In real-world recognition/classification tasks, limited by various objective factors, it is usually difficult to collect training samples exhaust all classes when a recognizer or classifier. A more realistic scenario open set recognition (OSR), where incomplete knowledge of the world exists at time, and unknown can be submitted an algorithm during testing, requiring classifiers not only accurat...

Open Set Recognition (OSR) has been an emerging topic. Besides recognizing predefined classes, the system needs to reject unknowns. Prototype learning is a potential manner handle problem, as its ability improve intra-class compactness of representations much needed in discrimination between known and In this work, we propose novel Mining And Learning (PMAL) framework. It prototype mining mecha...

In inference, open-set classification is to either classify a sample into known class from training or reject it as an unknown class. Existing deep classifiers train explicit closed-set classifiers, in some cases disjointly utilizing reconstruction, which we find dilutes the latent representation's ability distinguish classes. contrast, our model cooperatively learn reconstruction and perform c...

In this paper, we introduce fuzzy Banach algebra and study the properties of invertible elements and its relation with opensets. We obtain some interesting results.

We investigate two density questions for Sobolev, Besov and Triebel--Lizorkin spaces on rough sets. Our main results, stated in the simplest Sobolev space setting, are that: (i) an open set $\Omega\subset\mathbb R^n$, $\mathcal{D}(\Omega)$ is dense $\{u\in H^s(\mathbb R^n):{\rm supp}\, u\subset \overline{\Omega}\}$ whenever $\partial\Omega$ has zero Lebesgue measure $\Omega$ "thick" (in sense o...