Related papers: Stitch Fix for Mapper and Topological Gains
Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…
Many real-world complex networks are best modeled as bipartite (or 2-mode) graphs, where nodes are divided into two sets with links connecting one side to the other. However, there is currently a lack of methods to analyze properly such…
The univariate piecing-together approach (PT) fits a univariate generalized Pareto distribution (GPD) to the upper tail of a given distribution function in a continuous manner. We propose a multivariate extension. First it is shown that an…
We consider the task of drawing a graph on multiple horizontal layers, where each node is assigned a layer, and each edge connects nodes of different layers. Known algorithms determine the orders of nodes on each layer to minimize crossings…
Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…
Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of…
Over the past two decades, topological data analysis has emerged as a field of applied mathematics with new applications and algorithmic developments appearing rapidly. Two fundamental computations in this field are persistent homology and…
Given a set of snapshots from a temporal network we develop, analyze, and experimentally validate a so-called network interpolation scheme. Our method allows us to build a plausible, albeit random, sequence of graphs that transition between…
When modeling microstructures, the computational resource requirements increase rapidly as the simulation domain becomes larger. As a result, simulating a small representative fraction under periodic boundary conditions is often a necessary…
This work develops \emph{mixup for graph data}. Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. Traditionally, Mixup can work on…
We present \textit{RopStitch}, an unsupervised deep image stitching framework with both robustness and naturalness. To ensure the robustness of \textit{RopStitch}, we propose to incorporate the universal prior of content perception into the…
This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph…
We present methods for approximating the mapping that defines the invariant manifold for two systems exhibiting generalized synchronization. If the equations of motion are known then an analytic approximation to the mapping can be found. If…
Motivated by applications to a wide range of assemble-to-order systems, operations scheduling, healthcare systems and collaborative economy applications, we introduce a stochastic matching model on hypergraphs, extending the model in [15]…
Multiplex networks are collections of networks with identical nodes but distinct layers of edges. They are genuine representations for a large variety of real systems whose elements interact in multiple fashions or flavors. However,…
For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
We give a generalized definition of stretch that simplifies the efficient construction of low-stretch embeddings suitable for graph algorithms. The generalization, based on discounting highly stretched edges by taking their $p$-th power for…
The topological classification of the inner mappings on the fully invariant regular components of the wandering set with a special attracting boundary up to the topological conjugacy is defined in terms of distinguishing graph. Two inner…
We propose an algorithm to estimate the topology of an embedded metric graph from a well-sampled finite subset of the underlying graph.