Oballe, Christopher; Cherne, Alan; Boothe, Dave; Kerick, Scott; Franaszczuk, Piotr J.; Maroulas, Vasileios Bayesian topological signal processing. (English) Zbl 1500.55005 Discrete Contin. Dyn. Syst., Ser. S 15, No. 4, 797-817 (2022). This paper works on giving an interpretable framework for signal processing via sublevel homology. The paper is trying to establish interpretable links between sublevel set persistence diagrams of signals and their frequency domain which are used to study time series analysis. The authors explore Bayesian framework for the time series classification, from which they find that the Bayesian topological features are pretty useful just as other well-known features, such as those from power spectral densities and continuous wavelets. Finally, they apply their results to electroencephalography which is a neuroimaging technique wherein electrodes are placed on a subject’s head to measure local changes in voltage over time, which are reported as a collection of time series. Reviewer: Qingyun Zeng (Philadelphia) Cited in 1 Document MSC: 55N31 Persistent homology and applications, topological data analysis 68T07 Artificial neural networks and deep learning Keywords:topological data analysis; Bayesian; signal processing; autoregressive; EEG; machine learning Software:PersistenceImages PDFBibTeX XMLCite \textit{C. Oballe} et al., Discrete Contin. Dyn. Syst., Ser. S 15, No. 4, 797--817 (2022; Zbl 1500.55005) Full Text: DOI References: [1] H. Adams; T. Emerson; M. Kirby; R. Neville; C. Peterson; P. Shipman; S. Chepushtanova; E. Hanson; F. Motta; L. Ziegelmeier, Persistence images: A stable vector representation of persistent homology, The Journal of Machine Learning Research, 18, 218-252 (2017) · Zbl 1431.68105 [2] M. 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