Regularization methods are a key tool in the solution of inverse problems. They are used to
introduce prior knowledge and allow a robust approximation of ill-posed (pseudo-) inverses …

This chapter characterises the scope of this book. It explains the reasons why one should be
interested in cluster analysis, lists major application areas, basic theoretical and practical …

This is an elementary introduction to the Hodge Laplacian on a graph, a higher-order
generalization of the graph Laplacian. We will discuss basic properties including …

It is an open question whether preferences for visual art can be lawfully predicted from the
basic constituent elements of a visual image. Here, we developed and tested a …

Little is known about how the brain computes the perceived aesthetic value of complex
stimuli such as visual art. Here, we used computational methods in combination with …

There are currently several communities working on algorithms for classification of high
dimensional data. This work develops a class of variational algorithms that combine recent …

Hypergraphs allow to encode higher-order relationships in data and are thus a very flexible
modeling tool. Current learning methods are either based on approximations of the …

The analysis of signals defined over a graph is relevant in many applications, such as social
and economic networks, big data or biological networks, and so on. A key tool for analyzing …

We introduce submodular hypergraphs, a family of hypergraphs that have different
submodular weights associated with different cuts of hyperedges. Submodular hypergraphs …

In this paper we introduce a new family of partial difference operators on graphs and study
equations involving these operators. This family covers local variational p-Laplacian, ∞ …