Topological signatures for fast mobility analysis

Ghosh, Abhirup; Rózemberczki, Benedek; Ramamoorthy, Subramanian; Sarkar, Rik

doi:10.1145/3274895.3274952

Cited by 10 publications

(11 citation statements)

References 29 publications

(27 reference statements)

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“…From a modeling perspective, simplices may not always capture the appropriate notion of a "cell" in a higher-order interaction network. For instance, in traffic and street networks it may be beneficial to consider cubical complexes or other types of models that can better represent the grid-like structure of many of these networks [57].…”

Section: Discussionmentioning

confidence: 99%

“…Such an approach may also be of interest for a number of applications: One can construct simplicial complexes and appropriate trajectory embedding from a variety of flow data, including physical flows such as buoys drifting in the ocean [50], or "virtual" flows such as click streams or flows of goods and money. Related ideas for analyzing trajectories have also been considered in the context of traffic prediction [57].…”

Section: Fourier Analysis: Edge-flow and Trajectory Embeddingsmentioning

confidence: 99%

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Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond

Schaub,

Zhu,

Seby

et al. 2021

Preprint

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This tutorial paper presents a didactic treatment of the emerging topic of signal processing on higher-order networks. Drawing analogies from discrete and graph signal processing, we introduce the building blocks for processing data on simplicial complexes and hypergraphs, two common abstractions of higher-order networks that can incorporate polyadic relationships. We provide basic introductions to simplicial complexes and hypergraphs, making special emphasis on the concepts needed for processing signals on them. Leveraging these concepts, we discuss Fourier analysis, signal denoising, signal interpolation, node embeddings, and non-linear processing through neural networks in these two representations of polyadic relational structures. In the context of simplicial complexes, we specifically focus on signal processing using the Hodge Laplacian matrix, a multi-relational operator that leverages the special structure of simplicial complexes and generalizes desirable properties of the Laplacian matrix in graph signal processing. For hypergraphs, we present both matrix and tensor representations, and discuss the trade-offs in adopting one or the other. We also highlight limitations and potential research avenues, both to inform practitioners and to motivate the contribution of new researchers to the area.

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Section: Discussionmentioning

confidence: 99%

Section: Fourier Analysis: Edge-flow and Trajectory Embeddingsmentioning

confidence: 99%

Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond

Schaub,

Zhu,

Seby

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Each triangle also induces a hyper-edge among all three pairs of its constituent nodes. This type of edge inducement allows us to formally model the data with a simplicial complex, which is the basis for the mathematics of Edge PageRank and many other network analyses using ideas from algebraic topology [7,12,20,23,55,28].…”

Section: Characterizing Weak Tiesmentioning

confidence: 99%

Which Bridges Are Weak Ties? Algebraic Topological Insights on Network Structure and Tie Strength

Sarker¹,

Seby²,

Benson³

et al. 2021

Preprint

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A key question in the analysis of sociological processes on networks is to identify pairs of individuals who have strong or weak social ties. Existing approaches mathematically model the social network as a graph, and tie strength is often inferred by examining the number of shared neighbors between individuals, or equivalently, the number of triangles in the graph which contain a specific pair of individuals. However, this approach misses out on critical information because it does not distinguish the case where interactions occur among groups involving more than two individuals. In this work, we measure tie strength by explicitly accounting for these higher order interactions in the network, through the use of a new measure called Edge PageRank. We show how Edge PageRank can be interpreted as the steady-state outcome of a dynamic, message-passing social process that characterizes the strength of weak ties by appropriately discounting the effect of higher-order interactions involving three individuals. Empirically, we find that Edge PageRank outperforms standard measures in identifying tie strength in several large-scale social networks. These results provide a new perspective on tie strength and demonstrate the importance of incorporating higher-order interactions in social network analysis.

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“…In [25], θ is computed by constructing a spanning tree on the dual graph of G, and for each face, adding its count to the edges on the path to the exterior face. Other ideas of differential form constructions for geospatial data analysis are discussed in [13].…”

Section: Range Query Algorithms Using P-summentioning

confidence: 99%

Differentially Private Range Counting in Planar Graphs for Spatial Sensing

Ghosh

Ding

Sarkar

et al. 2020

IEEE INFOCOM 2020 - IEEE Conference on Computer Communications

Self Cite

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This paper considers the problem of privately reporting counts of events recorded by devices in different regions of the plane. Unlike previous range query methods, our approach is not limited to rectangular ranges. We devise novel hierarchical data structures to answer queries over arbitrary planar graphs. This construction relies on balanced planar separators to represent shortest paths using O(log n) number of canonical paths, where n is the number of nodes in the graph. Pre-computed sums along these canonical paths allow efficient computations of 1D counting range queries along any shortest path. We make use of differential forms together with the 1D mechanism to answer 2D queries in which a range is a union of faces in the planar graph. The methods are designed such that the range queries could be answered with differential privacy guarantee on any single event, with only a poly-logarithmic error. They also allow private range queries to be performed in a distributed setup. Theoretical and experimental results confirm that the methods are efficient and accurate on real data and incur less error than competing existing methods.

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Topological signatures for fast mobility analysis

Cited by 10 publications

References 29 publications

Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond

Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond

Which Bridges Are Weak Ties? Algebraic Topological Insights on Network Structure and Tie Strength

Differentially Private Range Counting in Planar Graphs for Spatial Sensing

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