PCA dimensionality reduction under opencv

In the past two days, I checked PCA Dimensionality Reduction and tested it with opencv. Refer to [1] and [2]. According to my understanding, the code is recorded.

#include <opencv/cv.h>#include <opencv/highgui.h>#include <stdio.h>#include <stdlib.h>using namespace cv;using namespace std;#define DIMENTIONS7#define SAMPLE_NUM31float Coordinates[DIMENTIONS*SAMPLE_NUM]={ 101.5,100.4,97.0,98.7,100.8,114.2,104.2,100.8,93.5,95.9,100.7,106.7,104.3,106.4,100.8,97.4,98.2,98.2,99.5,103.6,102.4,99.4,96.0,98.2,97.8,99.1,98.3,104.3,101.8,97.7,99.0,98.1,98.4,102.0,103.7,101.8,96.8,96.4,92.7,99.6,101.3,103.4,101.3,98.2,99.4,103.7,98.7,101.4,105.3,101.9,100.0,98.4,96.9,102.7,100.3,102.3,100.3,98.9,97.2,97.4,98.1,102.1,102.3,99.3,97.7,97.6,101.1,96.8,110.1,100.4,98.7,98.4,97.0,99.6,95.6,107.2,99.8,99.7,97.7,98.0,99.3,97.3,104.1,102.7,97.6,96.5,97.6,102.5,97.2,100.6,99.9,98.0,98.4,97.1,100.5,101.4,103.0,99.9,101.1,98.6,98.7,102.4,96.9,108.2,101.7,100.4,98.6,98.0,100.7,99.4,102.4,103.3,99.3,96.9,94.0,98.1,99.7,109.7,99.2,98.6,97.4,96.4,99.8,97.4,102.1,100.0,98.2,98.2,99.4,99.3,99.7,101.5,99.9,98.5,96.3,97.0,97.7,98.7,112.6,100.4,98.4,99.2,98.1,100.2,98.0,98.2,97.8,99.2,97.4,95.7,98.9,102.4,114.8,102.6,101.3,97.9,99.2,98.8,105.4,111.9,99.9,98.5,97.8,94.6,102.4,107.0,115.0,99.5,98.3,96.3,98.5,106.2,92.5,98.6,101.6,99.3,101.1,99.4,100.1,103.6,98.7,101.3,99.2,97.3,96.2,99.7,98.2,112.6,100.5,100.0,99.9,98.2,98.3,103.6,123.2,102.8,102.2,99.4,96.2,98.6,102.4,115.3,101.2,100.1,98.7,97.4,99.8,100.6,112.4,102.5,104.3,98.7,100.2,116.1,105.2,101.6,102.6};float Coordinates_test[DIMENTIONS]={104.3,98.7,100.2,116.1,105.2,101.6,102.6};#define PCA_MEAN"mean"#define PCA_EIGEN_VECTOR"eigen_vector"int main(){//load samplesMat SampleSet(SAMPLE_NUM, DIMENTIONS, CV_32FC1);for (int i=0; i<(SAMPLE_NUM); ++i){for (int j=0; j<DIMENTIONS; ++j){SampleSet.at<float>(i, j) = Coordinates[i*DIMENTIONS + j];}}//TrainingPCA *pca = new PCA(SampleSet, Mat(), CV_PCA_DATA_AS_ROW);///////////////cout << "eigenvalues:" <<endl << pca->eigenvalues <<endl<<endl;//cout << "eigenvectors" <<endl << pca->eigenvectors << endl;Mat input(1,DIMENTIONS, CV_32FC1);//Test inputfor (int j=0; j<DIMENTIONS; ++j){input.at<float>(0, j) = Coordinates_test[j];}//calculate the decreased dimensionsint index;float sum=0, sum0=0, ratio;for (int d=0; d<pca->eigenvalues.rows; ++d){sum += pca->eigenvalues.at<float>(d,0);}for (int d=0; d<pca->eigenvalues.rows; ++d){sum0 += pca->eigenvalues.at<float>(d,0);ratio = sum0/sum;if(ratio > 0.9){index = d;break;}}Mat eigenvetors_d;eigenvetors_d.create((index+1), DIMENTIONS, CV_32FC1);//eigen values of decreased dimensionfor (int i=0; i<(index+1); ++i){pca->eigenvectors.row(i).copyTo(eigenvetors_d.row(i));}cout << "eigenvectors" <<endl << eigenvetors_d << endl;FileStorage fs_w("config.xml", FileStorage::WRITE);//write mean and eigenvalues into xml filefs_w << PCA_MEAN << pca->mean;fs_w << PCA_EIGEN_VECTOR << eigenvetors_d;fs_w.release();//EncodingPCA *pca_encoding = new PCA();FileStorage fs_r("config.xml", FileStorage::READ);fs_r[PCA_MEAN] >> pca_encoding->mean;fs_r[PCA_EIGEN_VECTOR] >> pca_encoding->eigenvectors;fs_r.release();Mat output_encode(1, pca_encoding->eigenvectors.rows, CV_32FC1);pca_encoding->project(input, output_encode);cout << endl << "pca_encode:" << endl << output_encode;//DecodingPCA *pca_decoding = new PCA();FileStorage fs_d("config.xml", FileStorage::READ);fs_d[PCA_MEAN] >> pca_decoding->mean;fs_d[PCA_EIGEN_VECTOR] >> pca_decoding->eigenvectors;fs_d.release();Mat output_decode(1, DIMENTIONS, CV_32FC1);pca_decoding->backProject(output_encode,output_decode);cout <<endl<< "pca_Decode:" << endl << output_decode;delete pca;delete pca_encoding;return 0;}

