Method, manufacture, and system for recommending items to users

1. A method, comprising:

generating, by at least one processor included in one or more processors, a first matrix based on an interaction matrix, wherein the interaction matrix reflects a plurality of interactions between a plurality of users and a plurality of items;

generating, by at least one processor included in the one or more processors, a weight matrix based on the first matrix and a closed-form solution that minimizes a Lagrangian, wherein the Lagrangian is formed based on a constrained convex optimization problem associated with the interaction matrix;

generating, by at least one processor included in the one or more processors, a linear preference prediction model that uses the weight matrix;

generating, by at least one processor included in the one or more processors, a first application interface that is to be presented to a first user included in the plurality of users, wherein the first application interface includes a plurality of interface elements, and each interface element is individually selectable when the first application interface is displayed and is associated with a different item included in the plurality of items;

computing, by at least one processor included in the one or more processors, one or more predicted scores using the linear preference prediction model, wherein each predicted score predicts a preference of the first user for a different item included in the plurality of items;

determining, by at least one processor included in the one or more processors, a first item from the plurality of items to present to the first user via a first interface element included within the first application interface based on the one or more predicted scores; and

causing a representation of the first item to be displayed via the first interface element included in the first application interface.

2. The method of claim 1 , wherein the determining the first item from the plurality of items comprises:

ranking the items that are associated with the one or more predicted scores based on the one or more predicted scores to generate a ranked item list; and

determining that the first item is the highest-ranked item included in the ranked item list with which the first user has not interacted.

3. The method of claim 1 , wherein each item included in the plurality of items comprises a media item, and a first interaction included in the plurality of interactions comprises a rating that the first user assigned to a second item included in the plurality of items via a second application interface.

4. The method of claim 1 , wherein each item included in the plurality of items comprises a selectable item, and a first interaction included in the plurality of interactions comprises a purchase that a second user included in the plurality of users made of the first item via a second application interface.

5. The method of claim 1 , wherein the linear preference prediction model comprises a linear regression model that includes the weight matrix.

6. The method of claim 1 , wherein the weight matrix includes at least one negative weight.

7. The method of claim 1 , wherein the weight matrix is a square weight matrix having an order that is equal to a number of items included in the plurality of items, and wherein each of the diagonal elements of the square weight matrix is equal to zero.

8. The method of claim 1 , wherein computing the one or more predicted scores comprises performing a vector-vector multiplication operation between a row of the interaction matrix associated with the first user and a column of the weight matrix associated with the first item.

9. The method of claim 1 , wherein the constrained convex optimization problem comprises a convex objective that includes a square loss function computed using a Frobenius norm.

10. The method of claim 1 , wherein the first matrix comprises a Gram matrix, and further comprising pre-multiplying the interaction matrix by a transpose of the interaction matrix to compute the first matrix.

11. One or more non-transitory computer readable media including instructions that, when executed by one or more processors, cause the one or more processors to perform the steps of:

generating a first matrix based on an interaction matrix, wherein the interaction matrix reflects a plurality of interactions between a plurality of users and a plurality of items;

generating a weight matrix based on the first matrix and a closed-form solution that minimizes a Lagrangian, wherein the Lagrangian is formed based on a constrained convex optimization problem associated with the interaction matrix;

generating a linear preference prediction model that uses the weight matrix;

generating a first application interface that is to be presented to a first user included in the plurality of users, wherein the first application interface includes a plurality of interface elements, and each interface element is individually selectable when the first application interface is displayed and is associated with a different item included in the plurality of items;

computing one or more predicted scores using the linear preference prediction model, wherein each predicted score predicts a preference of the first user for a different item included in the plurality of items;

determining a first item from the plurality of items to present to the first user via a first interface element included within the first application interface based on the one or more predicted scores; and

causing a representation of the first item to be displayed via the first interface element included in the first application interface.

12. The one or more non-transitory computer readable media of claim 11 , wherein determining the first item from the plurality of items comprises:

ranking the items that are associated with the one or more predicted scores based on the one or more predicted scores to generate a ranked item list; and

determining that the first item is the highest-ranked item included in the ranked item list with which the first user has not interacted.

13. The one or more non-transitory computer readable media of claim 11 , wherein each item included in the plurality of items comprises a media item, and a first interaction included in the plurality of interactions comprises a rating that the first user assigned to a second item included in the plurality of items via a second application interface.

14. The one or more non-transitory computer readable media of claim 11 , wherein each item included in the plurality of items comprises a selectable item, and a first interaction included in the plurality of interactions comprises a purchase that a second user included in the plurality of users made of the first item via a second application interface.

15. The one or more non-transitory computer readable media of claim 11 , wherein the weight matrix is a square weight matrix that optimizes the preference prediction model with respect to the interaction matrix subject to a constraint that each of the diagonal elements of the square weight matrix is equal to zero.

16. The one or more non-transitory computer readable media of claim 11 , wherein computing the one or more predicted scores comprises inputting a row of the interaction matrix that corresponds to the first user into the linear preference prediction model.

17. The one or more non-transitory computer readable media of claim 11 , wherein computing the one or more predicted score comprises performing a vector-matrix multiplication operation between a row of the interaction matrix associated with the first user and the weight matrix.

18. The one or more non-transitory computer readable media of claim 11 , wherein the constrained convex optimization problem comprises a convex objective that includes an L2-norm regularization term.

19. The one or more non-transitory computer readable media of claim 11 , further comprising:

performing one or more preprocessing operations on the interaction matrix to generate a preprocessed matrix; and

pre-multiplying the preprocessed matrix by a transpose of the preprocessed matrix to generate the first matrix.

20. A system, comprising:

one or more memories storing instructions; and

one or more processors that are coupled to the one or more memories and,

when executing the instructions, are configured to:

generate a first matrix based on an interaction matrix, wherein the interaction matrix reflects a plurality of interactions between a plurality of users and a plurality of items;

generate a weight matrix based on the first matrix and a closed-form solution that minimizes a Lagrangian, wherein the Lagrangian is formed based on a constrained convex optimization problem associated with the interaction matrix;

generate a linear preference prediction model that uses the weight matrix;

generate a first application interface that is to be presented to a first user included in the plurality of users, wherein the first application interface includes a plurality of interface elements, and each interface element is individually selectable when the first application interface is displayed and is associated with a different item included in the plurality of items;

compute one or more predicted scores using the linear preference prediction model, wherein each predicted score predicts a preference of the first user for a different item included in the plurality of items;

determining a first item from the plurality of items to present to the first user via a first interface element included within the first application interface based on the one or more predicted scores; and

cause a representation of the first item to be displayed via the first interface element included in the first application interface.