Bezdek, J. C., Ehrlich, R., and Full, W.: FCM: The Fuzzy c-Means Clustering
Algorithm, Comput. Geosci., 10, 191–203,
https://doi.org/10.1109/igarss.1988.569600, 1984.
a
Bregman, L.: The relaxation method of finding the common point of convex sets
and its application to the solution of problems in convex programming, USSR
Comp. Math. Math+, 7, 200–217,
https://doi.org/10.1016/0041-5553(67)90040-7,
1967.
a
Damianou, A. C., Titsias, M. K., and Lawrence, N. D.: Variational Gaussian Process Dynamical Systems, in: Advances in Neural Information Processing Systems 24 (NIPS 2011), 12–17 December 2011, Granada, Spain, 2510–2518, 2011. a
Ding, C. and He, X.: K-means clustering via principal component analysis, in:
Proceedings of the twenty-first international conference on Machine learning (ICML 2004),
4–8 July 2004, Banff, Canada, 29–37, 2004. a
Dole, R. M., Hoerling, M., Perlwitz, J., Eischeid, J., Pegion, P., Zhang, T.,
Quan, X.-W., Xu, T., and Murray, D.: Was there a basis for anticipating the
2010 Russian heat wave?, Geophys. Res. Lett., 38, L06702,
https://doi.org/10.1029/2010GL046582,
2011.
a,
b
Fereday, D. R., Knight, J. R., Scaife, A. A., Folland, C. K., and Philipp, A.:
Cluster Analysis of North Atlantic–European Circulation Types and Links
with Tropical Pacific Sea Surface Temperatures, J. Climate, 21,
3687–3703,
https://doi.org/10.1175/2007JCLI1875.1, 2008.
a
Forgey, E.: Cluster analysis of multivariate data: Efficiency vs.
interpretability of classification, Biometrics, 21, 768–769, 1965. a
Gerber, S., Pospisil, L., Navandar, M., and Horenko, I.: Low-cost scalable
discretization, prediction, and feature selection for complex systems,
Sci. Adv., 6, eaaw0961,
https://doi.org/10.1126/sciadv.aaw0961, 2020.
a,
b,
c,
d,
e,
f
Gönen, M., Khan, S., and Kaski, S.: Kernelized Bayesian matrix
factorization, in: Proceedings of the 30th International Conference on Machine Learning (ICML 2013), 17–19 June 2013, Atlanta, USA, 864–872,
2013. a
Hannachi, A. and Trendafilov, N.: Archetypal analysis: Mining weather and
climate extremes, J. Climate, 30, 6927–6944,
https://doi.org/10.1175/JCLI-D-16-0798.1, 2017.
a,
b,
c,
d
Hannachi, A., Jolliffe, I. T., and Stephenson, D. B.: Empirical orthogonal
functions and related techniques in atmospheric science: A review,
Int. J. Climatol., 27, 1119–1152,
https://doi.org/10.1002/joc.1499,
2007.
a
Harada, Y., Kamahori, H., Kobayashi, C., Endo, H., Kobayashi, S., Ota, Y.,
Onoda, H., Onogi, K., Miyaoka, K., and Takahashi, K.: The JRA-55 Reanalysis:
Representation of Atmospheric Circulation and Climate Variability, J. Meteorol. Soc. Jpn. Ser. II, 94, 269–302,
https://doi.org/10.2151/jmsj.2016-015, 2016.
a
Hartigan, J. A. and Wong, M. A.: Algorithm AS 136: A K-Means Clustering
Algorithm, J. Roy. Stat. Soc. C-App., 28, 100–108,
https://doi.org/10.2307/2346830, 1979.
a
Hastie, T., Tibshirani, R., and Friedman, J.: The Elements of Statistical
Learning: Data Mining, Inference and Prediction, Springer, New York, USA, 2005. a
Horenko, I.: On a scalable entropic breaching of the overfitting barrier in
machine learning, Neural Computation, arXiv [preprint],
arXiv:2002.03176, 8 February 2020.
a
Huth, R., Beck, C., Philipp, A., Demuzere, M., Ustrnul, Z., Cahynová, M.,
Kyselý, J., and Tveito, O. E.: Classifications of Atmospheric Circulation
Patterns, Ann. NY Acad. Sci., 1146, 105–152,
https://doi.org/10.1196/annals.1446.019, 2008.
a
Jenatton, R., Obozinski, G., and Bach, F.: Structured Sparse Principal Component Analysis, in: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, 13–15 May 2010, Sardinia, Italy, 366–373, 2010.
a,
b
Jolliffe, I.: Principal component analysis, Springer Verlag, New York, USA, 1986.
a,
b
Jolliffe, I. T., Trendafilov, N. T., and Uddin, M.: A Modified Principal
Component Technique Based on the LASSO, J. Comput.
