_P3, dec_values_P3] = svmpredict(test_label, Ktest3, model_precomputed3);

%% Display the accuracy
accuracyL = accuracy_L(1) % Display the accuracy using linear kernel
accuracyP1 = accuracy_P1(1) % Display the accuracy using precomputed kernel One
accuracyP2 = accuracy_P2(1) % Display the accuracy using precomputed kernel Two
accuracyP3 = accuracy_P3(1) % Display the accuracy using precomputed kernel Three
%%
toc;

运行结果：

Accuracy = 85% (102/120) (classification)
Accuracy = 85% (102/120) (classification)
Accuracy = 67.5% (81/120) (classification)
Accuracy = 84.1667% (101/120) (classification)
accuracyL =
 85
accuracyP1 =
 85
accuracyP2 =
 67.5000
accuracyP3 =
 84.1667
Elapsed time is 1.424549 seconds.