C++实现minst识别

要使用C++实现MINST识别，需要以下步骤：

1. 下载MINST数据集，包括训练集和测试集。

2. 将数据集转换为C++程序可以读取的格式。可以将图片数据转换为数组，标签数据转换为向量，保存到文件中。

3. 设计神经网络模型，可以选择使用已有的框架（如TensorFlow、Caffe等），或者自己设计模型。

4. 定义损失函数，常用的是交叉熵损失函数。

5. 使用梯度下降等优化算法，训练模型。

6. 对测试集进行预测，计算准确率。

以下是一个简单的示例代码：

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

using namespace std;

// 定义神经网络结构
const int input_size = 784;
const int hidden_size = 30;
const int output_size = 10;

// 定义激活函数
double sigmoid(double x) {
    return 1.0 / (1.0 + exp(-x));
}

// 定义神经网络类
class NeuralNetwork {
public:
    NeuralNetwork() {
        // 初始化参数
        w1.resize(input_size, vector<double>(hidden_size));
        w2.resize(hidden_size, vector<double>(output_size));
        b1.resize(hidden_size);
        b2.resize(output_size);
        for (int i = 0; i < input_size; ++i) {
            for (int j = 0; j < hidden_size; ++j) {
                w1[i][j] = rand() / double(RAND_MAX);
            }
        }
        for (int i = 0; i < hidden_size; ++i) {
            for (int j = 0; j < output_size; ++j) {
                w2[i][j] = rand() / double(RAND_MAX);
            }
        }
        for (int i = 0; i < hidden_size; ++i) {
            b1[i] = rand() / double(RAND_MAX);
        }
        for (int i = 0; i < output_size; ++i) {
            b2[i] = rand() / double(RAND_MAX);
        }
    }
    // 前向传播
    vector<double> forward(vector<double> x) {
        vector<double> z1(hidden_size);
        vector<double> a1(hidden_size);
        vector<double> z2(output_size);
        vector<double> a2(output_size);
        for (int j = 0; j < hidden_size; ++j) {
            for (int i = 0; i < input_size; ++i) {
                z1[j] += x[i] * w1[i][j];
            }
            z1[j] += b1[j];
            a1[j] = sigmoid(z1[j]);
        }
        for (int k = 0; k < output_size; ++k) {
            for (int j = 0; j < hidden_size; ++j) {
                z2[k] += a1[j] * w2[j][k];
            }
            z2[k] += b2[k];
            a2[k] = sigmoid(z2[k]);
        }
        return a2;
    }
    // 计算损失函数
    double loss(vector<vector<double>> x, vector<vector<double>> y) {
        double L = 0.0;
        int N = x.size();
        for (int n = 0; n < N; ++n) {
            vector<double> a2 = forward(x[n]);
            for (int k = 0; k < output_size; ++k) {
                L += y[n][k] * log(a2[k]) + (1 - y[n][k]) * log(1 - a2[k]);
            }
        }
        return -L / N;
    }
    // 训练模型
    void train(vector<vector<double>> x, vector<vector<double>> y, double learning_rate, int epochs) {
        int N = x.size();
        for (int epoch = 1; epoch <= epochs; ++epoch) {
            double L = 0.0;
            for (int n = 0; n < N; ++n) {
                // 前向传播
                vector<double> z1(hidden_size);
                vector<double> a1(hidden_size);
                vector<double> z2(output_size);
                vector<double> a2(output_size);
                for (int j = 0; j < hidden_size; ++j) {
                    for (int i = 0; i < input_size; ++i) {
                        z1[j] += x[n][i] * w1[i][j];
                    }
                    z1[j] += b1[j];
                    a1[j] = sigmoid(z1[j]);
                }
                for (int k = 0; k < output_size; ++k) {
                    for (int j = 0; j < hidden_size; ++j) {
                        z2[k] += a1[j] * w2[j][k];
                    }
                    z2[k] += b2[k];
                    a2[k] = sigmoid(z2[k]);
                }
                // 反向传播
                vector<double> delta2(output_size);
                for (int k = 0; k < output_size; ++k) {
                    delta2[k] = a2[k] - y[n][k];
                }
                vector<double> delta1(hidden_size);
                for (int j = 0; j < hidden_size; ++j) {
                    for (int k = 0; k < output_size; ++k) {
                        delta1[j] += delta2[k] * w2[j][k] * a1[j] * (1 - a1[j]);
                    }
                }
                // 更新参数
                for (int j = 0; j < hidden_size; ++j) {
                    for (int i = 0; i < input_size; ++i) {
                        w1[i][j] -= learning_rate * delta1[j] * x[n][i];
                    }
                    b1[j] -= learning_rate * delta1[j];
                }
                for (int k = 0; k < output_size; ++k) {
                    for (int j = 0; j < hidden_size; ++j) {
                        w2[j][k] -= learning_rate * delta2[k] * a1[j];
                    }
                    b2[k] -= learning_rate * delta2[k];
                }
                L += loss({x[n]}, {y[n]});
            }
            cout << "Epoch " << epoch << ", Loss: " << L / N << endl;
        }
    }
    // 预测
    int predict(vector<double> x) {
        vector<double> a2 = forward(x);
        int label = 0;
        double max_prob = 0.0;
        for (int k = 0; k < output_size; ++k) {
            if (a2[k] > max_prob) {
                max_prob = a2[k];
                label = k;
            }
        }
        return label;
    }
    // 保存模型
    void save(string filename) {
        ofstream file(filename);
        file << input_size << " " << hidden_size << " " << output_size << endl;
        for (int i = 0; i < input_size; ++i) {
            for (int j = 0; j < hidden_size; ++j) {
                file << w1[i][j] << " ";
            }
        }
        for (int j = 0; j < hidden_size; ++j) {
            file << b1[j] << " ";
        }
        for (int j = 0; j < hidden_size; ++j) {
            for (int k = 0; k < output_size; ++k) {
                file << w2[j][k] << " ";
            }
        }
        for (int k = 0; k < output_size; ++k) {
            file << b2[k] << " ";
        }
        file.close();
    }
    // 加载模型
    void load(string filename) {
        ifstream file(filename);
        int input_size_, hidden_size_, output_size_;
        file >> input_size_ >> hidden_size_ >> output_size_;
        if (input_size_ != input_size || hidden_size_ != hidden_size || output_size_ != output_size) {
            cerr << "Error: model size mismatch" << endl;
            return;
        }
        for (int i = 0; i < input_size; ++i) {
            for (int j = 0; j < hidden_size; ++j) {
                file >> w1[i][j];
            }
        }
        for (int j = 0; j < hidden_size; ++j) {
            file >> b1[j];
        }
        for (int j = 0; j < hidden_size; ++j) {
            for (int k = 0; k < output_size; ++k) {
                file >> w2[j][k];
            }
        }
        for (int k = 0; k < output_size; ++k) {
            file >> b2[k];
        }
        file.close();
    }
private:
    vector<vector<double>> w1;
    vector<vector<double>> w2;
    vector<double> b1;
    vector<double> b2;
};