Graph. Stat., 12, 531–547,
https://doi.org/10.1198/1061860032148, 2003.
a,
b
Kaiser, E., Noack, B. R., Cordier, L., Spohn, A., Segond, M., Abel, M.,
Daviller, G., Östh, J., Krajnović, S., and Niven, R. K.:
Cluster-based reduced-order modelling of a mixing layer, J. Fluid
Mech., 754, 365–414, 2014. a
Kobayashi, S., Ota, Y., Harada, Y., Ebita, A., Moriya, M., Onoda, H., Onogi,
K., Kamahori, H., Kobayashi, C., Endo, H., Miyaoka, K., and Takahashi, K.:
The JRA-55 Reanalysis: General Specifications and Basic Characteristics,
J. Meteorol. Soc. Jpn. Ser. II, 93, 5–48,
https://doi.org/10.2151/jmsj.2015-001, 2015 (data available at:
https://jra.kishou.go.jp/JRA-55/index_en.html, last access: 12 April 2019).
a,
b
Lawrence, N.: Probabilistic Non-linear Principal Component Analysis with
Gaussian Process Latent Variable Models, J. Mach. Learn. Res., 6, 1783–1816, 2005. a
Lee, D. D. and Seung, H. S.: Unsupervised Learning by Convex and Conic Coding, in: Advances in Neural Information Processing Systems 9 (NIPS 1996), 2–5 December 1996, Denver, USA, 515–521, 1997.
a,
b
Lee, H., Battle, A., Raina, R., and Ng, A. Y.: Efficient Sparse Coding Algorithms, in: Advances in Neural Information Processing Systems 19 (NIPS 2006), 4–7 December 2006, Vancouver, Canada, 801–808, 2007.
a,
b
Legras, B., Desponts, T., and Piguet, B.: Cluster analysis and weather regimes, in: Seminar on the Nature and Prediction of Extra Tropical Weather Systems, 7–11 September 1987, Reading, UK, 123–150, 1987. a
Li, T. and Ding, C.: The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering, in: Proceedings of the Sixth International Conference on Data Mining (ICDM'06), 18–22 December 2006, Hong Kong, China, 362–371, 2006. a
Lorenz, E. N.: Empirical Orthogonal Functions and Statistical Weather
Prediction, Tech. rep., Massachusetts Institute of Technology, Cambridge, UK,
1956. a
MacKay, D. J. C.: Information theory, inference and learning algorithms,
Cambridge University Press, Cambridge, UK, 2003. a
MacQueen, J.: Some methods for classification and analysis of multivariate observations, in: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Statistics, 21 June–18 July 1965 and 27 December 1965–7 January 1966, Berkeley, USA, 281–297, 1967. a
Mahajan, M., Nimbhorkar, P., and Varadarajan, K.: The planar k-means problem is NP-hard, Theor. Comput. Sci., 442, 13–21,
https://doi.org/10.1016/j.tcs.2010.05.034,
2012.
a
Mairal, J., Bach, F., Ponce, J., and Sapiro, G.: Online Dictionary Learning for Sparse Coding, in: Proceedings of the Twenty-Sixth International Conference on Machine Learning, 14–18 June 2009, Montreal, Canada, 689–696, 2009.
a,
b
Michelangeli, P.-A., Vautard, R., and Legras, B.: Weather Regimes: Recurrence
and Quasi Stationarity, J. Atmos. Sci., 52, 1237–1256,
https://doi.org/10.1175/1520-0469(1995)052<1237:WRRAQS>2.0.CO;2,
1995.
a,
b
Mnih, A. and Salakhutdinov, R. R.: Probabilistic Matrix Factorization, in: Advances in Neural Information Processing Systems 20 (NIPS 2007), 3–6 December 2007, Vancouver, Canada, 1257–1264, 2008. a
Molteni, F., Tibaldi, S., and Palmer, T. N.: Regimes in the wintertime
circulation over northern extratropics. I: Observational evidence, Q.
