| [1] |
Adams, H., & Carlsson, G. (2015). Evasion paths in mobile sensor networks. The International Journal of Robotics Research, 34(1), 90-104. |
| [2] |
Adams, H., Tausz, A., & Vejdemo‐Johansson, M. (2014). JavaPlex: A research software package for persistent (co) homology. In International congress on mathematical software (pp. 129-136). Springer. · Zbl 1402.65186 |
| [3] |
Alaa, H., & Mohamed, S. (2017). On the topological data analysis extensions and comparisons. Journal of the Egyptian Mathematical Society, 25(4), 406-413. · Zbl 1385.55005 |
| [4] |
Bendich, P., Marron, J. S., Miller, E., Pieloch, A., & Skwerer, S. (2016). Persistent homology analysis of brain artery trees. The Annals of Applied Statistics, 10(1), 198-218. |
| [5] |
Berwald, J., Gidea, M., & Vejdemo‐Johansson, M. (2013). Automatic recognition and tagging of topologically different regimes in dynamical systems. arXiv preprint arXiv:1312.2482. |
| [6] |
Berwald, J., Gottlieb, J. M., & Munch, E. (2018). Computing Wasserstein distance for persistence diagrams on a quantum computer. arXiv preprint arXiv:1809.06433. |
| [7] |
Bonis, T., Ovsjanikov, M., Oudot, S., & Chazal, F. (2016). Persistence‐based pooling for shape pose recognition. Proceedings of the 6th international workshop on computational topology in image context (Vol. 9667, pp. 19-29). Springer. |
| [8] |
Brécheteau, C. (2019). A statistical test of isomorphism between metric‐measure spaces using the distance‐to‐a‐measure signature. Electronic Journal of Statistics, 13(1), 795-849. · Zbl 1417.62112 |
| [9] |
Bubenik, P. (2015). Statistical topological data analysis using persistence landscapes. The Journal of Machine Learning Research, 16(1), 77-102. · Zbl 1337.68221 |
| [10] |
Carlsson, G. (2009). Topology and data. Bulletin of the American Mathematical Society, 46(2), 255-308. · Zbl 1172.62002 |
| [11] |
Carlsson, G., Zomorodian, A., Collins, A., & Guibas, L. (2004). Persistence barcodes for shapes. Proceedings of the 2004 Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, 124-135. https://doi.org/10.1145/1057432.1057449. · doi:10.1145/1057432.1057449 |
| [12] |
Carrière, M., Oudot, S., & Ovsjanikov, M. (2015). Stable topological signatures for points on 3D shapes. Computer Graphics Forum, 34(5), 1-12. |
| [13] |
Chazal, F., Cohen‐Steiner, D., Guibas, L. J., Mémoli, F., & Oudot, S. (2009). Gromov‐Hausdorff stable signatures for shapes using persistence. Computer Graphics Forum, 1393-1403. |
| [14] |
Chazal, F., Fasy, B., Lecci, F., Michel, B., Rinaldo, A., & Wasserman, L. (2018). Robust topological inference: Distance to a measure and kernel distance. Journal of Machine Learning Research, 18(159), 1-40. · Zbl 1435.62452 |
| [15] |
Chazal, F., & Michel, B. (2017). An introduction to topological data analysis: Fundamental and practical aspects for data scientists. arXiv preprint arXiv:1710.04019. |
| [16] |
Chen, R., Zhang, J., Ravishanker, N., & Konduri, K. (2019). Clustering activity-travel behavior time series using topological data analysis. Journal of Big Data Analytics in Transportation, 1(2-3), 109-121. |
| [17] |
Costantino, R. F., Cushing, J. M., Dennis, B., & Desharnais, R. A. (1995). Experimentally induced transitions in the dynamic behaviour of insect populations. Nature, 375(6528), 227-230. |
| [18] |
De Silva, V., & Carlsson, G. E. (2004). Topological estimation using witness complexes. Eurographics Symposium on Point‐Based Graphics, 4, 157-166. |
| [19] |