Result:

Eigenvalues:
[43.182041; 14.599923; 9.2121401; 4.0877957; 2.8236785; 0.88751495; 0.66496396]

EIGENVECTORS
[0.01278889, 0.03393811,-0.099844977,-0.13044992, 0.20732452, 0.96349025,-0.020049129;
0.15659945, 0.037932698, 0.12129638, 0.89324093, 0.39454412, 0.046447847, 0.060190294;
0.21434425, 0.018043749,-0.0012475925,-0.40428901, 0.81335503,-0.22759444, 0.2773709;
0.43591988,-0.047541384, 0.19851086,-0.0035106051,-0.35545754, 0.10898948, 0.79376709]

Pca_encode:
[-5.6273661, 17.138182,-0.078819014, 0.68144321]
Pca_decode:
[102.88557, 98.402702, 100.33086, 116.21081, 105.37261, 101.63729, 103.39891]

In this example, the result of the backproject is not very different from that of the original input.

Float coordinates_test [dimentions] = {
104.3, 98.7, 100.2, 116.1, 105.2, 101.6, 102.6
};

The principal component analysis, as its name implies, finds the most important information in the data and removes secondary information to reduce the data volume.

The procedure is as follows:

1. extract useful information from each sample to form a vector;

2. Calculate the average value of all sample vectors;

3. A matrix is formed after each sample vector is subtracted from the mean value of the vector;

4. the matrix is multiplied by the inverse of the Matrix to the covariance matrix. The covariance matrix is right-corner, and the remaining elements after the right-corner are feature values, each feature value corresponds to a feature vector (feature vectors must be standardized );

5. select the N largest feature values (n is the number of PCA's main component (PC). I feel that this number of primary elements is the core of PCa and can be selected by myself, the smaller the number, the smaller the data volume, but the worse the recognition effect). The feature vectors corresponding to the N feature values form a new matrix;

6. after the new matrix is transposed and multiplied by the sample vector, the Dimensionality Reduction data can be obtained (these data are relatively dominant in the original data, and the data volume is generally far smaller than the original data volume, of course, this depends on the number of primary elements you select ).

[1] http://blog.csdn.net/yang_xian521/article/details/7445536

[2] http://blog.csdn.net/abcjennifer/article/details/8002329