1. Metric tensor for Riemannian Classifier.
- Author
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Wereszczyński, Kamil, Michalczuk, Agnieszka, Staniszewski, Michał, Josiński, Henryk, Świtoński, Adam, and Wojciechowski, Konrad
- Subjects
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CURVED surfaces , *GEOMETRIC surfaces , *RIEMANNIAN manifolds , *CALCULUS of tensors , *MANIFOLDS (Mathematics) - Abstract
A novel method of classification and current progress of work is presented in this paper. Its concept is based on application of curved and smooth surface being Riemannian manifold as the classifier. The model in the form of such a manifold is created using samples from a training set which are points in multidimensional linear space. This model is a structure where the greater group of points curves the surface around it more than a smaller group. Therefore if a new, unknown sample appears in such a surface, it will "fall" on an object and gets a label of object which it has fallen on. In this paper we present the progress of work leading to implementation of the first stage of the training phase: finding the best metric tensor for the set of points being feature vectors of samples from the training set reduced to minimization problem. Finally, the perspective of development of Riemannian Classifier was shown. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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