Autoencoding any Data through Kernel Autoencoders

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Pierre Laforgue, Stéphan Clémençon, Florence d’Alche-Buc ;
Proceedings of Machine Learning Research, PMLR 89:1061-1069, 2019.

Abstract

This paper investigates a novel algorithmic approach to data representation based on kernel methods. Assuming that the observations lie in a Hilbert space X , the introduced Kernel Autoencoder (KAE) is the composition of mappings from vector-valued Reproducing Kernel Hilbert Spaces (vv-RKHSs) that minimizes the expected reconstruction error. Beyond a first extension of the autoencoding scheme to possibly infinite dimensional Hilbert spaces, KAE further allows to autoencode any kind of data by choosing X to be itself a RKHS. A theoretical analysis of the model is carried out, providing a generalization bound, and shedding light on its connection with Kernel Principal Component Analysis. The proposed algorithms are then detailed at length: they crucially rely on the form taken by the minimizers, revealed by a dedicated Representer Theorem. Finally, numerical experiments on both simulated data and real labeled graphs (molecules) provide empirical evidence of the KAE performances.

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