Class (philosophy)

About: Class (philosophy) is a research topic. Over the lifetime, 821 publications have been published within this topic receiving 28000 citations.

The Mittag–Leffler Functions for a Class of First-Order Fractional Initial Value Problems: Dual Solution via Riemann–Liouville Fractional Derivative

Abstract: In this paper, a new approach is developed to solve a class of first-order fractional initial value problems. The present class is of practical interest in engineering science. The results are based on the Riemann–Liouville fractional derivative. It is shown that the dual solution can be determined for the considered class. The first solution is obtained by means of the Laplace transform and expressed in terms of the Mittag–Leffler functions. The second solution was determined through a newly developed approach and given in terms of exponential and trigonometric functions. Moreover, the results reduce to the ordinary version as the fractional-order tends to unity. Characteristics of the dual solution are discussed in detail. Furthermore, the advantages of the second solution over the first one is declared. It is revealed that the second solution is real at certain values of the fractional-order. Such values are derived theoretically and accordingly, and the behavior of the real solution is shown through several plots. The present analysis may be introduced for obtaining the solution in a straightforward manner for the first time. The developed approach can be further extended to include higher-order fractional initial value problems of oscillatory types.

Collective Decision for Open Set Recognition

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.

Recognizing similarity through a constrained non-rigid transform

Abstract: The recognition of the class or category of an object based on shape similarity, is an important problem in image databases. Categorizing objects not only helps in efficient image database organization for faster indexing but also allows shape similarity-based querying. The recognition of category is, however, a difficult problem since member objects of a class can show considerable variation in the size and position of individual features even when the overall shape similarity is maintained. In this paper we present an approach to recognizing the class or category of an object in the case where the similarity between member objects is specified by a constrained non-rigid transform. The class is characterized by a single model or prototype consisting of a set of non-overlapping regions and a set of motion (direction and extent) constraints that capture the relation between members of the class. The recognition of category is done by using region correspondence between model and image and recovering the constrained non-rigid transform corresponding to a member of the class that is nearest in shape to the image.