You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
In open set recognition (OSR), almost all existing methods are designed specially for recognizing individual instances, even these instances are collectively coming in batch. Recognizers in decision either reject or categorize them to some known class using empirically-set threshold. Thus the decision threshold plays a key role. However, the selection for it usually depends on the knowledge of known classes, inevitably incurring risks due to lacking available information from unknown classes. On the other hand, a more realistic OSR system should NOT just rest on a reject decision but should go further, especially for discovering the hidden unknown classes among the reject instances, whereas existing OSR methods do not pay special attention. In this paper, we introduce a novel collective batch decision strategy with an aim to extend existing OSR for new class discovery while considering correlations among the testing instances. Specifically, a collective decision-based OSR framework (CD-OSR) is proposed by slightly modifying the Hierarchical Dirichlet process (HDP). Thanks to HDP, our CD-OSR does not need to define the decision threshold and can implement the open set recognition and new class discovery simultaneously. Finally, extensive experiments on benchmark datasets indicate the validity of CD-OSR.

Cited Abstract(s):
[1]: To date, almost all experimental evaluations of machine learning-based recognition algorithms in computer vision have taken the form of “closed set” recognition, whereby all testing classes are known at training time. A more realistic scenario for vision applications is “open set” recognition, where incomplete knowledge of the world is present at training time, and unknown classes can be submitted to an algorithm during testing. This paper explores the nature of open set recognition and formalizes its definition as a constrained minimization problem. The open set recognition problem is not well addressed by existing algorithms because it requires strong generalization. As a step toward a solution, we introduce a novel “1-vs-set machine,” which sculpts a decision space from the marginal distances of a 1-class or binary SVM with a linear kernel. This methodology applies to several different applications in computer vision where open set recognition is a challenging problem, including object recognition and face verification. We consider both in this work, with large scale cross-dataset experiments performed over the Caltech 256 and ImageNet sets, as well as face matching experiments performed over the Labeled Faces in the Wild set. The experiments highlight the effectiveness of machines adapted for open set evaluation compared to existing 1-class and binary SVMs for the same tasks.
With the formalization of OSR developed in [1] , the openness of a particular problem or data universe is defined by considering the number of training, target, and testing classes: Larger openness corresponds to more open problems, while the problem is completely closed when @math Furthermore, the OSR problem can be defined as follows: given a set of training data @math , an open space risk @math , and an empirical risk @math , the goal of OSR is to find a measurable recognition function @math defined by minimizing the following open set risk where @math is a regularization constant. Thanks to the guidance of this definition, a large number of OSR algorithms have been proposed. Next, we will briefly review the relevant representative approaches.