A classification system includes memory which stores, for each of a set of classes, a classifier model for assigning a class probability to a test sample from a target domain. The classifier model has been learned with training samples from the target domain and from at least one source domain. Each classifier model models the respective class as a mixture of components, the component mixture including a component for each source domain and a component for the target domain. Each component is a function of a distance between the test sample and a domain-specific class representation which is derived from the training samples of the respective domain that are labeled with the class, each of the components in the mixture being weighted by a respective mixture weight. Instructions, implemented by a processor, are provided for labeling the test sample based on the class probabilities assigned by the classifier models.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A classification system comprising: memory which stores: for each of a set of classes, a classifier model for assigning a class probability to a test sample from a target domain, the classifier model having been learned with training samples from the target domain and training samples from at least one source domain different from the target domain, each classifier model modeling the respective class as a mixture of components, the mixture of components including a component for each of the at least one source domain and a component for the target domain, each component being a function of a distance between the test sample and a domain-specific class representation which is derived from the training samples of the respective domain that are labeled with the class, each of the components in the mixture being weighted by a respective mixture weight; and instructions for labeling the test sample based on the class probabilities assigned by the classifier models; and a processor in communication with the memory which executes the instructions. 2. The system of claim 1, wherein each component is an exponentially decreasing function of the distance between the test sample and the domain-specific class representation. 3. The system of claim 1, wherein each domain-specific class representation is an average of the training samples of the respective domain that are labeled with the class. 4. The system of claim 1, wherein the distance between the test sample and each domain-specific class representation is computed in an embedding space into which the test sample and each domain-specific class representation is embedded with the same metric. 5. The system of claim 1, where the mixture components are Gaussian functions and the inverse of their covariance is shared and approximated by a low-rank matrix. 6. The system of claim 1, wherein the classifier models are learned by maximizing a sum of the log of the training sample class posteriors. 7. The system of claim 1, wherein the classifier model is of the form: p  ( c | x i ) = 1 z i  w c  ∑ d = 1 D  w d  ( exp  ( - 1 2  d W  ( x i , μ d c ) ) ) ( 6 ) or is a function thereof, where p(c|xi) represents the posterior probability of the class c for the test sample xi; wc represents the class specific mixture weight, that can be constant; wd represents the mixture weight for a respective mixture component exp(−½dW(xi,μdc), where dW(xi,μdc) represents the distance between sample xi and the domain-specific class representation μdc for a domain d selected from the target domain and the at least one source domain, and W represents an optional metric for embedding sample xi and each of the domain-specific class representations μdc in a common embedding space; and Zi is an optional normalizing factor. 8. The system of claim 1, wherein the training samples and test sample are multidimensional representations. 9. The system of claim 7, wherein the multidimensional representations are derived from images, videos, sounds, text or other multimedia documents. 10. The system of claim 1, wherein each of the source domain training samples is labeled with a label for one of the classes and fewer than all of the target domain training samples are labeled with a label for any of the classes. 11. The system of claim 9, wherein at least some of the target domain training samples are labeled with a label for at least one of the classes. 12. The system of claim 10, wherein the learning includes for each of a plurality of iterations, performing at least one of: adding to an active training set, which is derived from the source domain samples and labeled target domain samples, a most confident unlabeled target domain sample for each class, and removing from the active training set a least confident source domain sample from each class; and retraining a metric based on the active training set which is used to embed the test sample and a domain-specific class representation into an embedding space in which the distance is computed. 13. The system of claim 1, wherein the mixture weight for the target domain is higher than for each of the at least one source domains. 14. The system of claim 1, wherein for the test sample, inference is performed by computing the max of the class posteriors. 15. A classifier learning method, comprising: for each of a set of domains including a target domain and at least one source domain, providing a set of samples, the source domain samples each being labeled with a class label for one of a set of classes, fewer than all of the target domain samples being labeled with any of the class labels; with a processor, learning a classifier model for each class with the target domain training samples and the training samples from the at least one source domain, each classifier model modeling the respective class as a mixture of components, the mixture of components including a component for each of the at least one source domain and a component for the target domain, each component being a function of a distance between the test sample and a domain-specific class representation which is derived from the training samples of the respective domain that are labeled with the class, each of the components in the mixture being weighted by a respective mixture weight. 16. The method of claim 15, further comprising learning the weights in an iterative process. 17. The method of claim 15, wherein the classifier model includes a metric for embedding samples into an embedding space, the method further comprising learning the metric. 18. The method of claim 15, wherein the learning of the metric comprises: composing an active training set from the labeled training samples; initializing the metric for embedding samples in an embedding space; for each of a plurality of iterations, a) performing at least one of: adding to the active training set a most confident unlabeled target domain sample for each class, and removing from the active training set a least confident source domain sample from each class; and b) retraining the metric based on the active training set. 19. The method of claim 18, wherein the confidence used to remove and add samples is based on the performance of the classifier model when the metric is used for embedding training samples into the embedding space in which the distance is computed. 20. A system comprising memory which stores instructions for performing the method of claim 15 and a processor in communication with the memory for executing the instructions. 21. A computer program product comprising non-transitory memory storing instructions, which when executed by a processor, perform the method of claim 15. 22. A method for learning a metric for a classifier model comprising: for each of a set of domains including a target domain and at least one source domain, providing a set of samples, the source domain samples each being labeled with a class label for one of a set of classes, fewer than all of the target domain samples being labeled with any of the class labels; composing an active training set from the labeled training samples; providing a metric for embedding samples in an embedding space; for each of a plurality of iterations, performing at least one of: a) adding to the active training set a most confident unlabeled target domain sample for each class, and b) removing from the active training set a least confident source domain sample from each class; and retraining the metric based on the active training set, the confidence used to remove and add samples being based on a classifier model that includes the trained metric, where each class is modeled as a mixture of components, and where there is one mixture component for each source domain and one for the target domain. 23. The method of claim 22, wherein for each mixture component there is a weight and the method includes iteratively learning the weights by evaluating a confidence of the classifier model on a set of labeled target domain samples.