De Silva, V., & Ghrist, R. (2007a). Coverage in sensor networks via persistent homology. Algebraic & Geometric Topology, 7(1), 339-358. · Zbl 1134.55003 |
| [20] |
De Silva, V., & Ghrist, R. (2007b). Homological sensor networks. Notices of the American Mathematical Society, 7(1), 10-17. · Zbl 1142.94006 |
| [21] |
DeWoskin, D., Climent, J., Cruz‐White, I., Vazquez, M., Park, C., & Arsuaga, J. (2010). Applications of computational homology to the analysis of treatment response in breast cancer patients. Topology and its Applications, 157(1), 157-164. · Zbl 1176.92026 |
| [22] |
Di Fabio, B., & Landi, C. (2011). A Mayer-Vietoris formula for persistent homology with an application to shape recognition in the presence of occlusions. Foundations of Computational Mathematics, 11(5), 499-527. · Zbl 1231.55004 |
| [23] |
Di Fabio, B., & Landi, C. (2012). Persistent homology and partial similarity of shapes. Pattern Recognition Letters, 33(11), 1445-1450. |
| [24] |
Edelsbrunner, H., & Harer, J. (2010). Computational topology. An introduction. American Mathematical Society. · Zbl 1193.55001 |
| [25] |
Emrani, S., Gentimis, T., & Krim, H. (2014). Persistent homology of delay embeddings and its application to wheeze detection. IEEE Signal Processing Letters, 21(4), 459-463. |
| [26] |
Fasy, B. T., Kim, J., Lecci, F., & Maria, C. (2014). “Introduction to the R package TDA.” arXiv preprint arXiv:1411.1830. |
| [27] |
Fasy, B. T., Lecci, F., Rinaldo, A., Wasserman, L., Balakrishnan, S., & Singh, A. (2014). Confidence sets for persistence diagrams. The Annals of Statistics, 42(6), 2301-2339. · Zbl 1310.62059 |
| [28] |
Gholizadeh, S., & Zadrozny, W. (2018). “A short survey of topological data analysis in time series and systems analysis.” arXiv preprint arXiv:1809.10745. |
| [29] |
Gidea, M. (2017). Topological data analysis of critical transitions in financial networks. Paper presented at the International conference and school on network science (pp. 47-59). Springer. |
| [30] |
Gidea, M., Goldsmith, D., Katz, Y., Roldan, P., & Shmalo, Y. (2020). Topological recognition of critical transitions in time series of cryptocurrencies. Physica A: Statistical Mechanics and its Applications, 548, 123843 · Zbl 07530523 |
| [31] |
Gidea, M., & Katz, Y. (2018). Topological data analysis of financial time series: Landscapes of crashes. Physica A: Statistical Mechanics and its Applications, 491, 820-834. · Zbl 1514.62206 |
| [32] |
Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning (Vol. 1, 2nd Ed.,). New York, NY: Springer Series in Statistics. · Zbl 1273.62005 |
| [33] |
Hegger, R., Kantz, H., & Schreiber, T. (1999). Practical implementation of nonlinear time series methods: The TISEAN package. Chaos: An Interdisciplinary Journal of Nonlinear Science, 9(2), 413-435. · Zbl 0990.37522 |
| [34] |
Heo, G., Gamble, J., & Kim, P. T. (2012). Topological analysis of variance and the maxillary complex. Journal of the American Statistical Association, 107(498), 477-492. · Zbl 1261.62096 |
| [35] |
Huang, N. E., Shen, Z., Long, S. R., Wu, M. C., Shih, H. H., Zheng, Q., Yen, N.‐C., Tung, C. C., & Liu, H. H. (1998). The empirical mode decomposition and the Hilbert spectrum for nonlinear and non‐stationary time series analysis. Proceedings of the Royal Society of London, Series A: Mathematical, Physical and Engineering Sciences, 454, 903-995. · Zbl 0945.62093 |
| [36] |
Kantz, H., & Schreiber, T. (2003). Nonlinear time series analysis. Cambridge University Press. |
| [37] |
