Deep Kernelized Autoencoders
This work addresses the need for explicit kernel space mappings in unsupervised learning, but it is incremental as it builds on traditional autoencoders.
The paper tackled the problem of mapping between input and kernel spaces using autoencoders, resulting in a model that approximates these mappings with control over hidden representations through kernel alignment, achieving promising results in emulating kPCA for denoising.
In this paper we introduce the deep kernelized autoencoder, a neural network model that allows an explicit approximation of (i) the mapping from an input space to an arbitrary, user-specified kernel space and (ii) the back-projection from such a kernel space to input space. The proposed method is based on traditional autoencoders and is trained through a new unsupervised loss function. During training, we optimize both the reconstruction accuracy of input samples and the alignment between a kernel matrix given as prior and the inner products of the hidden representations computed by the autoencoder. Kernel alignment provides control over the hidden representation learned by the autoencoder. Experiments have been performed to evaluate both reconstruction and kernel alignment performance. Additionally, we applied our method to emulate kPCA on a denoising task obtaining promising results.