Representation Learning of Compositional Data

Marta Avalos Fernandez (1, 2) , Richard Nock (3, 4, 5) , Cheng Soon Ong (3, 5) , Julien Rouar (1, 2) , Ke Sun (3)

1 SISTM - Statistics In System biology and Translational Medicine
2 BPH - Bordeaux population health
3 CSIRO - Data61 [Canberra]
4 The University of Sydney
5 ANU - Australian National University

We consider the problem of learning a low dimensional representation for compositional data. Compositional data consists of a collection of nonnegative data that sum to a constant value. Since the parts of the collection are statistically dependent, many standard tools cannot be directly applied. Instead, compositional data must be first transformed before analysis. Focusing on principal component analysis (PCA), we propose an approach that allows low dimensional representation learning directly from the original data. Our approach combines the benefits of the log-ratio transformation from compositional data analysis and exponential family PCA. A key tool in its derivation is a generalization of the scaled Bregman theorem, that relates the perspective transform of a Bregman divergence to the Bregman divergence of a perspective transform and a remainder conformal divergence. Our proposed approach includes a convenient surrogate (upper bound) loss of the exponential family PCA which has an easy to optimize form. We also derive the corresponding form for nonlinear autoencoders. Experiments on simulated data and microbiome data show the promise of our method.

Mots clés: Microbiome data; PCA; Bregman divergences; Compositional data; Relative abundance data

Domaines: Machine Learning [stat.ML]; Méthodologie [stat.ME]; Calcul [stat.CO]; Applications [stat.AP]; Apprentissage [cs.LG]; Santé publique et épidémiologie

Marta Avalos Fernandez, Richard Nock, Cheng Soon Ong, Julien Rouar, Ke Sun. Representation Learning of Compositional Data. NIPS 2018 - Thirty-second Conference on Neural Information Processing Systems, Dec 2018, Montréal, Canada. ⟨hal-01945508⟩