A system and method are provided for deep high-order exemplar learning of a data set. Feature vectors and class labels are received. Each of the feature vectors represents a respective one of a plurality of high-dimensional data points of the data set. The class labels represent classes for the high-dimensional data points. Each of the feature vectors are processed, using a deep high-order convolutional neural network, to obtain respective low-dimensional embedding vectors within each class. A minimization operation is performed on high-order embedding parameters of the high-dimensional data points to output a set of synthetic exemplars. A binarizing operation is performed on the low-dimensional embedding vectors and the set of synthetic exemplars to output hash codes representing the data set. The hash codes are utilized as a search key to increase the efficiency of a processor-based machine searching the data set.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A computer-implemented method for deep high-order exemplar learning of a data set, 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 of the data set, the class labels representing classes for the high-dimensional data points; processing, by the processor using a deep high-order convolutional neural network, each of the feature vectors to obtain respective low-dimensional embedding vectors; performing, by the processor, a minimization operation on high-order embedding parameters of the high-dimensional data points to output a set of synthetic exemplars within each class that have (i) high-order feature interactions representative of the class labels and (ii) data separation properties in low-dimensional space; performing, by the processor, a binarizing operation on the low-dimensional embedding vectors and the set of synthetic exemplars to output hash codes representing the data set; and utilizing, by the processor, the hash codes as a search key to increase the efficiency of a processor-based machine when retrieving one or more images or one or more documents from the data set. 2. The computer-implemented method of claim 1, wherein the minimization operation maximally collapses the classes for the high-dimensional data points. 3. The computer-implemented method of claim 2, wherein the maximally collapsed classes for the high-dimensional data points maximize a sum of pairwise probabilities between the high-dimensional data points in a same one of the classes, to spread out clusters in a low-dimensional code space while preserving original cluster patterns in a high-dimensional space. 4. The computer-implemented method of claim 1, wherein the minimization operation includes using a deterministic expectation-maximization method that uses a conjugate gradient descent. 5. The computer-implemented method of claim 1, wherein the feature vectors are output from the deep high-order convolutional neural network based on one or more input images. 6. The computer-implemented method of claim 1, wherein the class labels represent data points within a predetermined distance to each other in a high-dimensional space. 7. The computer-implemented method of claim 1, wherein the deep high-order convolutional neural network uses one or more interaction matrices to capture high-order interactions in an input feature space. 8. The computer-implemented method of claim 1, further comprising controlling an operation of the processor-based machine to change the state of the processor-based machine, responsive to at least a portion of the hash codes output by the binarizing operation. 9. The computer-implemented method of claim 1, wherein the minimization operation to output the set of synthetic exemplars include an operation selected from the group consisting of (i) joint optimization for updating the low-dimensional embedding vectors and the set of synthetic exemplars with new feature vectors and new class labels and (ii) k-means clustering to fix the set of synthetic exemplars to k-means clusters of each class. 10. A computer program product for deep high-order exemplar learning of a data set, 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 of the data set, the class labels representing classes for the high-dimensional data points; processing, by the processor using a deep high-order convolutional neural network, each of the feature vectors to obtain respective low-dimensional embedding vectors; performing, by the processor, a minimization operation on high-order embedding parameters of the high-dimensional data points to output a set of synthetic exemplars within each class that have (i) high-order feature interactions representative of the class labels and (ii) data separation properties in low-dimensional space; performing, by the processor, a binarizing operation on the low-dimensional embedding vectors and the set of synthetic exemplars to output hash codes representing the data set; and utilizing, by the processor, the hash codes as a search key to increase the efficiency of a processor-based machine when retrieving one or more images or one or more documents from the data set. 11. The computer-implemented method of claim 10, wherein the minimization operation maximally collapses the classes for the high-dimensional data points. 12. The computer-implemented method of claim 11, wherein the maximally collapsed classes for the high-dimensional data points maximize a sum of pairwise probabilities between the high-dimensional data points in a same one of the classes, to spread out clusters in a low-dimensional code space while preserving original cluster patterns in a high-dimensional space. 13. The computer-implemented method of claim 10, wherein the minimization operation includes using a deterministic expectation-maximization method that uses a conjugate gradient descent. 14. The computer-implemented method of claim 10, wherein the feature vectors are output from the deep high-order convolutional neural network based on one or more input images. 15. The computer-implemented method of claim 10, wherein the class labels represent data points within a predetermined distance to each other in a high-dimensional space. 16. The computer-implemented method of claim 10, wherein the deep high-order convolutional neural network uses one or more interaction matrices to capture high-order interactions in an input feature space. 17. The computer-implemented method of claim 10, further comprising controlling an operation of the processor-based machine to change the state of the processor-based machine, responsive to at least a portion of the hash codes output by the binarizing operation. 18. The computer-implemented method of claim 10, wherein the minimization operation to output the set of synthetic exemplars include an operation selected from the group consisting of (i) joint optimization for updating the low-dimensional embedding vectors and the set of synthetic exemplars with new feature vectors and new class labels and (ii) k-means clustering to fix the set of synthetic exemplars to k-means clusters of each class. 19. A system for deep high-order exemplar learning of a data set, 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 of the data set, the class labels representing classes for the high-dimensional data points; process, using a deep high-order convolutional neural network, each of the feature vectors to obtain respective low-dimensional embedding vectors; perform a minimization operation on high-order embedding parameters of the high-dimensional data points to output a set of synthetic exemplars within each class that have (i) high-order feature interactions representative of the class labels and (ii) data separation properties in low-dimensional space; and perform a binarizing operation on the low-dimensional embedding vectors and the set of synthetic exemplars to output hash codes representing the data set; and utilize the hash codes as a search key to increase the efficiency of a processor-based machine when retrieving one or more images or one or more documents from the data set. 20. The system of claim 19, wherein the minimization operation includes using a deterministic expectation-maximization method that uses a conjugate gradient descent.