Times Series Averaging and Denoising from a Probabilistic Perspective on Time–Elastic Kernels

Abdulla, W., Chow, D. and Sin, G. (2003). Cross-words reference template for DTW-based speech recognition systems, Conference on Convergent Technologies for the Asia-Pacific Region TENCON 2003, Bangalore, India, Vol. 4, pp. 1576–1579.Search in Google Scholar

Carrillo, H. and Lipman, D. (1988). The multiple sequence alignment problem in biology, SIAM Journal on Applied Mathematics48(5): 1073–1082.10.1137/0148063Search in Google Scholar

Chen, L. and Ng, R. (2004). On the marriage of Lp-norms and edit distance, Proceedings of the 30th International Conference on Very Large Data Bases, VLDB’04, Toronto, Canada, pp. 792–803.10.1016/B978-012088469-8.50070-XSearch in Google Scholar

Chudova, D., Gaffney, S. and Smyth, P. (2003). Probabilistic models for joint clustering and time-warping of multidimensional curves, Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, UAI’03, San Francisco, CA, USA, pp. 134–141.Search in Google Scholar

Cuturi, M., Vert, J.-P., Birkenes, O. and Matsui, T. (2007). A kernel for time series based on global alignments, IEEE ICASSP 2007, Honolulu, HI, USA, Vol. 2, pp. II-413–II-416.10.1109/ICASSP.2007.366260Search in Google Scholar

Fasman, K.H. and Salzberg, S.L. (1998). An introduction to biological sequence analysis, in S.L. Salzberg et al., Computational Methods in Molecular Biology, Elsevier, Amsterdam, pp. 21–42.10.1016/S0167-7306(08)60460-3Search in Google Scholar

Fréchet, M. (1906). Sur quelques points du calcul fonctionnel, Thèse, Faculté des sciences de Paris, Paris.10.1007/BF03018603Search in Google Scholar

Ghouaiel, N., Marteau, P.-F. and Dupont, M. (2017). Continuous pattern detection and recognition in stream—a benchmark for online gesture recognition, International Journal of Applied Pattern Recognition4(2): 146–160.10.1504/IJAPR.2017.085315Search in Google Scholar

Gupta, L., Molfese, D., Tammana, R. and Simos, P. (1996). Nonlinear alignment and averaging for estimating the evoked potential, IEEE Transactions on Biomedical Engineering43(4): 348–356.10.1109/10.486255Search in Google Scholar

Gupta, M., Gao, J., Aggarwal, C.C. and Han, J. (2014). Outlier detection for temporal data: A survey, IEEE Transactions on Knowledge and Data Engineering26(9): 2250–2267.10.1109/TKDE.2013.184Search in Google Scholar

Hassan, U. and Anwar, M.S. (2010). Reducing noise by repetition: Introduction to signal averaging, European Journal of Physics31(3): 453.10.1088/0143-0807/31/3/003Search in Google Scholar

Hautamaki, V., Nykanen, P. and Franti, P. (2008). Time-series clustering by approximate prototypes, 19th International Conference on Pattern Recognition, ICPR 2008, Tampa, FL, USA, pp. 1–4.10.1109/ICPR.2008.4761105Search in Google Scholar

Juang, B. (1985). On the hidden Markov model and dynamic time warping for speech recognition—A unified view, AT&T Bell Laboratories Technical Journal63(7): 1213–1242.10.1002/j.1538-7305.1984.tb00034.xSearch in Google Scholar

Just, W. and Just, W. (1999). Computational complexity of multiple sequence alignment with SP-score, Journal of Computational Biology8(6): 615–623.10.1089/106652701753307511Search in Google Scholar

Kaiser, R. and Knight, W. (1979). Digital signal averaging, Journal of Magnetic Resonance (1969)36(2): 215–220.10.1016/0022-2364(79)90096-9Search in Google Scholar

Keogh, E.J., Xi, X., Wei, L. and Ratanamahatana, C. (2006). The UCR time series classification-clustering datasets, Repository, http://www.cs.ucr.edu/êamonn/time_series_data/.Search in Google Scholar

Lichman, M. (2013). UCI Machine Learning Repository, http://archive.ics.uci.edu/ml.Search in Google Scholar

