The Deep Kernelized Autoencoder

TL;DR

The paper introduces a kernelized autoencoder that aligns data codes with a kernel matrix to learn similarity-preserving representations, improving interpretability and efficiency in tasks like classification and visualization.

Contribution

It proposes a novel autoencoder variant that incorporates kernel alignment, enabling explicit control over data similarity in learned representations.

Findings

Effective in classification and visualization tasks

Capable of emulating kernel PCA with lower computational cost

Achieves competitive results in denoising tasks

Abstract

Autoencoders learn data representations (codes) in such a way that the input is reproduced at the output of the network. However, it is not always clear what kind of properties of the input data need to be captured by the codes. Kernel machines have experienced great success by operating via inner-products in a theoretically well-defined reproducing kernel Hilbert space, hence capturing topological properties of input data. In this paper, we enhance the autoencoder's ability to learn effective data representations by aligning inner products between codes with respect to a kernel matrix. By doing so, the proposed kernelized autoencoder allows learning similarity-preserving embeddings of input data, where the notion of similarity is explicitly controlled by the user and encoded in a positive semi-definite kernel matrix. Experiments are performed for evaluating both reconstruction and kernel alignment performance in classification tasks and visualization of high-dimensional data. Additionally, we show that our method is capable to emulate kernel principal component analysis on a denoising task, obtaining competitive results at a much lower computational cost.