Machine learning using partial order hypergraphs
A machine learning method comprises: receiving input data comprising a set of feature variables each indicating features of a plurality of entities; encoding partial order relations between entities of the plurality of entities as a set of logic rules; constructing a hypergraph comprising a plurality of vertices representing the entities of the plurality of entities and a plurality of hyperlinks linking similar entities of the plurality of entities; adding directed edges to the hypergraph to represent partial order interactions between entities to form a partial order hypergraph; representing the partial order hypergraph as a set of matrices; forming an objective function using the logic rules and matrices of the set of matrices; minimizing the objective function to obtain a prediction function; and outputting an indication of the prediction function.
1. A machine learning method comprising:
receiving input data comprising a set of feature variables each indicating features of a plurality of entities;
encoding partial order relations between entities of the plurality of entities as a set of logic rules;
constructing a hypergraph comprising a plurality of vertices representing the entities of the plurality of entities and a plurality of hyperlinks linking similar entities of the plurality of entities;
adding directed edges to the hypergraph to represent partial order interactions between entities to form a partial order hypergraph;
representing the partial order hypergraph as a set of matrices;
forming an objective function by replacing a binary logic function derived from the set of logic rules with a continuous function and using matrices of the set of matrices;
minimizing the objective function to obtain a prediction function; and
outputting an indication of the prediction function.
2. A method according to claim 1 , wherein the set of matrices comprises a partial incidence matrix representing the directed edges.
3. A method according to claim 2 wherein the partial incidence matrix is derived from a product of a binary relation matrix indicating pairs of entities having partial order relations and a co-occurrence matrix indicating a number of hyperedges connecting pairs of entities.
4. A method according to claim 1 , wherein directed edges are only added between pairs of vertices connected by at least one hyperedge.
5. A method according to claim 1 , wherein representing the partial order hypergraph as a set of matrices comprises assigning weights to pairs of vertices, the weights being dependent on the number of hyperedges connecting a pair of vertices.
6. A method according to claim 1 , wherein the objective function comprises a regularization term that encodes the logic rules.
7. A method according to claim 1 , wherein minimizing the objective function comprises applying a gradient based method to the objective function.
8. A ranking method comprising the method according to claim 1 .
9. A prediction method comprising the method according to claim 1 .
10. A non-transitory computer readable medium carrying processor executable instructions which when executed on a processor cause the processor to carry out a method according to claim 1 .
11. A data processing system comprising a processor and a data storage device, the data storage device storing computer executable instructions operable by the processor to:
receive input data comprising a set of feature variables each indicating features of a plurality of entities;
encode partial order relations between entities of the plurality of entities as a set of logic rules;
construct a hypergraph comprising a plurality of vertices representing the entities of the plurality of entities and a plurality of hyperlinks linking similar entities of the plurality of entities;
add directed edges to the hypergraph to represent partial order interactions between entities to form a partial order hypergraph;
represent the partial order hypergraph as a set of matrices;
form an objective function by replacing a binary logic function derived from the set of logic rules with a continuous function and using matrices of the set of matrices;
minimize the objective function to obtain a prediction function; and
output an indication of the prediction function.
12. A data processing system according to claim 11 , wherein the set of matrices comprises a partial incidence matrix representing the directed edges.
13. A data processing system according to claim 12 wherein the partial incidence matrix is derived from a product of a binary relation matrix indicating pairs of entities having partial order relations and a co-occurrence matrix indicating a number of hyperedges connecting pairs of entities.
14. A data processing system according to claim 11 , wherein directed edges are only added between pairs of vertices connected by at least one hyperedge.
15. A data processing system according to claim 11 , wherein representing the partial order hypergraph as a set of matrices comprises assigning weights to pairs of vertices, the weights being dependent on the number of hyperedges connecting a pair of vertices.
16. A data processing system according to claim 11 , wherein the objective function comprises a regularization term that encodes the logic rules.
17. A data processing system according to claim 11 , wherein the data storage device stores computer executable instructions operable by the processor to minimize the objective function by applying a gradient based method to the objective function.
18. A data processing system according to claim 11 , wherein the prediction function indicates a ranking of the entities.