Representation learning of compositional data

Marta Avalos-Fernandez, Richard Nock, Cheng Soon Ong, Julien Rouar, Ke Sun

    Research output: Contribution to journalConference articlepeer-review

    5 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)6679-6689
    Number of pages11
    JournalAdvances in Neural Information Processing Systems
    Volume2018-December
    Publication statusPublished - 2018
    Event32nd Conference on Neural Information Processing Systems, NeurIPS 2018 - Montreal, Canada
    Duration: 2 Dec 20188 Dec 2018

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