Alternating Least Squares Fundamentals

#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <sstream>
#include <random>
#include <algorithm>
#include <Eigen/Dense>

using Eigen::MatrixXd;

// Function to load a matrix from a text file
MatrixXd load_matrix(const std::string& filename) {
    std::ifstream file(filename);
    std::string line;
    std::vector<std::vector<double>> data;
    int cols = 0;
    while (std::getline(file, line)) {
        std::stringstream ss(line);
        double value;
        std::vector<double> row;
        while (ss >> value) row.push_back(value);
        if (!row.empty()) {
            if (cols == 0) cols = row.size();
            data.push_back(row);
        }
    }
    MatrixXd matrix(data.size(), cols);
    for (size_t i = 0; i < data.size(); ++i) {
        for (size_t j = 0; j < data[i].size(); ++j) matrix(i, j) = data[i][j];
    }
    return matrix;
}

int main() {
    // Initialize user-item interaction matrix from file
    MatrixXd R = load_matrix("../data/explicit-ratings.txt");

    long num_users = R.rows();
    long num_items = R.cols();

    // Mark some entries as missing (-1) for testing
    std::vector<std::pair<int, int>> all_rated_indices;
    for (int r = 0; r < num_users; ++r) {
        for (int c = 0; c < num_items; ++c) {
            if (R(r, c) != -1) all_rated_indices.push_back({r, c});
        }
    }
    double missing_ratio = 0.1;  // Density of missing entries
    size_t num_missing = static_cast<size_t>(missing_ratio * all_rated_indices.size());

    std::random_device rd;
    std::mt19937 g(rd());
    std::shuffle(all_rated_indices.begin(), all_rated_indices.end(), g);

    std::vector<std::pair<int, int>> missing_indices(all_rated_indices.begin(), all_rated_indices.begin() + num_missing);

    // Save the original matrix for evaluation
    MatrixXd original_R = R;

    for (const auto& p : missing_indices) R(p.first, p.second) = -1;

    // ... (rest of the code)
}