Metric tensor for Riemannian Classifier

被引：0

作者：

Wereszczynski, Kamil ^{[1
,2
]}

Michalczuk, Agnieszka ^{[1
]}

Staniszewski, Michal ^{[1
]}

Josinski, Henryk ^{[1
]}

Switonski, Adam ^{[1
]}

Wojciechowski, Konrad ^{[2
]}

机构：

[1] Silesian Tech Univ, Inst Informat, Akad 16, PL-44100 Gliwice, Poland

[2] Polish Japanese Acad Informat Technol, Koszykowa 86, PL-02008 Warsaw, Poland

来源：

PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016) | 2017年 / 1863卷

关键词：

Riemannian Classification; Riemannian manifold; metric tensor; classification; genetic algorithm;

D O I：

10.1063/1.4992573

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页数：4

共 50 条

[1] A Characterization of the Dependence of the Riemannian Metric on the Curvature Tensor by Young Symmetrizers
Fiedler, B.
[J]. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, 1998, 17 (01): : 135 - 157
[2] SUFFICIENT CONDITIONS FOR A CURVATURE TENSOR TO BE RIEMANNIAN AND FOR DETERMINING ITS METRIC
EDGAR, SB
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 1991, 32 (04) : 1011 - 1016
[3] ON THE GEOMETRY OF THE RESCALED RIEMANNIAN METRIC ON TENSOR BUNDLES OF ARBITRARY TYPE
Gezer, Aydin
Altunbas, Murat
[J]. KODAI MATHEMATICAL JOURNAL, 2015, 38 (01) : 37 - 64
[4] Graph Cuts using a Riemannian Metric induced by Tensor Voting
Koo, Hyung Il
Cho, Nam Ik
[J]. 2009 IEEE 12TH INTERNATIONAL CONFERENCE ON COMPUTER VISION (ICCV), 2009, : 514 - 520
[5] Nearest neighbor classifier based on Riemannian metric in radar target recognition
Meng, JC
Yang, WL
[J]. 2005 IEEE International Radar, Conference Record, 2005, : 851 - 853
[6] THE HOMOGENEOUS LIFT TO THE (1,1)-TENSOR BUNDLE OF A RIEMANNIAN METRIC
Peyghan, Esmaeil
Nasrabadi, Hassan
Tayebi, Akbar
[J]. INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2013, 10 (04)
[7] ALMOST CONTACT METRIC MANIFOLDS WITH SOME CONDITIONS FOR THE RIEMANNIAN CURVATURE TENSOR
ALEXIEV, VA
[J]. DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 1985, 38 (02): : 195 - 198
[8] To the question of interrelation between the metric and the curvature tensor in n-dimensional Riemannian space
Gadzhisalikhoglu, GG
Amirov, AK
[J]. SIBERIAN MATHEMATICAL JOURNAL, 1998, 39 (05) : 864 - 871
[9] To the question of interrelation between the metric and the curvature tensor inn-dimensional riemannian space
G. G. Gadzhisalikhoglu
A. Kh. Amirov
[J]. Siberian Mathematical Journal, 1998, 39 : 864 - 871
[10] CURVATURE AND CRITICAL RIEMANNIAN METRIC
MUTO, Y
[J]. JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1974, 26 (04) : 686 - 697

← 1 2 3 4 5 →