Sonny Achten

Sonny Achten, Francesco Tonin, Panagiotis Patrinos et al.

We present a deep Graph Convolutional Kernel Machine (GCKM) for semi-supervised node classification in graphs. The method is built of two main types of blocks: (i) We introduce unsupervised kernel machine layers propagating the node features in a one-hop neighborhood, using implicit node feature mappings. (ii) We specify a semi-supervised classification kernel machine through the lens of the Fenchel-Young inequality. We derive an effective initialization scheme and efficient end-to-end training algorithm in the dual variables for the full architecture. The main idea underlying GCKM is that, because of the unsupervised core, the final model can achieve higher performance in semi-supervised node classification when few labels are available for training. Experimental results demonstrate the effectiveness of the proposed framework.

David Winant, Sonny Achten, Johan A. K. Suykens

Modern clustering approaches often trade interpretability for performance, particularly in deep learning-based methods. We present Generative Kernel Spectral Clustering (GenKSC), a novel model combining kernel spectral clustering with generative modeling to produce both well-defined clusters and interpretable representations. By augmenting weighted variance maximization with reconstruction and clustering losses, our model creates an explorable latent space where cluster characteristics can be visualized through traversals along cluster directions. Results on MNIST and FashionMNIST datasets demonstrate the model's ability to learn meaningful cluster representations.

Sonny Achten, Arun Pandey, Hannes De Meulemeester et al.

We propose a unifying setting that combines existing restricted kernel machine methods into a single primal-dual multi-view framework for kernel principal component analysis in both supervised and unsupervised settings. We derive the primal and dual representations of the framework and relate different training and inference algorithms from a theoretical perspective. We show how to achieve full equivalence in primal and dual formulations by rescaling primal variables. Finally, we experimentally validate the equivalence and provide insight into the relationships between different methods on a number of time series data sets by recursively forecasting unseen test data and visualizing the learned features.