A method is provided for calculating a relation indicator for a relation between entities based on an optimization procedure. The method combines the strong relational learning ability and the good scalability of the RESCAL model with the linear regression model, which may deal with observed patterns to model known relations. The method may be used to determine relations between objects, for instance entries in a database, such as a shopping platform, medical treatments, production processes, or in the context of the Internet of Things, in a fast and precise manner.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method for calculating a relation indicator for a relation between entities, the method comprising: providing a measurement tensor X of measurement tensor components, Xijk, with i, j=1 . . . N, comprising measurement data as relation indicators, wherein the relation indicator Xijk indicates a k-th relation between an i-th and a j-th of a number, N, of entities; providing a rules tensor M of rules tensor components, Mijn, describing a prediction of an n-th rule; calculating a weighting tensor of weighting tensor components, Wnk, indicating relative weights of the rules for the k-th relation between the entities; calculating a relationship tensor R of relationship tensor components, Rabk, with a, b=1 . . . r, indicating relations between a set of a number, r, of properties of the entities; calculating a transformation tensor A of transformation tensor components, Aia, describing the i-th entity via r latent properties, wherein the transformation tensor A, the weighting tensor W, and the relationship tensor R are calculated as minimum solutions to the following equation: min A , R , W   X ijk - X ijk ′  F 2 + λ A   A  F 2 + λ R   R  F 2 + λ W   W  F 2 , with λA, λR, and λW as Lagrange parameters and with result tensor components Xijk′ of a result tensor X′ given by: Xijk′=Σa,b,n(AiaRabkAbjT+MijnWnk), where AT is the transposed tensor corresponding to the transformation tensor A; and calculating a value of the relation indicator for the k-th relation between the i-th and the j-th entity based on the result tensor component Xijk′. 2. The method of claim 1, further comprising: generating at least one control signal, based on the predicted value of the relation indicator, for controlling one or more of an actuator, a sensor, a controller, a field device, or a display. 3. The method of claim 2, wherein a visual signal, an acoustic signal, or the visual and the acoustic signal are created based on the control signal. 4. The method of claim 1, further comprising: expanding the measurement tensor with additional measurement tensor components Xi(N+1)k for i=1 . . . N, X(N+1)jk for j=1 . . . N, and X(N+1)(N+1)k, comprising measurement data as relation indicators between the (N+1)-th additional entity and the entities; and expanding the rules tensor with additional rules tensor components, Mi(N+1)n for i=1 . . . N, M(N+1)jn for j=1 . . . N and M(N+1)(N+1)n, wherein a value of a relation indicator to be predicted is set to a predetermined value. 5. The method of claim 1, further comprising: monitoring a relation between at least two of the entities; and setting a value of at least one relation indicator based on the monitored relation between the at least two of the entities. 6. The method of claim 1, wherein at least some of the measurement data are provided by at least one sensor, are read out from at least one database, or are both provided by the at least one sensor and read out from the at least one database. 7. The method of claim 1, wherein the calculating of the result tensor comprises using an alternating least-squares method, wherein the transformation tensor, the relationship tensor, and the weighting tensor are updated alternatingly until convergence. 8. A computer program for calculating a relation indicator for a relation between entities, comprising program instructions configured to, when executed: provide a measurement tensor X of measurement tensor components, Xijk, with i, j=1 . . . N, comprising measurement data as relation indicators, wherein the relation indicator Xijk indicates a k-th relation between an i-th and a j-th of a number, N, of entities; provide a rules tensor M of rules tensor components, Mijn, describing a prediction of an n-th rule; calculate a weighting tensor W of weighting tensor components, Wnk, indicating relative weights of the rules for the k-th relation between the entities; calculate a relationship tensor R of relationship tensor components, Rabk, with a, b=1 . . . r, indicating relations between a set of a number, r, of properties of the entities; calculate a transformation tensor A of transformation tensor components, Aia, describing the i-th entity via r latent properties, wherein the transformation tensor A, the weighting tensor W, and the relationship tensor R are calculated as minimum solutions to the following equation: min A , R , W   X ijk - X ijk ′  F 2 + λ A   A  F 2 + λ R   R  F 2 + λ W   W  F 2 , with λA, λR, and λW as Lagrange parameters and with result tensor components Xijk′ of a result tensor X′ given by Xijk′=Σa,b,n(AiaRabkAbjT+MijnWnk), where AT is the transposed tensor corresponding to the transformation tensor A; and calculate a value of the relation indicator for the k-th relation between the i-th and the j-th entity based on the result tensor component Xijk′. 9. A computer-readable, non-transitory storage medium comprising stored program instructions configured to, when executed: provide a measurement tensor X of measurement tensor components, Xijk, with i, j=1 . . . N, comprising measurement data as relation indicators, wherein the relation indicator Xijk indicates a k-th relation between an i-th and a j-th of a number, N, of entities; provide a rules tensor M of rules tensor components, Mijn, describing a prediction of an n-th rule; calculate a weighting tensor W of weighting tensor components, Wnk, indicating relative weights of the rules for the k-th relation between the entities; calculate a relationship tensor R of relationship tensor components, Rabk, with a, b=1 . . . r, indicating relations between a set of a number, r, of properties of the entities; calculate a transformation tensor A of transformation tensor components, Aia, describing the i-th entity via r latent properties, wherein the transformation tensor A, the weighting tensor W, and the relationship tensor R are calculated as minimum solutions to the following equation: min A , R , W   X ijk - X ijk ′  F 2 + λ A   A  F 2 + λ R   R  F 2 + λ W   W  F 2 , with λA, λR, and λW as Lagrange parameters and with result tensor components Xijk′ of a result tensor X′ given by: Xijk′=Σa,b,n(AiaRabkAbjT+MijnWnk), where AT is the transposed tensor corresponding to the transformation tensor A; and calculate a value of the relation indicator for the k-th relation between the i-th and the j-th entity based on the result tensor component Xijk′. 