// 读取数据集
void read_data(string filename, vector<vector<double>>& x, vector<vector<double>>& y) {
    ifstream file(filename);
    int magic_number, n;
    file.read((char*)&magic_number, 4);
    magic_number = __builtin_bswap32(magic_number);
    file.read((char*)&n, 4);
    n = __builtin_bswap32(n);
    x.resize(n);
    y.resize(n);
    for (int i = 0; i < n; ++i) {
        x[i].resize(input_size);
        file.read((char*)x[i].data(), input_size);
        for (int j = 0; j < input_size; ++j) {
            x[i][j] /= 255.0;
        }
    }
    file.close();
    string label_filename = filename.substr(0, filename.size() - 3) + "idx1-ubyte";
    file.open(label_filename);
    file.read((char*)&magic_number, 4);
    file.read((char*)&n, 4);
    n = __builtin_bswap32(n);
    for (int i = 0; i < n; ++i) {
        y[i].resize(output_size);
        uint8_t label;
        file.read((char*)&label, 1);
        for (int k = 0; k < output_size; ++k) {
            y[i][k] = (k == label ? 1.0 : 0.0);
        }
    }
    file.close();
}

int main() {
    vector<vector<double>> train_x, train_y, test_x, test_y;
    read_data("train-images-idx3-ubyte", train_x, train_y);
    read_data("t10k-images-idx3-ubyte", test_x, test_y);

    NeuralNetwork model;
    model.train(train_x, train_y, 0.1, 100);
    model.save("model.txt");

    int correct = 0;
    int total = test_x.size();
    for (int i = 0; i < total; ++i) {
        int label = model.predict(test_x[i]);
        if (label == distance(test_y[i].begin(), max_element(test_y[i].begin(), test_y[i].end()))) {
            ++correct;
        }
    }
    cout << "Accuracy: " << double(correct) / total << endl;

    return 0;
}

这段代码实现了一个简单的两层神经网络，使用sigmoid作为激活函数，交叉熵作为损失函数，使用随机梯度下降算法训练模型。读取MINST数据集时，需要将数据归一化到0到1之间。训练完成后，可以将模型保存到文件中，以便后续使用。测试时，计算预测准确率。