Kennel, M. B., Brown, R., & Abarbanel, H. D. (1992). Determining embedding dimension for phase‐space reconstruction using a geometrical construction. Physical Review A, 45(6), 3403-3411. |
| [38] |
Khasawneh, F. A., & Munch, E. (2016). Chatter detection in turning using persistent homology. Mechanical Systems and Signal Processing, 70, 527-541. |
| [39] |
Khasawneh, F. A., Munch, E., & Perea, J. A. (2018). Chatter classification in turning using machine learning and topological data analysis. IFAC‐PapersOnLine, 51(14), 195-200. |
| [40] |
Kim, K., Kim, J., & Rinaldo, A. (2018). “Time series featurization via topological data analysis.” arXiv preprint arXiv:1812.02987. |
| [41] |
Kovacev‐Nikolic, V., Bubenik, P., Nikolić, D., & Heo, G. (2016). Using persistent homology and dynamical distances to analyze protein binding. Statistical Applications in Genetics and Molecular Biology, 15(1), 19-38. · Zbl 1343.92380 |
| [42] |
Krizhevsky, A., Sutskever, I., & Hinton, G. E. (2017). Imagenet classification with deep convolutional neural networks. Communications of the ACM, 60(6), 84-90. |
| [43] |
Li, C., Ovsjanikov, M., & Chazal, F. (2014). Persistence‐based structural recognition. IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2014, 1995-2002. |
| [44] |
Mileyko, Y., Mukherjee, S., & Harer, J. (2011). Probability measures on the space of persistence diagrams. Inverse Problems, 27(12), 124007. · Zbl 1247.68310 |
| [45] |
Munkres, J. R. (2018). Elements of algebraic topology. CRC Press. |
| [46] |
Myers, A., Munch, E., & Khasawneh, F. A. (2019). Persistent homology of complex networks for dynamic state detection. Physical Review E, 100(2), 022314. |
| [47] |
Nicolau, M., Levine, A. J., & Carlsson, G. E. (2011). Topology based data analysis identifies a subgroup of breast cancers with a unique mutational profile and excellent survival. Proceedings of the National Academy of Sciences of the United States of America, 108(17), 7265-7270. |
| [48] |
Palais, R. S. (1963). Morse theory on Hilbert manifolds. Topology, 2(4), 299-340. · Zbl 0122.10702 |
| [49] |
Perea, J. A. (2018). A brief history of persistence. arXiv preprint arXiv:1809.03624. |
| [50] |
Perea, J. A., Deckard, A., Haase, S. B., & Harer, J. (2015). SW1PerS: Sliding windows and 1‐persistence scoring; discovering periodicity in gene expression time series data. BMC Bioinformatics, 16(1), 257. |
| [51] |
Perea, J. A., & Harer, J. (2015). Sliding windows and persistence: An application of topological methods to signal analysis. Foundations of Computational Mathematics, 15(3), 799-838. · Zbl 1325.37054 |
| [52] |
Pereira, C. M., & deMello, R. F. (2015). Persistent homology for time series and spatial data clustering. Expert Systems with Applications, 42(15), 6026-6038. |
| [53] |
Phillips, J. M., Wang, B., & Zheng, Y. (2015). Geometric inference on kernel density estimates. 31st International symposium on computational geometry (SoCG 2015) Leibniz International Proceedings in Informatics Schloss Dagstuhl - Leibniz‐Zentrum für Informatik. Germany: Dagstuhl Publishing. (Vol. 34, pp. 857-871). · Zbl 1422.68257 |
| [54] |
Robinson, A., & Turner, K. (2017). Hypothesis testing for topological data analysis. Journal of Applied and Computational Topology, 1(2), 241-261. · Zbl 1396.62085 |
| [55] |
Robinson, M. (2014). Topological signal processing. Springer. · Zbl 1294.94001 |
| [56] |
Sanderson, N., Shugerman, E., Molnar, S., Meiss, J. D., & Bradley, E. (2017). Computational topology techniques for characterizing time‐series data. In International symposium on intelligent data analysis (pp. 284-296). Springer. |
