支持向量机对线性不可分数据的处理

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118

#include <iostream>
#include <opencv2/core/core.hpp>
#include <opencv2/highgui/highgui.hpp>
#include <opencv2/ml/ml.hpp>

#define NTRAINING_SAMPLES   100         // Number of training samples per class
#define FRAC_LINEAR_SEP     0.9f        // Fraction of samples which compose the linear separable part

using namespace cv;
using namespace std;

int main()
{
// Data for visual representation
const int WIDTH = 512, HEIGHT = 512;
Mat I = Mat::zeros(HEIGHT, WIDTH, CV_8UC3);

//--------------------- 1. Set up training data randomly ---------------------------------------
Mat trainData(2*NTRAINING_SAMPLES, 2, CV_32FC1);
Mat labels   (2*NTRAINING_SAMPLES, 1, CV_32FC1);

RNG rng(100); // Random value generation class

// Set up the linearly separable part of the training data
int nLinearSamples = (int) (FRAC_LINEAR_SEP * NTRAINING_SAMPLES);

// Generate random points for the class 1
Mat trainClass = trainData.rowRange(0, nLinearSamples);
// The x coordinate of the points is in [0, 0.4)
Mat c = trainClass.colRange(0, 1);
rng.fill(c, RNG::UNIFORM, Scalar(1), Scalar(0.4 * WIDTH));
// The y coordinate of the points is in [0, 1)
c = trainClass.colRange(1,2);
rng.fill(c, RNG::UNIFORM, Scalar(1), Scalar(HEIGHT));

// Generate random points for the class 2
trainClass = trainData.rowRange(2*NTRAINING_SAMPLES-nLinearSamples, 2*NTRAINING_SAMPLES);
// The x coordinate of the points is in [0.6, 1]
c = trainClass.colRange(0 , 1);
rng.fill(c, RNG::UNIFORM, Scalar(0.6*WIDTH), Scalar(WIDTH));
// The y coordinate of the points is in [0, 1)
c = trainClass.colRange(1,2);
rng.fill(c, RNG::UNIFORM, Scalar(1), Scalar(HEIGHT));

//------------------ Set up the non-linearly separable part of the training data ---------------

// Generate random points for the classes 1 and 2
trainClass = trainData.rowRange(  nLinearSamples, 2*NTRAINING_SAMPLES-nLinearSamples);
// The x coordinate of the points is in [0.4, 0.6)
c = trainClass.colRange(0,1);
rng.fill(c, RNG::UNIFORM, Scalar(0.4*WIDTH), Scalar(0.6*WIDTH));
// The y coordinate of the points is in [0, 1)
c = trainClass.colRange(1,2);
rng.fill(c, RNG::UNIFORM, Scalar(1), Scalar(HEIGHT));

//------------------------- Set up the labels for the classes ---------------------------------
labels.rowRange(                0,   NTRAINING_SAMPLES).setTo(1);  // Class 1
labels.rowRange(NTRAINING_SAMPLES, 2*NTRAINING_SAMPLES).setTo(2);  // Class 2

//------------------------ 2. Set up the support vector machines parameters --------------------
CvSVMParams params;
params.svm_type    = SVM::C_SVC;
params.C           = 0.1;
params.kernel_type = SVM::LINEAR;
params.term_crit   = TermCriteria(CV_TERMCRIT_ITER, (int)1e7, 1e-6);

//------------------------ 3. Train the svm ----------------------------------------------------
cout << "Starting training process" << endl;
CvSVM svm;
svm.train(trainData, labels, Mat(), Mat(), params);
cout << "Finished training process" << endl;

//------------------------ 4. Show the decision regions ----------------------------------------
Vec3b green(0,100,0), blue (100,0,0);
for (int i = 0; i < I.rows; ++i)
for (int j = 0; j < I.cols; ++j)
{
Mat sampleMat = (Mat_<float>(1,2) << i, j);
float response = svm.predict(sampleMat);

if      (response == 1)    I.at<Vec3b>(j, i)  = green;
else if (response == 2)    I.at<Vec3b>(j, i)  = blue;
}

//----------------------- 5. Show the training data --------------------------------------------
int thick = -1;
int lineType = 8;
float px, py;
// Class 1
for (int i = 0; i < NTRAINING_SAMPLES; ++i)
{
px = trainData.at<float>(i,0);
py = trainData.at<float>(i,1);
circle(I, Point( (int) px,  (int) py ), 3, Scalar(0, 255, 0), thick, lineType);
}
// Class 2
for (int i = NTRAINING_SAMPLES; i <2*NTRAINING_SAMPLES; ++i)
{
px = trainData.at<float>(i,0);
py = trainData.at<float>(i,1);
circle(I, Point( (int) px, (int) py ), 3, Scalar(255, 0, 0), thick, lineType);
}

//------------------------- 6. Show support vectors --------------------------------------------
thick = 2;
lineType  = 8;
int x     = svm.get_support_vector_count();

for (int i = 0; i < x; ++i)
{
const float* v = svm.get_support_vector(i);
circle( I,  Point( (int) v[0], (int) v[1]), 6, Scalar(128, 128, 128), thick, lineType);
}

imwrite("result.png", I);                      // save the Image
imshow("SVM for Non-Linear Training Data", I); // show it to the user
waitKey(0);
}