caa a22 4500 605478546 CHVBK 20210128100406.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10994-014-5446-z doi (NATIONALLICENCE)springer-10.1007/s10994-014-5446-z Adaptive Euclidean maps for histograms: generalized Aitchison embeddings [Elektronische Daten] [Tam Le, Marco Cuturi] Learning distances that are specifically designed to compare histograms in the probability simplex has recently attracted the attention of the machine learning community. Learning such distances is important because most machine learning problems involve bags of features rather than simple vectors. Ample empirical evidence suggests that the Euclidean distance in general and Mahalanobis metric learning in particular may not be suitable to quantify distances between points in the simplex. We propose in this paper a new contribution to address this problem by generalizing a family of embeddings proposed by Aitchison (J R Stat Soc 44:139-177, 1982) to map the probability simplex onto a suitable Euclidean space. We provide algorithms to estimate the parameters of such maps by building on previous work on metric learning approaches. The criterion we study is not convex, and we consider alternating optimization schemes as well as accelerated gradient descent approaches. These algorithms lead to representations that outperform alternative approaches to compare histograms in a variety of contexts. The Author(s), 2014 Metric learning for histograms nationallicence Aitchison geometry nationallicence Probability simplex nationallicence Embeddings nationallicence Le Tam Graduate School of Informatics, Kyoto University, Kyoto, Japan aut Cuturi Marco Graduate School of Informatics, Kyoto University, Kyoto, Japan aut Machine Learning Springer US; http://www.springer-ny.com 99/2(2015-05-01), 169-187 0885-6125 99:2<169 2015 99 10994 https://doi.org/10.1007/s10994-014-5446-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10994-014-5446-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Le Tam Graduate School of Informatics, Kyoto University, Kyoto, Japan aut NATIONALLICENCE 700 1- Cuturi Marco Graduate School of Informatics, Kyoto University, Kyoto, Japan aut NATIONALLICENCE 773 0- Machine Learning Springer US; http://www.springer-ny.com 99/2(2015-05-01), 169-187 0885-6125 99:2<169 2015 99 10994