On the optimality of the max-depth and max-rank classifiers for spherical data
Ondřej Vencálek; Houyem Demni; Amor Messaoud; Giovanni C. Porzio
Applications of Mathematics (2020)
- Volume: 65, Issue: 3, page 331-342
- ISSN: 0862-7940
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topVencálek, Ondřej, et al. "On the optimality of the max-depth and max-rank classifiers for spherical data." Applications of Mathematics 65.3 (2020): 331-342. <http://eudml.org/doc/297301>.
@article{Vencálek2020,
abstract = {The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers for directional data are optimal. We show that such classifiers are equivalent to the Bayes (optimal) classifier when the considered distributions are rotationally symmetric, unimodal, differ only in location and have equal priors. The necessity of such assumptions is also discussed.},
author = {Vencálek, Ondřej, Demni, Houyem, Messaoud, Amor, Porzio, Giovanni C.},
journal = {Applications of Mathematics},
keywords = {depth-based classifier; von Mises-Fisher distribution; directional data; cosine depth},
language = {eng},
number = {3},
pages = {331-342},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the optimality of the max-depth and max-rank classifiers for spherical data},
url = {http://eudml.org/doc/297301},
volume = {65},
year = {2020},
}
TY - JOUR
AU - Vencálek, Ondřej
AU - Demni, Houyem
AU - Messaoud, Amor
AU - Porzio, Giovanni C.
TI - On the optimality of the max-depth and max-rank classifiers for spherical data
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 3
SP - 331
EP - 342
AB - The main goal of supervised learning is to construct a function from labeled training data which assigns arbitrary new data points to one of the labels. Classification tasks may be solved by using some measures of data point centrality with respect to the labeled groups considered. Such a measure of centrality is called data depth. In this paper, we investigate conditions under which depth-based classifiers for directional data are optimal. We show that such classifiers are equivalent to the Bayes (optimal) classifier when the considered distributions are rotationally symmetric, unimodal, differ only in location and have equal priors. The necessity of such assumptions is also discussed.
LA - eng
KW - depth-based classifier; von Mises-Fisher distribution; directional data; cosine depth
UR - http://eudml.org/doc/297301
ER -
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