Domain adaptation addresses the problem where training and test data belong to different domains. While previous work on domain adaptation assumes that both domains contain the same set of object classes (closed set), this paper considers a more realistic open set scenario where only a few categories of interest are shared between source and target domains. The authors propose a method that learns a mapping from the source to the target domain by jointly solving an assignment problem that labels those target instances that potentially belong to the categories of interest present in the source dataset. The approach handles both open set and closed set domain adaptation in a unified framework.

Acquiring annotated training data is costly, leading practitioners to leverage large public datasets despite domain differences. However, depending on the application, the type of sensor or the perspective of the sensor, the entire captured scene might greatly differ from pictures on the Internet. This creates a significant domain shift between the source and target distributions. Domain adaptation methods aim to bridge this gap by learning domain-invariant representations or transformations.

Critically, all available evaluation protocols for domain adaptation describe a closed set recognition task, where both domains contain images only of the same set of object classes. In real-world applications, however, the target domain often contains unknown categories that are absent from the source domain. The authors argue that a robust domain adaptation method must be able to identify and reject such unknown classes while still transferring knowledge for the shared categories.

Traditional domain adaptation methods can be broadly categorized into instance-based, feature-based, and parameter-based approaches. Instance-based methods re-weight source instances to match the target distribution. Feature-based methods learn shared representations that minimize domain discrepancy, such as through maximum mean discrepancy (MMD) or domain adversarial training. Parameter-based methods adapt model parameters from source to target. However, all these approaches assume a closed set setting where the label spaces of source and target are identical.

Open set recognition has been studied independently of domain adaptation. Methods such as nearest non-outlier (NNO) and open set SVM can reject test samples from unknown classes. However, these methods do not address the domain shift problem — they assume training and test data come from the same distribution. The authors identify the gap: combining open set recognition with domain adaptation is an under-explored but practically important direction.

Given a source domain with labeled data and a target domain with unlabeled (or partially labeled) data, the standard domain adaptation assumes the label sets are identical. In the proposed open set domain adaptation formulation, the target domain may contain classes not present in the source, and vice versa. The method must simultaneously adapt to the domain shift and identify which target instances belong to known versus unknown classes.

The core of the approach is a joint optimization that simultaneously learns a domain mapping and solves an assignment problem. Specifically, the method assigns pseudo-labels to target instances based on their similarity to source class prototypes in a shared feature space. Instances that cannot be confidently assigned to any source class are labeled as "unknown". The domain mapping is then updated using only the confidently assigned target instances, ensuring that unknown-class data does not corrupt the adaptation process. This alternating optimization iterates between assignment refinement and mapping update.

The assignment problem is formulated as an integer linear program that maximizes the total similarity between assigned target instances and source prototypes, subject to constraints that enforce class balance and allow for an "unknown" assignment. The domain mapping utilizes a linear transformation learned via the assigned pairs, projecting source features into the target feature space. By coupling the assignment and mapping objectives, the framework avoids the pitfall of adapting to irrelevant target classes.

The method is evaluated on standard domain adaptation benchmarks including Office dataset (Amazon, DSLR, Webcam) and cross-dataset recognition tasks. The authors design evaluation protocols for both open set and closed set scenarios, demonstrating that the approach is versatile. In the open set setting, varying numbers of unknown classes are introduced in the target domain. Results show that the proposed method outperforms the state-of-the-art domain adaptation methods that are modified to handle unknown classes, while also achieving competitive performance in the standard closed set setting.

This paper introduces the problem of open set domain adaptation, a more realistic formulation that relaxes the standard assumption of identical label spaces. The proposed method jointly optimizes domain mapping and instance assignment, effectively transferring knowledge for shared categories while rejecting unknown classes. Thorough evaluation demonstrates that the approach outperforms the state-of-the-art, providing a practical solution for realistic domain adaptation scenarios. Future work may explore deep neural network integration and extension to more complex recognition tasks.