Related papers: Stitch Fix for Mapper and Topological Gains
Real-world graphs have inherently complex and diverse topological patterns, known as topological heterogeneity. Most existing works learn graph representation in a single constant curvature space that is insufficient to match the complex…
Graphs provide an efficient tool for object representation in various computer vision applications. Once graph-based representations are constructed, an important question is how to compare graphs. This problem is often formulated as a…
We start with a simple introduction to topological data analysis where the most popular tool is called a persistent diagram. Briefly, a persistent diagram is a multiset of points in the plane describing the persistence of topological…
Multi-attributed graph matching is a problem of finding correspondences between two sets of data while considering their complex properties described in multiple attributes. However, the information of multiple attributes is likely to be…
Topological metrics of graphs provide a natural way to describe the prominent features of various types of networks. Graph metrics describe the structure and interplay of graph edges and have found applications in many scientific fields. In…
This paper designs and implements an explainable recommendation model that integrates knowledge graphs with structure-aware attention mechanisms. The model is built on graph neural networks and incorporates a multi-hop neighbor aggregation…
A new graphical calculus for operating with isometries of low dimensional spaces of classical geometries is proposed. It is similar to a well-known graphical representation for vectors and translations in an affine space. Instead of arrows,…
We describe a duality mapping between STRIPS planning tasks. By exchanging the initial and goal conditions, taking their respective complements, and swapping for every action its precondition and delete list, one obtains for every STRIPS…
Modern autonomous vehicles and robots utilize versatile sensors for localization and mapping. The fidelity of these maps is paramount, as an accurate environmental representation is a prerequisite for stable and precise localization. Factor…
Bigraphs are a versatile modelling formalism that allows easy expression of placement and connectivity relations in a graphical format. System evolution is user defined as a set of rewrite rules. This paper presents a practical, yet…
Many data-rich industries are interested in the efficient discovery and modelling of structures underlying large data sets, as it allows for the fast triage and dimension reduction of large volumes of data embedded in high dimensional…
A significant number of current industrial applications rely on web services. A cornerstone task in these applications is discovering a suitable service that meets the threshold of some user needs. Then, those services can be composed to…
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produced by the neurons at an instant of time is a binary state on…
This paper presents a novel method for structural data recognition using a large number of graph models. In general, prevalent methods for structural data recognition have two shortcomings: 1) Only a single model is used to capture…
Graph Signal Processing deals with the problem of analyzing and processing signals defined on graphs. In this paper, we introduce a novel filtering method for graph-based signals by employing ideas from topological data analysis. We begin…
Persistent homology is a tool that can be employed to summarize the shape of data by quantifying homological features. When the data is an object in $\mathbb{R}^d$, the (augmented) persistent homology transform ((A)PHT) is a family of…
Performing signal processing over graphs requires knowledge of the underlying fixed topology. However, graphs often grow in size with new nodes appearing over time, whose connectivity is typically unknown; hence, making more challenging the…
Autonomous high-speed navigation through large, complex environments requires real-time generation of agile trajectories that are dynamically feasible, collision-free, and satisfy state or actuator constraints. Modern trajectory planning…
Via a compactification of the cleavage operad, we describe two actions on the mapping spaces from spheres into compact, oriented manifolds. The map from the compactified version of the cleavage operad provides a version of intersection…
Although neural networks are capable of reaching astonishing performances on a wide variety of contexts, properly training networks on complicated tasks requires expertise and can be expensive from a computational perspective. In industrial…