Homological persistence in time series: an application to music classification

References

• Bakshi, B., and G. Stephanopoulos. 1994. “Representation of Process Trends-IV. Induction of Real-time Patterns From Operating Data for Diagnosis and Supervisory Control.” Computers & Chemical Engineering 18 (4): 303–332. doi: 10.1016/0098-1354(94)85029-1
   Web of Science ®Google Scholar
• Bergomi, M. G. 2015. Dynamical and Topological Tools for (Modern) Music Analysis. Paris: Université Pierre et Marie Curie.
   Google Scholar
• Bergomi, M. G., A. Baratè, and B. Di Fabio. 2016. “Towards a Topological Fingerprint of Music.” In International Workshop on Computational Topology in Image Context, Marseille, France, 88–100.
   Google Scholar
• Berndt, D. J., and J. Clifford. 1994. “Using Dynamic Time Warping to Find Patterns in Time Series.” In KDD workshop, 359–370. Vol. 16.
   Google Scholar
• Bigo, L., M. Andreatta, J. L. Giavitto, O. Michel, and A. Spicher. 2013. “Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes.” In Mathematics and Computation in Music, 38–51. Berlin: Springer.
   Google Scholar
• Burns, E. M., and W. D. Ward. 1999. “Intervals, Scales, and Tuning.” The Psychology of Music 2: 215–264. doi: 10.1016/B978-012213564-4/50008-1
   Google Scholar
• Casey, M., R. Veltkamp, M. Goto, M. Leman, C. Rhodes, and M. Slaney. 2008. “Content-based Music Information Retrieval: Current Directions and Future Challenges.” Proceedings of the IEEE 96 (4): 668–696. doi: 10.1109/JPROC.2008.916370
   Web of Science ®Google Scholar
• Cheveigné, de, A. 2005. “Pitch Perception Models.” In Pitch: Neural Coding and Perception, edited by C. J. Plack, A. J. Oxenham, A. N. Popper, and R. Fay. Springer, New York, NY.
   Google Scholar
• Cohen-Steiner, D., H. Edelsbrunner, and J. Harer. 2007. “Stability of Persistence Diagrams.” Discrete & Computational Geometry 37: 103–120. doi: 10.1007/s00454-006-1276-5
   Web of Science ®Google Scholar
• Cohen-Steiner, D., H. Edelsbrunner, and D. Morozov. 2006. “Vines and Vineyards by Updating Persistence in Linear Time.” In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, 119–126. Sedona Arizona, USA. https://dl.acm.org/doi/proceedings/10.1145/1137856
   Google Scholar
• Cohn, R. 1997. “Neo-Riemannian Operations, Parsimonious Trichords, and Their Tonnetz Representations.” Journal of Music Theory 41 (1): 1–66. doi: 10.2307/843761
   Web of Science ®Google Scholar
• d'Amico, M., P. Frosini, and C. Landi. 2006. “Using Matching Distance in Size Theory: A Survey.” International Journal of Imaging Systems and Technology 16: 154–161. doi: 10.1002/ima.20076
   Web of Science ®Google Scholar
• d'Amico, M., P. Frosini, and C. Landi. 2010. “Natural Pseudo-distance and Optimal Matching Between Reduced Size Functions.” Acta Applicandae Mathematicae 109 (2): 527–554. doi: 10.1007/s10440-008-9332-1
   Web of Science ®Google Scholar
• Douthett, J., and P. Steinbach. 1998. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42 (2): 241–263. doi: 10.2307/843877
   Web of Science ®Google Scholar
• Edelsbrunner, H., and J. Harer. 2009. Computational Topology: An Introduction. American Mathematical Society.
   Google Scholar
• Esling, P., and C. Agon. 2012. “Time-series Data Mining.” ACM Computing Surveys (CSUR) 45 (1): 12. doi: 10.1145/2379776.2379788
   Web of Science ®Google Scholar
• Euler, L. 1774. “De Harmoniae Veris Principiis Per Speculum Musicum Repraesentatis.” Novi commentarii Acad. Scient. Petropolitanae 18, 330–353, repr. in Leonhardi Euleri, Opera Omnia, Series III, T.1, Teubner, Liepzig, Berlin 1926.
