# Autoencoding any Data through Kernel Autoencoders

arXiv: https://arxiv.org/abs/1805.11028 · HTML: https://mlsanity.com/paper/1805.11028/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 May 2018.

## Built on by (most cited first, 10 of 10)

- [The quest for the GRAph Level autoEncoder (GRALE)](https://mlsanity.com/paper/2505.22109/) (2025)
- [Deep Learning with Kernels through RKHM and the Perron-Frobenius Operator](https://mlsanity.com/paper/2305.13588/) (2023)
- [Deep Kernel Principal Component Analysis for Multi-level Feature Learning](https://mlsanity.com/paper/2302.11220/) (2023)
- [Geometrically Inspired Kernel Machines for Collaborative Learning Beyond Gradient Descent](https://mlsanity.com/paper/2407.04335/) (2024)
- [C^*-Algebraic Machine Learning: Moving in a New Direction](https://mlsanity.com/paper/2402.02637/) (2024)
- [Spectral Truncation Kernels: Noncommutativity in C^*-algebraic Kernel Machines](https://mlsanity.com/paper/2405.17823/) (2024)
- [Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learning](https://mlsanity.com/paper/2512.19184/) (2025)
- [A Latent Space Correlation-Aware Autoencoder for Anomaly Detection in Skewed Data](https://mlsanity.com/paper/2301.00462/) (2023)
- [Combining Primal and Dual Representations in Deep Restricted Kernel Machines Classifiers](https://mlsanity.com/paper/2306.07015/) (2023)
- [Learning Reconstructive Embeddings in Reproducing Kernel Hilbert Spaces via the Representer Theorem](https://mlsanity.com/paper/2601.05811/) (2026)

## Abstract (arXiv)

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.