Related papers: Sheaves: A Topological Approach to Big Data
In recent years, the size of big linked data has grown rapidly and this number is still rising. Big linked data and knowledge bases come from different domains such as life sciences, publications, media, social web, and so on. However, with…
Existing deep hierarchical topic models are able to extract semantically meaningful topics from a text corpus in an unsupervised manner and automatically organize them into a topic hierarchy. However, it is unclear how to incorporate prior…
This article develops a new theoretical basis for decomposing signals that are formed by the linear superposition of a finite number of modes. Each mode depends nonlinearly upon several parameters; we seek both these parameters and the…
Knowledge graphs are graphical representations of large databases of facts, which typically suffer from incompleteness. Inferring missing relations (links) between entities (nodes) is the task of link prediction. A recent state-of-the-art…
A network is a typical expressive form of representing complex systems in terms of vertices and links, in which the pattern of interactions amongst components of the network is intricate. The network can be static that does not change over…
Sheaves are objects of a local nature: a global section is determined by how it looks locally. Hence, a sheaf cannot describe mathematical structures which contain global or nonlocal geometric information. To fill this gap, we introduce the…
Cellular sheaves equip graphs with a "geometrical" structure by assigning vector spaces and linear maps to nodes and edges. Graph Neural Networks (GNNs) implicitly assume a graph with a trivial underlying sheaf. This choice is reflected in…
Human knowledge provides a formal understanding of the world. Knowledge graphs that represent structural relations between entities have become an increasingly popular research direction towards cognition and human-level intelligence. In…
We generalise sheaf models of intuitionistic logic to univalent type theory over a small category with a Grothendieck topology. We use in a crucial way that we have constructive models of univalence, that can then be relativized to any…
We introduce a technique that is capable to filter out information from complex systems, by mapping them to networks, and extracting a subgraph with the strongest links. This idea is based on the Minimum Spanning Tree, and it can be applied…
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 the field of machine learning, data understanding is the practice of getting initial insights in unknown datasets. Such knowledge-intensive tasks require a lot of documentation, which is necessary for data scientists to grasp the meaning…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
We demonstrate that graph-based models are fully capable of representing higher-order interactions, and have a long history of being used for precisely this purpose. This stands in contrast to a common claim in the recent literature on…
While network science has become an indispensable tool for studying complex systems, the conventional use of pairwise links often shows limitations in describing high-order interactions properly. Hypergraphs, where each edge can connect…
Graphs are a representation of structured data that captures the relationships between sets of objects. With the ubiquity of available network data, there is increasing industrial and academic need to quickly analyze graphs with billions of…
Graph is an important data representation which appears in a wide diversity of real-world scenarios. Effective graph analytics provides users a deeper understanding of what is behind the data, and thus can benefit a lot of useful…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
Sheaf Neural Networks (SNNs) naturally extend Graph Neural Networks (GNNs) by endowing a cellular sheaf over the graph, equipping nodes and edges with vector spaces and defining linear mappings between them. While the attached geometric…
Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…