###Tl;dr Frobenius norm, limited to known entries.

Let $P$ be the matrix of predictions (so $P_{u,m}$ is the predicted rating for user $u$ and movie $m$).

Let $R^{train}$ and $R^{test}$ be the training and test sets of data. For convenience, I'll use notation $R^{test}_{u,m}$ to mean the rating of user $u$ of movie $m$ in the test set, but note that $R^{test}$ is not a matrix, because it's sparse: 99% of the entries are missing. Most users have not rated most movies. Only a tiny number of $(u,m)$ pairs are actually present in $R^{test}$.

The error of prediction matrix $P$ is

$\displaystyle\sum_{(u,m) \in R^{test}} (R^{test}_{u,m} - P_{u,m})^2$

That is, the sum over the squared error of known entries in the test set.

# Pseudocode for calculating error p = ... # prediction matrix, indexed by [u][m] r_test = ... # list of (user, movie, rating) tuples error = 0.0 for (u, m, r) in r_test: error += (r - predictions[u][m])^2

Important note on splitting test/train set

When splitting up the data into training and test sets, you should randomly select (user, movie) pairs, not select random users or movies. The whole idea of "collaborative filtering" (for Netflix) is to predict ratings for movies you haven't watched based on the ratings you provided for ones you have. If a user is present only in the testing set, the model cannot possibly be basing predictions based on their other ratings.

I need more help on the Netflix problem and SVD

See my other answer for a description of the netflix problem and matrix-factoring approaches to it.

###Tl;dr Frobenius norm, limited to known entries.

Let $P$ be the matrix of predictions (so $P_{u,m}$ is the predicted rating for user $u$ and movie $m$).

Let $R^{train}$ and $R^{test}$ be the training and test sets of data. For convenience, I'll use notation $R^{test}_{u,m}$ to mean the rating of user $u$ of movie $m$ in the test set, but note that $R^{test}$ is not a matrix, because it's sparse: 99% of the entries are missing. Most users have not rated most movies. Only a tiny number of $(u,m)$ pairs are actually present in $R^{test}$.

The error of prediction matrix $P$ is

$\displaystyle\sum_{(u,m) \in R^{test}} (R^{test}_{u,m} - P_{u,m})^2$

That is, the sum over the squared error of known entries in the test set.

# Pseudocode for calculating error p = ... # prediction matrix, indexed by [u][m] r_test = ... # list of (user, movie, rating) tuples error = 0.0 for (u, m, r) in r_test: error += (r - predictions[u][m])^2

Important note on splitting test/train set

When splitting up the data into training and test sets, you should randomly select (user, movie) pairs, not select random users or movies. The whole idea of "collaborative filtering" (for Netflix) is to predict ratings for movies you haven't watched based on the ratings you provided for ones you have. If a user is present only in the testing set, the model cannot possibly be basing predictions based on their other ratings.

I need more help on the Netflix problem and SVD

See my other answer for a description of the netflix problem and matrix-factoring approaches to it.

###Tl;dr Frobenius norm, limited to known entries.

predictions = U*M r_test = ... error = 0.0 for u in r_test.users: for m in r_test.movies[u]: error += (r_test[u][m] - predictions[u][m])^2

Why? What?

See my other answer for a description of the netflix problem and matrix-factoring approaches to it.

###Tl;dr Frobenius norm, limited to known entries.

Let $P$ be the matrix of predictions (so $P_{u,m}$ is the predicted rating for user $u$ and movie $m$).

Let $R^{train}$ and $R^{test}$ be the training and test sets of data. For convenience, I'll use notation $R^{test}_{u,m}$ to mean the rating of user $u$ of movie $m$ in the test set, but note that $R^{test}$ is not a matrix, because it's sparse: 99% of the entries are missing. Most users have not rated most movies. Only a tiny number of $(u,m)$ pairs are actually present in $R^{test}$.

The error of prediction matrix $P$ is

$\displaystyle\sum_{(u,m) \in R^{test}} (R^{test}_{u,m} - P_{u,m})^2$

That is, the sum over the squared error of known entries in the test set.

# Pseudocode for calculating error p = ... # prediction matrix, indexed by [u][m] r_test = ... # list of (user, movie, rating) tuples error = 0.0 for (u, m, r) in r_test: error += (r - predictions[u][m])^2

Important note on splitting test/train set

When splitting up the data into training and test sets, you should randomly select (user, movie) pairs, not select random users or movies. The whole idea of "collaborative filtering" (for Netflix) is to predict ratings for movies you haven't watched based on the ratings you provided for ones you have. If a user is present only in the testing set, the model cannot possibly be basing predictions based on their other ratings.

I need more help on the Netflix problem and SVD

See my other answer for a description of the netflix problem and matrix-factoring approaches to it.