A method is provided for scalable supervised high-order parametric embedding for big data visualization. The method is performed by a processor and includes receiving feature vectors and class labels. Each feature vector is representative of a respective one of a plurality of high-dimensional data points. The class labels denote classes for the high-dimensional data points. The method further includes multiplying each feature vector by one or more factorized high-order tensors to obtain respective product vectors. The method also includes performing a maximally collapsing metric learning on the product vectors using learned synthetic exemplars and learned high-order filters. The learned high-order filters represent high-order embedding parameters. The method additionally includes performing an output operation to output a set of data that includes (i) interpretable factorized high-order filters, (ii) exemplars representative of the class labels and data separation properties in two-dimensional space, and (iii) a two-dimensional embedding of the high-dimensional data points.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method for scalable supervised high-order parametric embedding for big data visualization, the method comprising: receiving, by a processor, feature vectors and class labels, each of the feature vectors being representative of a respective one of a plurality of high-dimensional data points, the class labels denoting classes for the high-dimensional data points; multiplying, by the processor, each of the feature vectors by one or more factorized high-order tensors to obtain respective product vectors; performing, by the processor, a maximally collapsing metric learning on the product vectors using learned synthetic exemplars and learned high-order filters, the learned high-order filters representing high-order embedding parameters; and performing, by the processor, an output operation to output a set of data that includes (i) interpretable factorized high-order filters, (ii) exemplars representative of the class labels and data separation properties in two-dimensional space, and (iii) a two-dimensional embedding of the high-dimensional data points. 2. The computer-implemented method of claim 1, wherein the high-order tensors are factorized in order to speed up respective multiplications involving the one or more factorized high-order tensors by reducing computational complexity. 3. The computer-implemented method of claim 1, wherein the high-order tensors are factorized to selectively and explicitly model different orders of feature interactions between the high-dimensional data points, responsive to a user-specified parameter. 4. The computer-implemented method of claim 1, wherein the high-order tensors are factorized using one or more matrix factorization techniques. 5. The computer-implemented method of claim 1, further comprising selectively performing one or more non-linear transformations on the product vectors to enhance the expressiveness of a resultant model formed by the method. 6. The computer-implemented method of claim 1, wherein the learned exemplars are absent in, but learned from, a same input data set that includes the high-dimensional data points from which the feature vectors and the class labels are determined. 7. The computer-implemented method of claim 6, wherein the learned exemplars are learned using a technique selected from the group consisting of a supervised k-means technique and a joint optimization of the learned synthetic exemplars and the high-order filters. 8. The computer-implemented method of claim 6, further comprising performing an information retrieval operation on only the learned synthetic exemplars in place of the input data set. 9. The computer-implemented method of claim 1, wherein the learned high-order filters are used to map the high-dimensional data points to a low-dimensional space by maximally collapsing classes corresponding to the high-dimensional data points. 10. The computer-implemented method of claim 9, wherein to maximally collapse classes, the learned high-order filters are learned by minimizing a sum of a Kullback-Leibler divergence between conditional probabilities computed in an embedding space and ground-truth probabilities calculated based on class labels of training data. 11. The computer-implemented method of claim 1, wherein the maximally collapsing metric learning comprises jointly updating the learned high-order filters and the learned synthetic exemplars. 12. The computer-implemented method of claim 1, further comprising displaying at least a portion of the set of data on a display device such that the high-dimensional data points in a same class stay closer to each other while the high-dimensional data points from different classes stay farther apart from each other to visually distinguish class members from among the different classes. 13. The computer-implemented method of claim 1, further comprising controlling an operation of a processor-based machine, responsive to at least a portion of the set of data output by the output operation. 14. The computer-implemented method of claim 1, wherein one or more components of at least some of the feature vectors is used for biasing. 15. A computer program product for scalable supervised high-order parametric embedding for big data visualization, the computer program product comprising a non-transitory computer readable storage medium having program instructions embodied therewith, the program instructions executable by a computer to cause the computer to perform a method comprising: receiving, by a processor, feature vectors and class labels, each of the feature vectors being representative of a respective one of a plurality of high-dimensional data points, the class labels denoting classes for the high-dimensional data points; multiplying, by the processor, each of the feature vectors by one or more factorized high-order tensors to obtain respective product vectors; performing, by the processor, a maximally collapsing metric learning on the product vectors using learned synthetic exemplars and learned high-order filters, the learned high-order filters representing high-order embedding parameters; and performing, by the processor, an output operation to output a set of data that includes (i) interpretable factorized high-order filters, (ii) exemplars representative of the class labels and data separation properties in two-dimensional space, and (iii) a two-dimensional embedding of the high-dimensional data points. 16. The computer program product of claim 15, wherein the learned exemplars are absent in, but learned from, a same input data set that includes the high-dimensional data points from which the feature vectors and the class labels are determined. 17. The computer program product of claim 16, wherein the learned exemplars are learned using a technique selected from the group consisting of a supervised k-means technique and a joint optimization of the learned synthetic exemplars and the high-order filters. 18. The computer program product of claim 16, wherein the method further comprises performing an information retrieval operation on only the learned synthetic exemplars in place of the input data set. 19. The computer program product of claim 15, wherein the method further comprises controlling an operation of a processor-based machine, responsive to at least a portion of the set of data output by the output operation. 20. A system for scalable supervised high-order parametric embedding for big data visualization, the system comprising: a processor, configured to: receive feature vectors and class labels, each of the feature vectors being representative of a respective one of a plurality of high-dimensional data points, the class labels denoting classes for the high-dimensional data points; multiply each of the feature vectors by one or more factorized high-order tensors to obtain respective product vectors; perform a maximally collapsing metric learning on the product vectors using learned synthetic exemplars and learned high-order filters, the learned high-order filters representing high-order embedding parameters; and perform an output operation to output a set of data that includes (i) interpretable factorized high-order filters, (ii) exemplars representative of the class labels and data separation properties in two-dimensional space, and (iii) a two-dimensional embedding of the high-dimensional data points.