Related papers: Representing Data by a Mixture of Activated Simpli…
High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull…
The Simplex Tree (ST) is a recently introduced data structure that can represent abstract simplicial complexes of any dimension and allows efficient implementation of a large range of basic operations on simplicial complexes. In this paper,…
Graphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods,…
Studying complex real-world phenomena often involves data from multiple views (e.g. sensor modalities or brain regions), each capturing different aspects of the underlying system. Within neuroscience, there is growing interest in…
We introduce a uniform representation of general objects that captures the regularities with respect to their structure. It allows a representation of a general class of objects including geometric patterns and images in a sparse, modular,…
Complex networks can be understood as graphs whose connectivity deviates from those of regular or near-regular graphs, which are understood as being `simple'. While a great deal of the attention so far dedicated to complex networks has been…
Many materials, processes, and structures in science and engineering have important features at multiple scales of time and/or space; examples include biological tissues, active matter, oceans, networks, and images. Explicitly extracting,…
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on…
In today's data-driven digital era, the amount as well as complexity, such as multi-view, non-Euclidean, and multi-relational, of the collected data are growing exponentially or even faster. Clustering, which unsupervisely extracts valid…
Higher-order networks are widely used to describe complex systems in which interactions can involve more than two entities at once. In this paper, we focus on inclusion within higher-order networks, referring to situations where specific…
We propose a novel method of introducing structure into existing machine learning techniques by developing structure-based similarity and distance measures. To learn structural information, low-dimensional structure of the data is captured…
We introduce the notion of a Tits arrangement on a convex open cone as a special case of (infinite) simplicial arrangements. Such an object carries a simplicial structure similar to the geometric representation of Coxeter groups. The…
We outline a novel clustering scheme for simplicial complexes that produces clusters of simplices in a way that is sensitive to the homology of the complex. The method is inspired by, and can be seen as a higher-dimensional version of,…
Simplicial-simplicial regression refers to the regression setting where both the responses and predictor variables lie within the simplex space, i.e. they are compositional. For this setting, constrained least squares, where the regression…
3D printing of surfaces has become an established method for prototyping and visualisation. However, surfaces often contain certain degenerations, such as self-intersecting faces or non-manifold parts, which pose problems in obtaining a 3D…
We propose the Medial Skeletal Diagram, a novel skeletal representation that tackles the prevailing issues around skeleton sparsity and reconstruction accuracy in existing skeletal representations. Our approach augments the continuous…
The self-expressive property of data points, i.e., each data point can be linearly represented by the other data points in the same subspace, has proven effective in leading subspace clustering methods. Most self-expressive methods usually…
Data augmentation is a key element for training accurate models by reducing overfitting and improving generalization. For image classification, the most popular data augmentation techniques range from simple photometric and geometrical…
We study approximations of polytopes in the standard model for computing polytopes using Minkowski sums and (convex hulls of) unions. Specifically, we study the ability to approximate a target polytope by polytopes of a given depth. Our…