Recommender system with fast matrix factorization using infinite dimensions
View Patent ↗A system is disclosed with a collaborative filtering engine to predict an active user's ratings/interests/preferences on a set of new products/items. The predictions are based on an analysis the database containing the historical data of many users' ratings/interests/preferences on a large set of products/items.
1. A computer-implemented method for generating a recommendation, comprising:
a. performing collaborative filtering on a matrix Y containing historical data of users' ratings on a set of products using an infinite dimensional matrix factorization with a probabilistic non-parametric model where parameters are in infinite-dimensional parameter spaces, wherein the infinite dimensional matrix factorization comprises
min
X
,
K
>
0
(
Y
-
X
)
O
2
+
γ
1
tr
(
XK
-
1
X
T
)
+
γ
2
tr
(
K
)
,
where K is a square matrix represeting a covarience of X, X is a recommendation matrix, wherein T represents a determinant, Y is the matrix containing missing values, tr is a transpose operation, O denotes indices of observed elements of Y and where γ 1 and γ 2 are constants>0;
b. generating one or more recommendations using the collaborative filtering from the recommendation matrix X; and
c. displaying the recommendations to a user.
2. The method of claim 1 , comprising performing probabilistic matrix factorization on data.
3. The method of claim 1 , comprising performing non-probabilistic matrix factorization on the data.
4. The method of claim 1 , comprising performing matrix factorization with iSVD (infinite-dimensional Singular Value Decomposition).
5. The method of claim 1 , comprising performing matrix factorization with pPCA (infinite-dimensional probabilistic Principal Component Analysis).
6. The method of claim 1 , comprising collecting user preferences on one or more items.
7. The method of claim 1 , comprising collecting a mean and a covariance on user preferences on one or more items.
8. The method of claim 1 , comprising determining a global item-to-item relationship or similarity for all the users.
9. The method of claim 1 , comprising determining an item to item relationship or similarity associated with each user.
10. The method of claim 9 , comprising applying the item to item relationship or similarity to infer user preferences.
11. The method of claim 10 , wherein local statistics are used to infer a mean and a covariance on user preferences on one or more items.
12. The method of claim 10 , wherein local statistics comprises covariance of user preference and data noise error.
13. The method of claim 12 , wherein the user preference and data noise error are processed in combination to reduce processing time.
14. The method of claim 1 , comprising generating global statistics including an item to item relationship or similarity associated with each user.
15. The method of claim 1 , comprising processing a canonical expectation-maximization (EM) operation.
16. The method of claim 1 , comprising determining
K
←
K
+
1
M
KBK
,
where M is a number of users and B is matrix storing intermediate results.
17. A system to generate a recommendation for a user, comprising:
a. a processor executing a collaborative filter on a matrix Y containing historical data of users' ratings on a set of products using an infinite dimensional matrix factorization with a probabilistic non-parametric model, where parameters are in infinite-dimensional parameter spaces, wherein the infinite dimensional matrix factorization comprises
min
X
,
K
>
0
(
Y
-
X
)
O
2
+
γ
1
tr
(
XK
-
1
X
T
)
+
γ
2
tr
(
K
)
,
where K is a square matrix represeting a covarience of X, X is a recommendation matrix, wherein T represents a determinant, Y is the matrix containing missing values, tr is a transpose operation, O denotes indices of observed elements of Y and where γ 1 and γ 2 are constants>0;
b. a recommender engine executed by the processor to generate one or more recommendations using the collaborative filter from the recommendation matrix X; and
c. a user interface engine executed by the processor to render the recommendations to a user.
18. The system of claim 17 , wherein the matrix factorization comprises iSVD (infinite-dimensional Singular Value Decomposition).
19. The system of claim 17 , wherein the matrix factorization comprises pPCA (infinite-dimensional probabilistic Principal Component Analysis).
20. The system of claim 17 , wherein the matrix factorization operates on a mean and a covariance on user preferences on one or more items.