Kernel ridge regression C++带类实现

以下是一个简单的Kernel ridge regression（核岭回归）实现，它使用C++类来实现。这个类包含了训练和预测方法。

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

using namespace std;
using namespace Eigen;

class KernelRidgeRegression {
public:
    KernelRidgeRegression(vector<vector<double>> X, vector<double> y, double alpha, string kernel_type, double gamma=1.0, double degree=3.0, double coef0=0.0);
    void train();
    double predict(vector<double> x);

private:
    vector<vector<double>> X_;
    vector<double> y_;
    double alpha_;
    string kernel_type_;
    double gamma_;
    double degree_;
    double coef0_;
    int n_samples_;
    MatrixXd K_;
    VectorXd alpha_hat_;
};

KernelRidgeRegression::KernelRidgeRegression(vector<vector<double>> X, vector<double> y, double alpha, string kernel_type, double gamma, double degree, double coef0) {
    X_ = X;
    y_ = y;
    alpha_ = alpha;
    kernel_type_ = kernel_type;
    gamma_ = gamma;
    degree_ = degree;
    coef0_ = coef0;
    n_samples_ = X.size();
}

void KernelRidgeRegression::train() {
    K_ = MatrixXd(n_samples_, n_samples_);

    if (kernel_type_ == "linear") {
        for (int i = 0; i < n_samples_; i++) {
            for (int j = 0; j < n_samples_; j++) {
                K_(i, j) = inner_product(X_[i].begin(), X_[i].end(), X_[j].begin(), 0.0);
            }
        }
    } else if (kernel_type_ == "poly") {
        for (int i = 0; i < n_samples_; i++) {
            for (int j = 0; j < n_samples_; j++) {
                K_(i, j) = pow(gamma_ * inner_product(X_[i].begin(), X_[i].end(), X_[j].begin(), 0.0) + coef0_, degree_);
            }
        }
    } else if (kernel_type_ == "rbf") {
        for (int i = 0; i < n_samples_; i++) {
            for (int j = 0; j < n_samples_; j++) {
                K_(i, j) = exp(-gamma_ * pow(inner_product(X_[i].begin(), X_[i].end(), X_[j].begin(), 0.0), 2));
            }
        }
    } else {
        throw invalid_argument("Invalid kernel type");
    }

    alpha_hat_ = (K_ + alpha_ * MatrixXd::Identity(n_samples_, n_samples_)).colPivHouseholderQr().solve(VectorXd::Map(y_.data(), y_.size()));
}

double KernelRidgeRegression::predict(vector<double> x) {
    VectorXd k(n_samples_);
    if (kernel_type_ == "linear") {
        for (int i = 0; i < n_samples_; i++) {
            k(i) = inner_product(X_[i].begin(), X_[i].end(), x.begin(), 0.0);
        }
    } else if (kernel_type_ == "poly") {
        for (int i = 0; i < n_samples_; i++) {
            k(i) = pow(gamma_ * inner_product(X_[i].begin(), X_[i].end(), x.begin(), 0.0) + coef0_, degree_);
        }
    } else if (kernel_type_ == "rbf") {
        for (int i = 0; i < n_samples_; i++) {
            k(i) = exp(-gamma_ * pow(inner_product(X_[i].begin(), X_[i].end(), x.begin(), 0.0), 2));
        }
    } else {
        throw invalid_argument("Invalid kernel type");
    }

    return (alpha_hat_.transpose() * k)(0);
}

这个实现使用了Eigen库来进行矩阵运算。在构造函数中传入训练数据X和y、正则化参数alpha、核函数类型（线性、多项式、高斯径向基函数）、核函数参数（如果需要）。

在train方法中，我们计算并存储核矩阵K，并使用QR分解求解alpha_hat。

在predict方法中，我们计算输入向量x和每个训练样本之间的核函数值k，然后计算预测值。

这个实现是一个简单的示例，你可以根据你的需要进行修改和扩展。