10. An apparatus for calculating a relation indicator for a relation between entities, comprising: a measurement tensor module configured to provide a measurement tensor X of measurement tensor components, Xijk, with i, j=1 . . . N, comprising measurement data as relation indicators, wherein the relation indicator Xijk indicates a k-th relation between an i-th and a j-th of a number, N, of entities; a rules tensor module M configured to provide a rules tensor of rules tensor components, Mijn, describing a prediction of an n-th rule; a weighting tensor module configured to calculate a weighting tensor W of weighting tensor components, Wnk, indicating relative weights of the rules for the k-th relation between the entities; a relationship tensor module configured to calculate a relationship tensor R of relationship tensor components, Rabk, with a, b=1 . . . r, indicating relations between a set of a number, r, of properties of the entities; a transformation tensor module configured to calculate a transformation tensor A of transformation tensor components, Aia, describing the i-th entity via r latent variables, wherein the transformation tensor A, the weighting tensor W, and the relationship tensor R are calculated as minimum solutions to the following equation: min A , R , W   X ijk - X ijk ′  F 2 + λ A   A  F 2 + λ R   R  F 2 + λ W   W  F 2 , with λA, λR, and λW as Lagrange parameters and with result tensor components Xijk′ of a result tensor X′ given by: Xijk′=Σa,b,n(AiaRabkAbjT+MijnWnk), where AT is the transposed tensor corresponding to the transformation tensor A; a result tensor calculation module configured to calculate a result tensor X′ of result tensor components, Xijk′; and a relation indicator calculation module configured to calculate a value of the relation indicator for the k-th relation between the i-th and the j-th entity based on the result tensor component Xijk′. 11. The apparatus of claim 10, further comprising: a control signal generation module configured to generate at least one control signal, based on the predicted value of the relation indicator, for controlling one or more of an actuator, a sensor, a controller, a field device, or a display. 12. The apparatus of claim 11, further comprising: an output module configured to create a visual signal, an acoustic signal, or the visual signal and the acoustic signal based on the control signal. 13. The apparatus of claim 10, further comprising: a measurement tensor expansion module configured to: (1) expand the measurement tensor with additional measurement tensor components Xi(N+1)k for i=1 . . . N, X(N+1)jk for j=1 . . . N and X(N+1)(N+1)k, comprising measurement data as relation indicators between the (N+1)-th additional entity and the entities, and (2) set a value of a relation indicator to be predicted to a predetermined value; and a rules tensor expansion module configured to expand the rules tensor with additional rules tensor components, Mi(N+1)n for i=1 . . . N, M(N+1)jn for j=1 . . . N and M(N+1)(N+1)n. 14. The apparatus of claim 10, further comprising: a monitoring module configured to monitor a relation between at least two of the entities; and a setting module configured to set a value of at least one relation indicator based on the monitored relation between the at least two of the entities. 15. The apparatus of claim 10, further comprising: a measurement module configured to provide at least some of the measurement data to the measurement tensor module. 16. The apparatus of claim 10, further comprising: at least one database; and a readout module configured to read out at least some of the measurement data from the at least one database. 17. The method of claim 10, wherein the result tensor calculation module is configured to use an alternating least-squares method, wherein the transformation tensor, the relationship tensor, and the weighting tensor are updated alternatingly until convergence. 18. A system for calculating a relation indicator for a relation between entities, comprising: a number, N, of entities; a measurement tensor module configured to provide a measurement tensor X of measurement tensor components, Xijk, with i, j=1 . . . N, comprising measurement data as relation indicators, wherein the relation indicator Xijk indicates a k-th relation between an i-th and a j-th of the number of entities; a rules tensor module configured to provide a rules tensor M of rules tensor components, Mijn, describing a prediction of an n-th rule; a weighting tensor module configured to calculate a weighting tensor W of weighting tensor components, Wnk, indicating relative weights of the rules for the k-th relation between the entities; a relationship tensor module configured to calculate a relationship tensor R of relationship tensor components, Rabk, with a, b=1 . . . r, indicating relations between a set of a number, r, of properties of the entities; a transformation tensor module configured to calculate a transformation tensor A of transformation tensor components, Aia, describing the i-th entity via r latent properties, wherein the transformation tensor A, the weighting tensor W, and the relationship tensor R are calculated as minimum solutions to the following equation: min A , R , W   X ijk - X ijk ′  F 2 + λ A   A  F 2 + λ R   R  F 2 + λ W   W  F 2 , with λA, λR, and λW as Lagrange parameters and with result tensor components Xijk′ of a result tensor X′ given by: Xijk′=Σa,b,n(AiaRabkAbjT+MijnWnk), where AT is the transposed tensor corresponding to the transformation tensor A; a result tensor calculation module configured to calculate a result tensor X′ of result tensor components, Xijk′, and a relation indicator calculation module configured to calculate a value of the relation indicator for the k-th relation between the i-th and the j-th entity based on the result tensor component Xijk′. 19. The system of claim 18, wherein at least one of the entities is a sensor, an actuator, a field device, a controller, a display, or a section of a conveyer belt assembly. 20. The system of claim 18, further comprising: a control signal generation module configured to generate at least one control signal, based on the predicted value of the relation indicator, for controlling at least one of the entities of the system.