调整后的余弦相似度无法正常工作

Question

我正在开发餐厅之间的 item-based collaborative filter using an adjusted cosine similarity 以生成推荐。我已经设置好一切并且运行良好，但是当我尝试模拟可能的测试场景时，我得到了一些有趣的结果。

我将从我的测试数据开始。我有 2 家餐厅，我想计算它们之间的相似度，以及 3 个用户都对这 2 家餐厅进行了相同的评价。我将使用以下矩阵对其进行解释：

               User 1 | User 2 | User 3
Restaurant 1 |   1    |   2    |   1
Restaurant 2 |   1    |   2    |   1

我正在尝试使用以下函数计算相似度：
餐厅在我的代码中被称为 Subject。

public double ComputeSimilarity(Guid subject1, Guid subject2, IEnumerable<Review> allReviews)
{
    //This will create an IEnumerable of reviews from the same user on the 2 restaurants.
    var matches = (from R1 in allReviews.Where(x => x.SubjectId == subject1)
                   from R2 in allReviews.Where(x => x.SubjectId == subject2)
                   where R1.UserId == R2.UserId
                   select new { R1, R2 });            
    double num = 0.0f;
    double dem1 = 0.0f;
    double dem2 = 0.0f;
    //For the similarity between subjects, we use an adjusted cosine similarity.
    //More information on this can be found here: http://www10.org/cdrom/papers/519/node14.html
    foreach (var item in matches)
    {
        //First get the average of all reviews the user has given. This is used in the adjusted cosine similarity, read the article from the link for further explanation
        double avg = allReviews.Where(x => x.UserId == item.R1.UserId)
                               .Average(x => x.rating);
        num += ((item.R1.rating - avg) * (item.R2.rating - avg));
        dem1 += Math.Pow((item.R1.rating - avg), 2);
        dem2 += Math.Pow((item.R2.rating - avg), 2);
    }
    return (num / (Math.Sqrt(dem1) * Math.Sqrt(dem2)));
}

我的评论是这样的：

public class Review
{
    public Guid Id { get; set; }
    public int rating { get; set; } //This can be an integer between 1-5
    public Guid SubjectId { get; set; } //This is the guid of the subject the review has been left on
    public Guid UserId { get; set; } //This is the guid of the user who left the review
}

在所有其他情况下，该函数将计算主题之间的正确相似性。但是当我使用上面的测试数据时（我期望完全相似的地方）它会导致 NaN。

这是我的代码错误还是调整后的余弦相似度错误？如果结果是 NaN，抓住它并插入一个 1 来获得相似性是不是很好？

编辑：我也尝试过其他矩阵，我得到了更有趣的结果。

               User 1 | User 2 | User 3 | User 4 | User 5
Restaurant 1 |   1    |   2    |   1    |   1    |   2
Restaurant 2 |   1    |   2    |   1    |   1    |   2

结果仍然是 NaN。

               User 1 | User 2 | User 3 | User 4 | User 5
Restaurant 1 |   2    |   2    |   1    |   1    |   2
Restaurant 2 |   1    |   2    |   1    |   1    |   2

这导致 -1 的相似性

Answer 1

看来你的算法实现正确。对于完全合理的集合，这个公式在某些点上确实可以是未定义的。您可以将这种情况视为 "this measure (adjusted cosine similarity) has nothing to say about provided sets"，因此分配任意值 (0, 1, -1) 是不正确的。相反，在这种情况下使用不同的措施。例如，简单的（未调整的）余弦相似度将给出“1”作为结果，这正是您所期望的。

调整后的余弦相似度无法正常工作

Adjusted cosine similarity not working correctly

c#

cosine-similarity

collaborative-filtering