A method for link prediction includes providing training samples for at least one relation. The training samples include positive training samples in which a first of a set of entities is a subject in the relation and a second of the set of entities is an object in the relation. An input matrix is generated for each of the at least one relation, based on the training samples. Parameters of a scoring function which minimize an error between a reconstructed matrix and the input matrix are learned, the parameters including a set of latent factors for each entity, each of the latent factors being a complex number. The parameters of the scoring function may be output for performing link prediction and/or used for predicting an entity for a relation from a part of the reconstructed matrix.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for link prediction comprising: providing training samples for at least one relation, the training samples comprising positive training samples in which a first of a set of entities is a subject in the relation and a second of the set of entities is an object in the relation; generating an input matrix for each of the at least one relation, based on the training samples; with a processor, learning parameters of a scoring function which minimize an error between a reconstructed matrix and the input matrix, the parameters including a set of latent factors for each entity, each of the latent factors being a complex number; performing at least one of: outputting the parameters of the scoring function for performing link prediction; and predicting an entity for a relation based on the parameters. 2. The method of claim 1, wherein the at least one relation comprises a plurality of relations. 3. The method of claim 2, where in the input matrices are composed as a three dimensional tensor. 4. The method of claim 1 wherein the at least one relation comprises an asymmetric relation. 5. The method of claim 1, wherein the parameters include parameters of the relation for each of the at least one relation, the relation parameters comprising a complex number. 6. The method of claim 5, wherein the scoring function computes a Hermitian dot product of the latent factors for a first entity, the complex conjugates of the latent factors for a second entity, and the parameters of the relation. 7. The method of claim 1, wherein for each pair of entities in the input matrix, the scoring function computes a sum, over all the latent factors, of the product of the relation embedding, and the latent factors of the respective entities. 8. The method of claim 7, wherein the scoring function is of the form: φ = Re  ( ∑ k = 1 K   w rk , e _ sk , e ok ) where Re represents a real part of a complex number; K represents the number of latent factors; wrk represents the relation embedding for the kth latent factor; ēsk represents the complex conjugate of the kth latent factor for the subject entity; and eok represents the kth latent factor for the object entity. 9. The method of claim 7, wherein the scoring function is of the form: φ=(Re(wr), Re(es), Re(eo))+(Re(wr), Im(es), Im(eo)) −(Im(wr), Re(es), Im(eo))+(Im(wr), Im(es), Re(eo)) where Re represents a real part of a complex number; Im represents an imaginary part of a complex number; wr represents the embedding of one of the at least one relation; eo represents the latent factors of the object entity; and es represents the latent factors of the subject entity. 10. The method of claim 1, wherein the method includes predicting an entity for a relation from the reconstructed matrix. 11. The method of claim 1, wherein the method includes predicting an entity for a relation from the parameters of the scoring function. 12. The method of claim 1, wherein the training samples further comprise artificially generated negative training samples. 13. The method of claim 1, wherein the learning of the parameters of the scoring function comprises jointly learning the latent factors and relation parameters for each of the at least one relation, the relation parameters comprising a set of complex numbers. 14. The method of claim 1, wherein the learning of the parameters of the scoring function is performed with gradient descent. 15. The method of claim 1, wherein the input matrix is a normal matrix. 16. A computer program product comprising a non-transitory recording medium storing instructions, which when executed on a computer, causes the computer to perform the method of claim 1. 17. A system comprising memory which stores instructions for link prediction using a reconstructed matrix generated by the method of claim 1 and a processor in communication with the memory for executing the instructions. 18. A link prediction system comprising: memory which stores values for training samples for at least one relation, the training samples comprising positive training samples in which a first of a set of entities is a subject in the relation and a second of the set of entities is an object in the relation; a generation component which generates an input matrix for each of the at least one relation, based on the training samples; a completion component which learns parameters of a scoring function which minimize an error between a reconstructed matrix and the input matrix, the parameters including a set of latent factors for each entity, each of the latent factors being a complex number; and a processor which implements the generation component and the completion component. 19. The link prediction system of claim 18, further comprising at least one of: a prediction component which predicts an entity for a relation based on the learned parameters; and an output component which outputs at least one of the reconstructed matrix and a prediction generated by the prediction component. 20. A method for link prediction comprising: providing an input matrix for each of at least one relation, each input matrix including a value for each of a subset of a set entity pairs represented in the input matrix, each entity pair including a first of the set of entities which is a subject in the respective relation and a second of the set of entities, which is an object in the respective relation; with a processor, for each of the at least one relation, learning parameters of a scoring function which minimize an error between a reconstructed matrix and the input matrix, the parameters including a set of latent factors for each entity, each of the latent factors being a complex number, and parameters of the relation, elements of the reconstructed matrix each corresponding to the dot product of the latent factors for a first entity, the complex conjugates of the latent factors for a second entity, and the parameters of the relation; performing at least one of: outputting the parameters of the scoring function for performing link prediction; and predicting an entity for a relation based on the parameters of the scoring function.