Welcome back! As you continue your journey through the fascinating world of recommendation systems, it's important to understand not just explicit feedback — such as star ratings — but also implicit feedback. Implicit feedback is obtained from user behavior patterns, like watch times or click histories. While it's much easier to gather, it doesn't directly reveal user satisfaction as explicit feedback does.

Most classical models utilize either implicit or explicit feedback separately due to the complexities involved in integrating both types into a unified system. In this course, we'll focus on analyzing implicit feedback independently.

Now, let's delve into the binary matrix of interactions. In the context of implicit feedback, this matrix is a simplified representation showing whether a user interacted with an item or not. Each entry in the matrix is a binary value:

• 1 indicates an interaction (e.g., a user watched an item),
• 0 implies no interaction.

For example, let's say User 1 interacted with Items 1, 2, and 4. The binary matrix would look like this:

| User/Item | Item 1 | Item 2 | Item 3 | Item 4 |
|-----------|--------|--------|--------|--------|
| User 1    |   1    |   1    |   0    |   1    |

This matrix is crucial, as it helps algorithms understand which items have been interacted with, providing a baseline for recommending new items to users.

The confidence matrix goes beyond the binary matrix by incorporating the confidence we have in each interaction. This confidence is calculated based on user behaviors such as watch_time. Longer watch times suggest higher interest and, thus, greater confidence in the interaction.

Here's how you might compute a confidence matrix in C++, where watch_time plays a significant role:

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

int main() {
    // Let's assume some watch times for User 1
    std::vector<int> watch_times = {30, 28, 11, 51}; // For Items 1, 2, 3, 4 respectively
    double alpha = 40.0; // Constant factor

    // Initializing a sample confidence matrix (1 user, 4 items)
    Eigen::MatrixXd confidence_matrix(1, 4);

    // Fill the confidence matrix using the formula
    for (int i = 0; i < watch_times.size(); ++i) {
        confidence_matrix(0, i) = 1 + alpha * watch_times[i];
    }

    // Print the confidence matrix
    std::cout << "Confidence Matrix:" << std::endl;
    std::cout << confidence_matrix << std::endl;

    return 0;
}

This might result in:

| User/Item | Item 1 | Item 2 | Item 3 | Item 4 |
|-----------|--------|--------|--------|--------|
| User 1    | 1201   | 1121   |  441   | 2041   |

Here, higher values denote greater confidence that the user is interested in those items, which is invaluable for personalizing recommendations.

Generally, there are various ways of evaluating implicit feedback. Of course, you can come up with your own! The approach described here is based on the article Collaborative Filtering for Implicit Feedback Datasets by researchers from AT&T Labs. We will use this approach to train a special version of ALS, called IALS, which works with implicit feedback efficiently, in the next lesson.

The dataset is a JSON file where each entry contains entries for user, item, rating, and watch_time. Each record describes an interaction a user had with an item.

[
    {"user": 1, "item": 1, "rating": 2, "watch_time": 30},
    {"user": 1, "item": 2, "rating": 2, "watch_time": 28},
    {"user": 1, "item": 4, "rating": -1, "watch_time": 11},
    ...
]

Here's an excerpt explaining how to read the data and determine the matrix dimensions in C++ using the nlohmann/json library:

#include <iostream>
#include <fstream>
#include <vector>
#include "nlohmann/json.hpp"

using json = nlohmann::json;

int main() {
    // Load the JSON data
    std::ifstream file("ratings.json");
    json data = json::parse(file);

    // Determine the size of the matrices
    int max_user = 0;
    int max_item = 0;
    for (const auto& entry : data) {
        if (entry["user"] > max_user) max_user = entry["user"];
        if (entry["item"] > max_item) max_item = entry["item"];
    }

    std::cout << "Number of users: " << max_user << std::endl;
    std::cout << "Number of items: " << max_item << std::endl;

    return 0;
}

In this block, we read the JSON file and calculate max_user and max_item to ascertain the dimensions of our matrices.

Here's a short example showing how the resulting matrices might look in C++:

Interaction Matrix (Binary):
1 1 0 0
0 0 1 1

Confidence Matrix:
1201 1121    0    0
   0    0  601  881

This output reflects interactions and confidence levels across users and items.

You might wonder, why don't we use only the confidence matrix, as it contains all the information? The reason is that splitting user preferences (interactions) and our confidence in their preferences allows us to work with these values distinctly and construct a model that treats them separately. It generally improves the model's performance.

In the next lesson, we will train one example of such a model. But before that, let's wrap it up and have some practice!

In this lesson, you focused on understanding and creating interaction and confidence matrices based on implicit feedback like user watch times. You now have both the theoretical understanding and practical skills to process implicit feedback. This enables you to create a more nuanced and personalized recommendation system.

In the next session, you'll have the opportunity to explore practice exercises that reinforce today's lesson. These exercises will help solidify your understanding and make the transition to advanced models seamless. Keep up the great work as you advance toward mastering recommendation systems with ALS!