Marteau, P.-F. (2007). Pulse width modulation data sets, http://people.irisa.fr/Pierre-Francois.Marteau/PWM/.Search in Google Scholar

Marteau, P.-F. (2009). Time warp edit distance with stiffness adjustment for time series matching, IEEE Transactions on Pattern Analysis and Machine Intelligence31(2): 306–318.10.1109/TPAMI.2008.76Search in Google Scholar

Marteau, P.-F. and Gibet, S. (2014). On recursive edit distance kernels with application to time series classification, IEEE Transactions on Neural Networks and Learning Systems26(6): 1121–1133.10.1109/TNNLS.2014.2333876Search in Google Scholar

Nakagawa, S. and Nakanishi, H. (1989). Speaker-independent English consonant and Japanese word recognition by a stochastic dynamic time warping method, Journal of Institution of Electronics and Telecommunication Engineers34(1): 87–95.10.1080/03772063.1988.11436710Search in Google Scholar

Niennattrakul, V. and Ratanamahatana, C. (2007). Inaccuracies of shape averaging method using dynamic time warping for time series data, in Y. Shi et al. (Eds.), Computational Science—ICCS 2007, Lecture Notes in Computer Science, Vol. 4487, Springer, Berlin/Heidelberg, pp. 513–520.10.1007/978-3-540-72584-8_68Search in Google Scholar

Niennattrakul, V. and Ratanamahatana, C. (2009). Shape averaging under time warping, 6th International Conference on Electronics, Computer, Telecommunications and Information Technology, ECTI-CON 2009, Pattaya, Chonburi, Thailand, Vol. 02, pp. 626–629.10.1109/ECTICON.2009.5137128Search in Google Scholar

Petitjean, F., Forestier, G., Webb, G., Nicholson, A., Chen, Y. and Keogh, E. (2014). Dynamic time warping averaging of time series allows faster and more accurate classification, Proceedings of the 14th IEEE International Conference on Data Mining, Shenzhen, China, pp. 470–479.10.1109/ICDM.2014.27Search in Google Scholar

Petitjean, F. and Gançarski, P. (2012). Summarizing a set of time series by averaging: From Steiner sequence to compact multiple alignment, Journal of Theoretical Computer Science414(1): 76–91.10.1016/j.tcs.2011.09.029Search in Google Scholar

Petitjean, F., Ketterlin, A. and Gançarski, P. (2011). A global averaging method for dynamic time warping, with applications to clustering, Pattern Recognition44(3): 678–693.10.1016/j.patcog.2010.09.013Search in Google Scholar

Rabiner, L.R. (1989). A tutorial on hidden Markov models and selected applications in speech recognition, Proceedings of the IEEE77(2): 257–286.10.1109/5.18626Search in Google Scholar

Saito, N. (1994). Local Feature Extraction and Its Applications Using a Library of Bases, PhD thesis, Yale University, New Haven, CT.Search in Google Scholar

Sakoe, H. and Chiba, S. (1971). A dynamic programming approach to continuous speech recognition, Proceedings of the 7th International Congress of Acoustic, Budapest, Hungary, pp. 65–68.Search in Google Scholar

Soheily-Khah, S., Douzal-Chouakria, A. and Gaussier, E. (2016). Generalized k-means-based clustering for temporal data under weighted and kernel time warp, Pattern Recognition Letters75: 63–69.10.1016/j.patrec.2016.03.007Search in Google Scholar

Velichko, V.M. and Zagoruyko, N.G. (1970). Automatic recognition of 200 words, International Journal of Man-Machine Studies2: 223–234.10.1016/S0020-7373(70)80008-6Search in Google Scholar

Wang, L. and Jiang, T. (1994). On the complexity of multiple sequence alignment, Journal of Computational Biology1(4): 337–348.10.1089/cmb.1994.1.3378790475Search in Google Scholar

Zhou, F. and De la Torre, F. (2009). Canonical time warping for alignment of human behavior, in Y. Bengio et al. (Eds.), Advances in Neural Information Processing Systems 22, Curran Associates, Inc., Vancouver, pp. 2286–2294.Search in Google Scholar

Zhou, F. and De la Torre, F. (2016). Generalized canonical time warping, IEEE Transactions on Pattern Analysis and Machine Intelligence38(2): 279–294.10.1109/TPAMI.2015.241442926761734Search in Google Scholar