带截距的多元偏最小二乘回归 C++ 正确实现及带数据的案例

以下是一个带数据的多元偏最小二乘回归模型实现示例：

#include <iostream>
#include <fstream>
#include <vector>
#include <Eigen/Dense>

using namespace std;
using namespace Eigen;

MatrixXd read_data(string file_name, int n_samples, int n_features) {
    MatrixXd X(n_samples, n_features);
    ifstream file(file_name);
    if (file.is_open()) {
        for (int i = 0; i < n_samples; i++) {
            for (int j = 0; j < n_features; j++) {
                file >> X(i, j);
            }
        }
    }
    file.close();
    return X;
}

VectorXd read_target(string file_name, int n_samples) {
    VectorXd y(n_samples);
    ifstream file(file_name);
    if (file.is_open()) {
        for (int i = 0; i < n_samples; i++) {
            file >> y(i);
        }
    }
    file.close();
    return y;
}

MatrixXd center(MatrixXd& X) {
    int n_samples = X.rows();
    int n_features = X.cols();
    VectorXd mean = X.colwise().mean();
    MatrixXd centered_X(n_samples, n_features);
    for (int i = 0; i < n_samples; i++) {
        centered_X.row(i) = X.row(i) - mean.transpose();
    }
    return centered_X;
}

MatrixXd scale(MatrixXd& X) {
    int n_samples = X.rows();
    int n_features = X.cols();
    VectorXd std = ((X.array().square()).colwise().sum() / (n_samples - 1)).sqrt();
    MatrixXd scaled_X(n_samples, n_features);
    for (int i = 0; i < n_samples; i++) {
        scaled_X.row(i) = X.row(i).array() / std.transpose().array();
    }
    return scaled_X;
}

MatrixXd pls_regression(MatrixXd& X, VectorXd& y, int n_components) {
    int n_samples = X.rows();
    int n_features = X.cols();
    MatrixXd centered_X = center(X);
    VectorXd centered_y = y.array() - y.mean();
    MatrixXd w(n_features, n_components);
    MatrixXd p(n_features, n_components);
    VectorXd b(n_components);
    for (int i = 0; i < n_components; i++) {
        VectorXd u = centered_X.transpose() * centered_y;
        u = u / u.norm();
        VectorXd t = centered_X * u;
        VectorXd q = centered_X.transpose() * t;
        q = q / q.norm();
        double c = t.transpose() * centered_y / (t.transpose() * t);
        centered_y = centered_y - c * t;
        w.col(i) = u;
        p.col(i) = q;
        b(i) = c;
    }
    MatrixXd X_scores = centered_X * p;
    MatrixXd X_loadings = w;
    MatrixXd y_scores = X_scores * b;
    MatrixXd beta = X_loadings * b.transpose();
    return beta;
}

int main() {
    // 读取数据
    int n_samples = 10;
    int n_features = 3;
    MatrixXd X = read_data("data.txt", n_samples, n_features);
    VectorXd y = read_target("target.txt", n_samples);

    // 带截距的多元偏最小二乘回归
    int n_components = 2;
    MatrixXd beta = pls_regression(X, y, n_components);

    // 输出结果
    cout << "Coefficients: " << endl << beta << endl;

    return 0;
}

在这个例子中，我们假设数据集中有 10 个样本和 3 个特征，并且已经将数据存储在 "data.txt" 和 "target.txt" 两个文件中。我们读取数据并调用 `pls_regression` 函数，使用 2 个主成分进行回归。最后，输出回归系数。

需要注意的是，由于没有提供数据集，上述示例代码未经测试，可能存在语法错误或逻辑错误。