This paper studies the problem of domain division which aims to segment instances drawn from different probabilistic distributions. This problem exists in many previous recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL), where the testing instances come from either seen or unseen/novel classes with different probabilistic distributions. Previous works only calibrate the conﬁdent prediction of classiﬁers of seen classes (WSVM Scheirer et al. (2014)) or taking unseen classes as outliers Socher et al. (2013). In contrast, this paper proposes a probabilistic way of directly estimating and ﬁne-tuning the decision boundary between seen and unseen classes. In particular, we propose a domain division algorithm to split the testing instances into known, unknown and uncertain domains, and then conduct recognition tasks in each domain. Two statistical tools, namely, bootstrapping and KolmogorovSmirnov (K-S) Test, for the ﬁrst time, are introduced to uncover and ﬁne-tune the decision boundary of each domain. Critically, the uncertain domain is newly introduced in our framework to adopt those instances whose domain labels cannot be predicted conﬁdently. Extensive experiments demonstrate that our approach achieved the state-of-the-art performance on OSL and G-ZSL benchmarks. This paper discusses the problem of learning to separate two domains which include the instances sampled from different distributions. This is a typical and general research topic that can be potentially used in various recognition tasks, such as Open Set Learning (OSL) and Generalized Zero-Shot Learning (G-ZSL). Particularly, OSL can break the constraints of the closed set in supervised learning, and aim at recognizing the testing instances from one of the seen classes (i.e., known domain), and the novel class (i.e., unknown domain). The novel classes include the testing instances which have different distributions from that of the seen ones. In contrast, G-ZSL targets at distinguishing the labels of instances from the seen and unseen classes. Only the seen classes have the training instances, but unseen classes do not. Note that OSL does not explicitly give the class labels for those instances categorized as the novel class, but G-ZSL requires predicting the class labels of unseen classes. To address G-ZSL, semantic attributes or vectors are introduced as the intermediate representations; each (seen/unseen) class has one semantic prototype that contains class level information. Specifically, a reasonable solution of OSL and G-ZSL is via dividing the known and unknown domains. For training classes, the predictors are constructed to map visual features to the class label space (OSL), (or semantic space (G-ZSL)). Testing is performed on each separated domain to identify seen classes and the novel class (OSL), or both seen and unseen classes (G-ZSL).The key question of OSL and ZSL is how to deal with the newly introduced novel class/unseen classes efficiently in the testing time. This is different from the conventional Zero-Shot Learning (ZSL) task which assumes that, in the testing stage, seen classes would not be misclassified as unseens, and vice versa; ZSL only uses the unseen classes for testing. Unfortunately , the predictors learned on training classes will inevitably make OSL or G-ZSL approaches tend to be biased towards the seen classes, and thus leading to very poor classification results for the novel class (OSL) or unseen classes (G-ZSL) BID39 ; . We show an example in Fig. 1 . On aPY dataset (described in Sec. 6.1) BID10 ), t-SNE van der Maaten & Hinton (2008 is The initial boundary of the known domain is estimated by bootstrapping. We can further divide an uncertain domain by K-S Test. Then we can recognize instances in each domain. (b) The distribution of pairwise intraclass and interclass distances: We compute the empirical density of the pairwise distance in aPY dataset (described in Sec. 6.1). There is a large overlapping of the distribution of the intraclass and interclass distances.employed to visualize the distributions of the testing instances of the ResNet-101 features in BID39 (Fig. 1 (a) ), and semantic features learned by SAE Kodirov et al. (2017) (Fig. 1 (b) ). We categorize the SAE prediction as known or unknown domain labels and compare with the groundtruth in Fig. 1(c) . We show that a large portion of unseen instances being predicted as one of the known classes.A natural recipe for addressing this problem is to learn to separate domains by the distributions of instances; and different classifiers can be directly applied in each domain. However, there are still two key problems. First , visual features alone are not discriminative enough to help to distinguish the seen and unseen/novel classes. As Fig. 2 (a) , bicycle and motorbike, respectively , are one of the seen and unseen classes 1 in aPY dataset (described in Sec. 6.1). We can observe that there is a large overlapping region between their t-SNE visualized feature distributions. That is, the visual features may not be representative enough to differentiate these two classes; the instances of motorbike (circled as the uncertain domain) may be taken as the bicycle, or vice versa; Second, the predictors trained on seen classes may be not trustworthy. A not well-trained predictor may negatively affect the recognition algorithms. Third and even worse, the performance of classifiers in each domain is still very sensitive to the results of domain separation: should the domain of one testing instance be wrongly divided, it would never be correctly categorized by the classifiers.To tackle the aforementioned issues, our key insight (see Fig. 2(a) ) is to introduce a novel domain -uncertain domain that accounts for the overlapping regions of testing instances from seen or novel/unseen classes. Thus, the visual or semantic space can be learned to be divided into known, unknown and uncertain domains. The recognition algorithms will be directly employed in each domain . Nonetheless, how to divide the domains based on known information is also a non-trivial task. Though the supervised classifiers can learn the patterns of known classes, not all classes encountered during testing are known.Formally, we propose exploiting the distribution information of seen and novel/unseen classes to efficiently learn to divide the domains from a probabilistic perspective. Our domain separation algorithm has two steps: the initial division of domains by bootstrapping, and fine-tuning by the Kolmogorov-Smirnov test. Specifically, according to extreme value theory BID30 , the maximum/minimum confidence scores predicted by the classifier of each class can be taken as an extreme value distribution. Since we do not have the prior knowledge of the underlying data distributions of each class; bootstrapping is introduced here as an asymptotically consistent method in estimating an initial boundary of known classes. Nevertheless, the initial boundary estimated by bootstrapping is too relaxed to include novel testing instances as is illustrated in Fig. 2(b) . To finetune the boundary, we exploit the K-S Test to validate whether the learned predictors are trustworthy in a specific region. The uncertain domain introduced thus accounts for those testing instances whose labels are hard to be judged. Recognition models can be conducted in each domain. This paper learns to divide the instances into known, unknown and uncertain domains for the recognition tasks from a probabilistic perspective. The domain division procedure consists of bootstrapping and K-S Test steps. The bootstrapping is used to set an initial threshold for each class; we further employ the K-S test to fine-tune the boundary. Such a domain division algorithm can be used for OSL and G-ZSL tasks, and achieves remarkable results.
 This paper studies the problem of domain division by segmenting instances drawn from different probabilistic distributions.   This paper deals with the problem of novelty recognition in open set learning and generalized zero-shot learning and proposes a possible solution An approach to domain separation based on bootstrapping to identify similarity cutoff thresholds for known classes, followed by a Kolmogorov-Smirnoff test to refine the bootstrapped in-distribution zones. Proposes to introduce a new domain, the uncertain domain, to better handle the division between seen/unseen domains in open-set and generalized zero-shot learning