回归模型——典型相关分析cross_decomposition C++ 带类实现及案例
时间: 2023-11-17 12:05:42 浏览: 32
典型相关分析(Canonical Correlation Analysis,CCA)是一种通过寻找两个变量集合之间的最大相关性来探索它们之间关系的统计方法。在实际应用中,典型相关分析被广泛用于多元数据分析、数据挖掘、生物统计学和社会科学等领域。
在C++中,我们可以使用cross_decomposition库来实现典型相关分析。下面是一个带类的实现及案例代码:
```cpp
#include <iostream>
#include <Eigen/Dense>
#include <Eigen/Eigenvalues>
#include <Eigen/SVD>
#include <Eigen/LU>
#include <Eigen/QR>
#include <unsupported/Eigen/MatrixFunctions>
using namespace Eigen;
class CCA {
public:
CCA(const MatrixXd& X, const MatrixXd& Y, int num_components) {
int n = X.rows(), p = X.cols(), q = Y.cols();
// Centering the data
MatrixXd X_centered = X.rowwise() - X.colwise().mean();
MatrixXd Y_centered = Y.rowwise() - Y.colwise().mean();
// Computing the covariance matrices
MatrixXd cov = X_centered.transpose() * Y_centered / (n - 1);
MatrixXd cov_xx = X_centered.transpose() * X_centered / (n - 1);
MatrixXd cov_yy = Y_centered.transpose() * Y_centered / (n - 1);
// Computing the SVD of the covariance matrix
JacobiSVD<MatrixXd> svd(cov, ComputeThinU | ComputeThinV);
// Extracting the canonical correlation coefficients and vectors
MatrixXd U = svd.matrixU();
MatrixXd V = svd.matrixV();
VectorXd d = svd.singularValues();
// Computing the canonical variates
MatrixXd A = X_centered * U;
MatrixXd B = Y_centered * V;
// Sorting the canonical correlation coefficients and vectors
MatrixXd D = d.asDiagonal();
MatrixXd D_inv = D.inverse();
MatrixXd A_tilde = A * D_inv;
MatrixXd B_tilde = B * D_inv;
Eigen::GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A_tilde.transpose() * cov_xx.inverse() * A_tilde, B_tilde.transpose() * cov_yy.inverse() * B_tilde);
VectorXd lambda = es.eigenvalues();
MatrixXd alpha = es.eigenvectors().leftCols(num_components);
// Storing the results
m_canonical_correlation_coefficients = d.head(num_components);
m_canonical_correlation_vectors_x = U.leftCols(num_components);
m_canonical_correlation_vectors_y = V.leftCols(num_components);
m_canonical_variates_x = A * alpha;
m_canonical_variates_y = B * alpha;
}
VectorXd get_canonical_correlation_coefficients() {
return m_canonical_correlation_coefficients;
}
MatrixXd get_canonical_correlation_vectors_x() {
return m_canonical_correlation_vectors_x;
}
MatrixXd get_canonical_correlation_vectors_y() {
return m_canonical_correlation_vectors_y;
}
MatrixXd get_canonical_variates_x() {
return m_canonical_variates_x;
}
MatrixXd get_canonical_variates_y() {
return m_canonical_variates_y;
}
private:
VectorXd m_canonical_correlation_coefficients;
MatrixXd m_canonical_correlation_vectors_x;
MatrixXd m_canonical_correlation_vectors_y;
MatrixXd m_canonical_variates_x;
MatrixXd m_canonical_variates_y;
};
int main() {
// Creating sample data
MatrixXd X(100, 3);
MatrixXd Y(100, 2);
for (int i = 0; i < 100; i++) {
X(i, 0) = i;
X(i, 1) = i * 2;
X(i, 2) = i * 3;
Y(i, 0) = i;
Y(i, 1) = i * 4;
}
// Running canonical correlation analysis
CCA cca(X, Y, 2);
// Printing the results
std::cout << "Canonical correlation coefficients: " << std::endl << cca.get_canonical_correlation_coefficients() << std::endl;
std::cout << "Canonical correlation vectors for X: " << std::endl << cca.get_canonical_correlation_vectors_x() << std::endl;
std::cout << "Canonical correlation vectors for Y: " << std::endl << cca.get_canonical_correlation_vectors_y() << std::endl;
std::cout << "Canonical variates for X: " << std::endl << cca.get_canonical_variates_x() << std::endl;
std::cout << "Canonical variates for Y: " << std::endl << cca.get_canonical_variates_y() << std::endl;
return 0;
}
```
在这个示例代码中,我们首先定义了一个名为CCA的类,它包含了计算典型相关分析的所有方法。在构造函数中,我们首先对数据进行中心化,然后计算协方差矩阵和奇异值分解。接下来,我们提取了典型相关系数和向量,并通过它们计算了典型变量。最后,我们对典型相关系数和向量进行排序,并存储结果。
在main函数中,我们创建了一个包含两个数据集的示例数据,并运行了我们刚刚定义的CCA类来计算典型相关分析。最后,我们打印了结果。
这是一个简单的示例,你可以根据自己的需求对代码进行修改和扩展。