   Google Scholar
• Ferri, M. 2017. “Persistent Topology for Natural Data Analysis – A Survey.” In Towards Integrative Machine Learning and Knowledge Extraction, 117–133. Cham, Switzerland: Springer.
   Google Scholar
• Govc, D. 2013. “On the Definition of Homological Critical Value.” arXiv:1301.6817.
   Google Scholar
• Harte, C., and M. Sandler. 2005. “Automatic Chord Identifcation Using a Quantised Chromagram.” In Audio Engineering Society Convention. Audio Engineering Society, New York, Vol. 118.
   Google Scholar
• Hatcher, A. 2002. Algebraic Topology. Cambridge: Cambridge University Press.
   Google Scholar
• Keogh, E., S. Chu, D. Hart, and M. Pazzani. 2004. “Segmenting Time Series: A Survey and Novel Approach.” Data Mining in Time Series Databases 57: 1–22. doi: 10.1142/9789812565402_0001
   Google Scholar
• Keogh, E., and S. Kasetty. 2003. “On the Need for Time Series Data Mining Benchmarks: A Survey and Empirical Demonstration.” Data Mining and Knowledge Discovery 7 (4): 349–371. doi: 10.1023/A:1024988512476
   Web of Science ®Google Scholar
• Liao, T. W. 2005. “Clustering of Time Series Data – a Survey.” Pattern Recognition 38 (11): 1857–1874. doi: 10.1016/j.patcog.2005.01.025
   Web of Science ®Google Scholar
• Lines, J., and A. Bagnall. 2015. “Time Series Classification with Ensembles of Elastic Distance Measures.” Data Mining and Knowledge Discovery 29 (3): 565–592. doi: 10.1007/s10618-014-0361-2
   Web of Science ®Google Scholar
• Munch, E. 2013. Applications of Persistent Homology to Time Varying Systems. Durham, North Carolina: Duke University.
   Google Scholar
• Munch, E., M. Shapiro, and J. Harer. 2012. “Failure Filtrations for Fenced Sensor Networks.” The International Journal of Robotics Research 31 (9): 1044–1056. doi: 10.1177/0278364912451671
   Web of Science ®Google Scholar
• Munkres, J. R. 1984. Elements of Algebraic Topology. Vol. 2. Cambridge Massachusetts: Addison-Wesley Reading.
   Google Scholar
• Perricone, J. 2000. Melody in Songwriting: Tools and Techniques for Writing Hit Songs. Boston: Hal Leonard Corporation.
   Google Scholar
• Pérez-Escudero, A., J. Vicente-Page, R. C. Hinz, S. Arganda, and G. G. Polaviejade. 2014. “idTracker: Tracking Individuals in a Group by Automatic Identification of Unmarked Animals.” Nature Methods 11 (7): 743–748. doi: 10.1038/nmeth.2994
   PubMed Web of Science ®Google Scholar
• Poincaré, H. 1895. Analysis Situs. Paris, France: Gauthier-Villars.
   Google Scholar
• Romero-Ferrero, F., M. G. Bergomi, R. C. Hinz, F. J. Heras, and G. G. Polaviejade. 2019. “idtracker. ai: Tracking All Individuals in Small Or Large Collectives of Unmarked Animals.” Nature Methods 16 (2): 179. doi: 10.1038/s41592-018-0295-5
   PubMed Web of Science ®Google Scholar
• Senin, P. 2008. Dynamic Time Warping Algorithm Review, 40. Information and Computer Science Department University of Hawaii at Manoa Honolulu, USA 855.
   Google Scholar
• Topaz, C. M., L. Ziegelmeier, and T. Halverson. 2015. “Topological Data Analysis of Biological Aggregation Models.” PloS One 10 (5): e0126383. doi: 10.1371/journal.pone.0126383
   PubMed Web of Science ®Google Scholar
• Turner, K., Y. Mileyko, S. Mukherjee, and J. Harer. 2014. “Fréchet Means for Distributions of Persistence Diagrams.” Discrete & Computational Geometry 52 (1): 44–70. doi: 10.1007/s00454-014-9604-7
   Web of Science ®Google Scholar
• Žabka, M. 2009. “Generalized Tonnetz and Well-Formed GTS: A Scale Theory Inspired by the Neo-Riemannians”. In International Conference on Mathematics and Computation in Music, edited by C.A.C.C.H. Chew Elaine, 286–298. Berlin: Springer.
   Google Scholar