Project: Generalized Aitchison Embeddings for Histograms

Abstract:

Learning distances that are specifically designed to compare histograms in the probability simplex has recently attracted the attention of the 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 (1982) to map the probability simplex onto a suitable Euclidean space. We provide algorithms to estimate the parameters of such maps, and show that these algorithms lead to representations that outperform alternative approaches to compare histograms. 

Matlab code is available here [Download / MirrorAtGithub]. (Version 0.1 - May 9th, 2014)

Related publications:

Tam Le, Marco Cuturi, Adaptive Euclidean Maps for Histograms: Generalized Aitchison Embeddings, Machine Learning Journal (MLJ), 2014. [Springer/PDF/Bibtex]

Tam Le, Marco Cuturi, Generalized Aitchison Embeddings for Histograms, The 5th Asian Conference for Machine Learning (ACML), Australia, 2013 (oral).  [PDF/SLIDE/Bibtex]