  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.
