Under the Movie Rated Dataset, we have
X (4778, 10) &
W (443, 10)
Here, the shape of X makes it understandable that the matrix has 4778 rows (1 for each movie), and we are considering 10 features, which is why there are 10 columns.
For W (443, 10), I understand that 443 refers to the number of users, but what does the column number 10 mean here? Please explain in detail.
Thanks
Hello @GAURAV_MANCHANDA
As explained by this paragraph of the exercise:
The rationales of the 10 in the shape of X and the 10 in the shape of W are the same. If we interpret the 10 in the shape of X as “we are considering 10 features (for each movie)”, then we interpret the 10 in the shape of Win the same way as “we are considering 10 features (for each user)”.
Moreover, there are no 2 choices. We are NOT choosing a feature size for user and a feature size for movie. We ARE choosing one feature size for both user and movie. We need them to be the same so that they (an user feature vector and a movie user feature vector) can be multiplied together.
The choice of 10, however, has no rule of thumb. We need to determine the best number by experiment. Such number should scale with the complexity of the problem. For example, it is obvious that for a very complex user-movie interaction pattern, using 1 as the number of features is very likely to be worse than another number which is larger than 1, since the latter can provide a richer information about each movie or each user. However, as mentioned, there is no rule of thumb as to which feature size must do well, so we need to figure it out by experimentation.
Cheers,
Raymond
Hi @rmwkwok, Thank you so much for the answer. That part is clear. But I am still confused with the elements of the matrix W.
As per my understanding, the first row of the X matrix is the feature vector of the first movie. And as we have assumed that there are 10 features by taking n = 10, That is why the feature vector of the first movie has 10 elements.
Now if I try to understand the 1st row of the W matrix, then it represents the parameter vector for the 1st user. And its 10 elements represents that how much weight the 1st user is giving to each feature.
Is this understanding correct?