| [57] |
Seversky, L. M., Davis, S., & Berger, M. (2016). On time‐series topological data analysis: New data and opportunities. Paper presented at the 2016 IEEE conference on computer vision and pattern recognition workshops (CVPRW) (pp. 1014-1022). Las Vegas, NV. https://doi.org/10.1109/CVPRW.2016.131. · doi:10.1109/CVPRW.2016.131 |
| [58] |
Shanks, J. L. (1969). Computation of the fast Walsh‐Fourier transform. IEEE Transactions on Computers, 18(5), 457-459. · Zbl 0174.20703 |
| [59] |
Shumway, R. H., & Stoffer, D. S. (2017). Time series analysis and its applications: With R examples. Springer. · Zbl 1367.62004 |
| [60] |
Stoffer, D. S. (1991). Walsh‐Fourier analysis and its statistical applications. Journal of the American Statistical Association, 86(414), 461-479. |
| [61] |
Stolz, B. J., Harrington, H. A., & Porter, M. A. (2017). Persistent homology of time‐dependent functional networks constructed from coupled time series. Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(4), 047410. |
| [62] |
Takens, F. (1981). Detecting strange attractors in turbulence. Lecture Notes in Mathematics, 898(1), 366-381. · Zbl 0513.58032 |
| [63] |
Tralie, C. J. (2018). Graphditty: A software suite for geometric music structure visualization. In 19th international society for music information retrieval (IS‐MIR). Late Breaking Session. |
| [64] |
Tralie, C. J., & Berger, M. (2018). Topological Eulerian synthesis of slow motion periodic videos. In 2018 25th IEEE international conference on image processing (ICIP) (pp. 3573-3577). IEEE. |
| [65] |
Tralie, C. J., & Harer, J. (2017). Mobius beats: The twisted spaces of sliding window audio novelty functions with rhythmic subdivisions. Paper presented at the 18th International society for music information retrieval (ISMIR), late breaking session. Suzhou, China. |
| [66] |
Tralie, C. J., & Perea, J. A. (2018). (Quasi) Periodicity quantification in video data, using topology. SIAM Journal on Imaging Sciences, 11(2), 1049-1077. · Zbl 1401.65025 |
| [67] |
Truong, P. (2017). An exploration of topological properties of high‐frequency one‐dimensional financial time series data using TDA (Ph.D. thesis). KTH Royal Institute of Technology. |
| [68] |
Umeda, Y. (2017). Time series classification via topological data analysis. Transactions of the Japanese Society for Artificial Intelligence, 32, 3. |
| [69] |
Van de Weygaert, R., Vegter, G., Edelsbrunner, H., Jones, B. J. T., Pranav, P., Park, C., Hellwing, W. A., Eldering, B., Kruithof, N., Bos, E. G. P. P., Hidding, J., Feldbrugge, J., tenHave, E., vanEngelen, M., Caroli, M., & Teillaud, M. (2011). Alpha, Betti and the Megaparsec universe: On the topology of the cosmic web. In M. L.Gavrilova (ed.), C. K.Tan (ed.), & M. A.Mostafavi (ed.) (Eds.), Transactions on computational science XIV (pp. 60-101). Berlin and Heidelberg: Springer‐Verlag. · Zbl 1250.85007 |
| [70] |
Wang, Y., Ombao, H., & Chung, M. K. (2018). Topological data analysis of single‐trial electroencephalographic signals. The Annals of Applied Statistics, 12(3), 1506-1534. · Zbl 1405.62212 |
| [71] |
Yesilli, M. C., Tymochko, S., Khasawneh, F. A., & Munch, E. (2019). Chatter diagnosis in milling using supervised learning and topological features vector. In 2019 18th IEEE international conference on machine learning and applications (ICMLA) (pp. 1211-1218). IEEE. |
| [72] |
Zomorodian, A., & Carlsson, G. (2005). Computing persistent homology. Discrete and Computational Geometry, 33(2), 249-274. · Zbl 1069.55003 |
