opencv实现PCA降维

《learning opencv 》 ex7-3 解决方案

PCA（主成分分析）算法是数据科学领域最经典的数据降维算法之一，在之前的文章中，已经介绍过了利用Python中numpy库实现的降维方法，本篇文章，会用opencv库提供的方法，实现数据降维。

利用随机数生成器，生成一个100*3 矩阵,
a. 第一维和第二维的数据服从均值为64，方差为192的高斯分布；
b. 第三维数据服从均值为128，方差为2的高斯分布；
c.利用PCA对象计算降维后的数据，其最大主成分设置为2

其实现代码如下所示：

#include<iostream>
#include<opencv2/opencv.hpp>

using namespace cv;

/*
1. Using cv::RNG random number generator,create an array of 100 three-byte objects such that:
    a. The first and second dimensions hava a Gaussian distribution ,centered at 64,and 192,respectively,each
        with variance of 10;
    b. The third dimension has a Guassian distribution,centered at 128,and with variance of 2;
    c. Using the cv::PCA object,compute a projection for which maxComponets=2
    d. Compute the mean in both dimensions of the projections;explain the result;
*/
int main()
{
    Mat m = Mat(100, 3, CV_32F, Scalar(0));
    RNG rng = theRNG();
    rng.fill(m.col(0), RNG::NORMAL, 64, 10);
    rng.fill(m.col(1), RNG::NORMAL, 192, 10);
    rng.fill(m.col(2), RNG::NORMAL, 128, 2);
    std::cout << m.size() << std::endl;
    Mat mean;
    reduce(m, mean, 0, ReduceTypes::REDUCE_AVG, -1);
    PCA pca_mean = PCA::PCA(m, mean,cv::PCA::Flags::DATA_AS_ROW, 2);
    Mat dst_mean = pca_mean.project(m);
    //std::cout << dst_mean << std::endl;
    //std::cout << dst_mean.size() <<std::endl;
    Mat pca_dst_mean;
    reduce(dst_mean, pca_dst_mean, 0, ReduceTypes::REDUCE_AVG, -1);
    std::cout << "带均值的PCA降维算法，其按列求取均值为：" << pca_dst_mean << std::endl;
    Mat mean_dst;

    PCA pca = PCA::PCA(m, Mat(), PCA::Flags::DATA_AS_ROW, 2);
    Mat dst = pca.project(m);
    reduce(dst, mean_dst, 0, ReduceTypes::REDUCE_AVG, -1);
    std::cout << "带均值的PCA降维算法，其按列求取均值为：" << mean_dst << std::endl;
    return 0;
}