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Why topological data analysis detects financial bubbles? [PDF]
Communications in nonlinear science & numerical simulation, 2023 We present a heuristic argument for the propensity of Topological Data Analysis (TDA) to detect early warning signals of critical transitions in financial time series.
S. W. Akingbade +3 more
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Analyzing Prospects for Quantum Advantage in Topological Data Analysis [PDF]
PRX Quantum, 2022 Lloyd et al. were first to demonstrate the promise of quantum algorithms for computing Betti numbers, a way to characterize topological features of data sets.
D. Berry +9 more
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Towards quantum advantage via topological data analysis [PDF]
Quantum, 2022 Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce.
Casper Gyurik, Chris Cade, Vedran Dunjko
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A Survey of Vectorization Methods in Topological Data Analysis [PDF]
IEEE Transactions on Pattern Analysis and Machine Intelligence, 2022 Attempts to incorporate topological information in supervised learning tasks have resulted in the creation of several techniques for vectorizing persistent homology barcodes. In this paper, we study thirteen such methods.
Dashti Ali +5 more
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Simplicial complex entropy for time series analysis
Scientific Reports, 2023 The complex behavior of many systems in nature requires the application of robust methodologies capable of identifying changes in their dynamics. In the case of time series (which are sensed values of a system during a time interval), several methods ...
Lev Guzmán-Vargas +2 more
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Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis [PDF]
PRX Quantum, 2022 Quantum algorithms for topological data analysis (TDA) seem to provide an exponential advantage over the best classical approach while remaining immune to dequantization procedures and the data-loading problem. In this paper, we give complexity-theoretic
Alexander Schmidhuber, S. Lloyd
semanticscholar +1 more source
Scientific Reports, 2022 The roughness of material surfaces is of greatest relevance for applications. These include wear, friction, fatigue, cytocompatibility, or corrosion resistance.
Jan F. Senge +4 more
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, 2022 It has been observed since a long time that data are often carrying interesting topological and geometric structures. Characterizing such structures and providing efficient tools to infer and exploit them is a challenging problem that asks for new mathematics and that is motivated by a real need from applications.
Boissonnat, Jean-Daniel +2 more
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Topological data analysis [PDF]
Nature Photonics, 2018 Topological data analysis (TDA) can broadly be described as a collection of data analysis methods that find structure in data. These methods include clustering, manifold estimation, nonlinear dimension reduction, mode estimation, ridge estimation and persistent homology. This paper reviews some of these methods.
openaire +3 more sources
A Primer on Topological Data Analysis to Support Image Analysis Tasks in Environmental Science [PDF]
arXiv.org, 2022 Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is particularly ...
Lander Ver Hoef +3 more
semanticscholar +1 more source