C++最小二乘法图像分类

最小二乘法是一种常用的回归分析方法，可以用于图像分类。下面是C++实现最小二乘法图像分类的示例代码：

#include <iostream>
#include <fstream>
#include <cmath>

using namespace std;

const int N = 100; // 样本数
const int M = 3; // 特征数

double x[N][M]; // 特征矩阵
int y[N]; // 标签向量

// 读取数据
void read_data() {
    ifstream fin("data.txt");
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            fin >> x[i][j];
        }
        fin >> y[i];
    }
    fin.close();
}

// 计算矩阵的转置
void transpose(double a[][M], double b[][N], int n, int m) {
    for (int i = 0; i < m; i++) {
        for (int j = 0; j < n; j++) {
            b[i][j] = a[j][i];
        }
    }
}

// 矩阵乘法
void matrix_multiply(double a[][N], double b[][M], double c[][M], int n, int m, int k) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < k; j++) {
            c[i][j] = 0;
            for (int l = 0; l < m; l++) {
                c[i][j] += a[i][l] * b[l][j];
            }
        }
    }
}

// 矩阵加法
void matrix_add(double a[][M], double b[][M], double c[][M], int n, int m) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            c[i][j] = a[i][j] + b[i][j];
        }
    }
}

// 矩阵数乘
void matrix_scalar_multiply(double a[][M], double b, int n, int m) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < m; j++) {
            a[i][j] *= b;
        }
    }
}

// 矩阵求逆
bool matrix_inverse(double a[][M], double b[][M], int n) {
    double temp[N][2 * N];
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            temp[i][j] = a[i][j];
        }
        for (int j = n; j < 2 * n; j++) {
            temp[i][j] = (i == j - n) ? 1 : 0;
        }
    }
    for (int i = 0; i < n; i++) {
        if (temp[i][i] == 0) {
            return false;
        }
        for (int j = i + 1; j < 2 * n; j++) {
            temp[i][j] /= temp[i][i];
        }
        temp[i][i] = 1;
        for (int j = 0; j < n; j++) {
            if (i != j) {
                for (int k = i + 1; k < 2 * n; k++) {
                    temp[j][k] -= temp[j][i] * temp[i][k];
                }
                temp[j][i] = 0;
            }
        }
    }
    for (int i = 0; i < n; i++) {
        for (int j = n; j < 2 * n; j++) {
            b[i][j - n] = temp[i][j];
        }
    }
    return true;
}

// 最小二乘法
void least_squares() {
    double xt[M][N], xtx[M][M], xtx_inv[M][M], xty[M], w[M];
    int cnt[2] = {0, 0};
    for (int i = 0; i < N; i++) {
        cnt[y[i]]++;
    }
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < M; j++) {
            xt[j][i] = x[i][j];
        }
        xty[0][i] = y[i];
    }
    matrix_multiply(xt, x, xtx, M, N, M);
    matrix_add(xtx, 0.01 * cnt[1] / cnt[0] * xtx, xtx, M, M);
    if (!matrix_inverse(xtx, xtx_inv, M)) {
        cout << "Matrix is not invertible." << endl;
        return;
    }
    matrix_multiply(xtx_inv, xt, w, M, M, N);
    matrix_multiply(w, xty, w, M, N, 1);
    cout << "w = [";
    for (int i = 0; i < M; i++) {
        cout << w[i][0];
        if (i < M - 1) {
            cout << ", ";
        }
    }
    cout << "]" << endl;
}

int main() {
    read_data();
    least_squares();
    return 0;
}