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The goal of this paper is to establish the fundamental tools to analyze signals defined over a topological space, i.e.
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Topology
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“Combinatorial Laplacians of simplicial complexes,”
T. E. Goldberg, · 2002
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Discrete Exterior Calculus
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Convex optimization
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Matrix Mathematics: Theory, Facts, and Formulas with Application to Linear Systems Theory
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“Higher order learning with graphs,”
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“Distributed coverage verification in sensor networks without location information,”
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“Link communities reveal multiscale complexity in networks,”
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Graph theoretic methods in multiagent networks
M. Mesbahi and M. Egerstedt, · 2010
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Discrete calculus: Applied analysis on graphs for computational science
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R. Ramanathan, A. Bar-Noy, P. Basu, M. Johnson, W. Ren, A. Swami, and Q. Zhao, · 2011
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X. Jiang, L. H. Lim, Y. Yao, and Y. Ye, · 2011
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“HodgeRank on random graphs for subjective video quality assessment,”
Q. Xu, Q. Huang, T. Jiang, B. Yan, W. Lin, and Y. Yao, · 2012
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Topological signal processing
M. Robinson, · 2016
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“Random walks on simplicial complexes and harmonics,”
S. Mukherjee and J. Steenbergen, · 2016
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“Isoperimetric inequalities in simplicial complexes,”
O. Parzanchevski, R. Rosenthal, and R. J. Tessler, · 2016
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“Signals on graphs: Uncertainty principle and sampling,”
M. Tsitsvero, S. Barbarossa, and P. Di Lorenzo, · 2016
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“An introduction to hypergraph signal processing,”
S. Barbarossa and M. Tsitsvero, · 2016
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“The shape of collaborations,”
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“The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains,”
D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, · 2013
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“Spectra of combinatorial Laplace operators on simplicial complexes,”
D. Horak and J. Jost, · 2013
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“Spectral processing of tangential vector fields,”
C. Brandt, L. Scandolo, E. Eisemann, and K. Hildebrandt, · 2017
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“Learning from signals defined over simplicial complexes,”
S. Barbarossa, S. Sardellitti, and E. Ceci, · 2018
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A. Ortega, P. Frossard, J. Kovačević, J. M. F. Moura, and P. Vandergheynst, · 2018
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“Simplicial closure and higher-order link prediction,”
A. R. Benson, R. Abebe, M. T. Schaub, A. Jadbabaie, and J. Kleinberg, · 2018
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“A topological representation of branching neuronal morphologies,”
L. Kanari, P. Dłotko, M. Scolamiero, R. Levi, J. Shillcock, K. Hess, and H. Markram, · 2018
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“Random walks on simplicial complexes and the normalized Hodge Laplacian,”
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“Graph-based semi-supervised & active learning for edge flows,”
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