Introduction to Recommendation Systems

Welcome to the first lesson of our course on Collaborative Filtering with ALS! In this lesson, we will begin our journey into the world of recommendation systems, an integral technology that powers many of the platforms we interact with daily. From helping you find movies you might like to suggesting products based on your past purchases, recommendation systems are all around us. We will begin by understanding user-item interactions and explicit ratings, which form the foundation of collaborative filtering techniques. This lesson will equip you with the necessary skills to handle explicit rating matrices, setting the stage for implementing the ALS (Alternating Least Squares) algorithm.

An explicit rating matrix is a foundational concept in recommendation systems. It refers to a table where users explicitly rate items. For instance, on a movie streaming service, you might rate a movie from 1 to 5 stars. These ratings help the service recommend other movies you might enjoy. The explicit rating matrix records these ratings in a structured form, making it easier to generate personalized recommendations.

Consider a movie platform where users have provided ratings for different films. Here's how a simplified explicit rating matrix might look:

In this table, each cell contains the rating a user has assigned to a movie, with -1 indicating that the user has not rated the movie. This type of matrix is crucial for generating recommendations based on user preferences.

Let's set up the explicit rating matrix using a dataset of user-item interactions. The matrix is loaded from the explicit-ratings.txt file, which we will use for further exploration and manipulation. The format of the file is as follows:

-1 2 5
5 3 -1
3 3 3

Each row represents a user, and each column represents an item. -1 means that the rating for this user-item pair is missing.

In C++, we can read this data from a file and store it in a matrix using the Eigen library. Here is how you can do it:

#include <iostream>
#include <fstream>
#include <vector>
#include <string>
#include <sstream>
#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() {
    // Load user-item interaction matrix with explicit feedback from file
    MatrixXd R = load_matrix("explicit-ratings.txt");

    // The resulting matrix R now contains the ratings data
    // For example, R(0, 0) is the rating of user 1 for item 1

    return 0;
}

In this block of code, we include the necessary headers and define a function to read user ratings from a file. Each line in the file corresponds to one user's ratings, and we store these in an Eigen matrix, R, for efficient mathematical operations.