J. Roy. Meteor. Soc., 116, 31–67,
https://doi.org/10.1002/qj.49711649103, 1990.
a
Monahan, A. H., Fyfe, J. C., Ambaum, M. H. P., Stephenson, D. B., and North,
G. R.: Empirical Orthogonal Functions: The Medium is the Message, J. Climate, 22, 6501–6514,
https://doi.org/10.1175/2009JCLI3062.1, 2009.
a
Mørup, M. and Hansen, L. K.: Archetypal analysis for machine learning and
data mining, Neurocomputing, 80, 54–63,
https://doi.org/10.1016/j.neucom.2011.06.033,
2012.
a,
b,
c,
d,
e
Neal, R., Fereday, D., Crocker, R., and Comer, R. E.: A flexible approach to
defining weather patterns and their application in weather forecasting over
Europe, Meteorol. Appl., 23, 389–400,
https://doi.org/10.1002/met.1563,
2016.
a
Rayner, N. A., Parker, D. E., Horton, E. B., Folland, C. K., Alexander, L. V., Rowell, D. P., Kent, E. C., and Kaplan, A.: Global analyses of sea surface temperature, sea ice, and night marine air temperature since the late
nineteenth century, J. Geophys. Res.-Atmos., 108, 4407,
https://doi.org/10.1029/2002JD002670,
2003 (data available at:
https://www.metoffice.gov.uk/hadobs/hadisst/, last access: 29 April 2019).
a,
b
Roweis, S. T.: EM algorithms for PCA and SPCA, in: Advances in Neural Information Processing Systems 10 (NIPS 1997), 1–6 December 1997, Denver, USA, 626–632, 1998.
a,
b
Ruspini, E. H.: A New Approach to Clustering, Inform. Control, 15,
22–32, 1969. a
Salakhutdinov, R. and Mnih, A.: Bayesian Probabilistic Matrix Factorization using Markov Chain Monte Carlo, in: Proceedings of the Twenty-Fifth International Conference on Machine Learning (ICML'08), 5–9 July 2008, Helsinki, Finland, 880–887, 2008. a
Shan, H. and Banerjee, A.: Generalized Probabilistic Matrix Factorizations for Collaborative Filtering, in: Proceedings of the Tenth IEEE International Conference on Data Mining, 14–17 December 2010, Sydney, Australia, 1025–1030, 2010. a
Shaposhnikov, D., Revich, B., Bellander, T., Bedada, G. B., Bottai, M., Kharkova, T., Kvasha, E., Lezina, E., Lind, T., Semutnikova, E., and Pershagen, G.:
Mortality related to air pollution with the Moscow heat wave and wildfire of
2010, Epidemiology, 25, 359–364,
https://doi.org/10.1097/EDE.0000000000000090, 2014.
a
Singh, A. P. and Gordon, G. J.: A Unified View of Matrix Factorization Models, in: Proceedings of the Joint European Conference on Machine Learning and Knowledge Discovery in Databases, Part II, 15–19 September 2008, Antwerp, Belgium, 358–373, 2008.
a,
b
Steinschneider, S. and Lall, U.: Daily Precipitation and Tropical Moisture
Exports across the Eastern United States: An Application of Archetypal
Analysis to Identify Spatiotemporal Structure, J. Climate, 28,
8585–8602,
https://doi.org/10.1175/JCLI-D-15-0340.1, 2015.
a
Stone, R. C.: Weather types at Brisbane, Queensland: An example of the use of
principal components and cluster analysis, Int. J.
Climatol., 9, 3–32,
https://doi.org/10.1002/joc.3370090103, 1989.
a
Straus, D. M., Corti, S., and Molteni, F.: Circulation Regimes: Chaotic
Variability versus SST-Forced Predictability, J. Climate, 20,
2251–2272,
https://doi.org/10.1175/JCLI4070.1, 2007.
a
Tibshirani, R., Walther, G., and Hastie, T.: Estimating the number of clusters in a data set via the gap statistic, J. Roy. Stat. Soc. B, 63, 411–423,
https://doi.org/10.1111/1467-9868.00293, 2001.
a,
b
Virtanen, T., Cemgil, A. T., and Godsill, S.: Bayesian extensions to non-negative matrix factorisation for audio signal modelling, in: Proceedings of the 2008 IEEE International Conference on Acoustics, Speech, and Signal Processing, 30 March–4 April 2008, Las Vegas, USA, 1825–1828, 2008. a
Wang, C., Xie, S.-P., and Carton, J. A.: A Global Survey of Ocean–Atmosphere
Interaction and Climate Variability, American Geophysical Union (AGU), 1–19,
https://doi.org/10.1029/147GM01, 2004.
a
Wang, J., Hertzmann, A., and Fleet, D. J.: Gaussian Process Dynamical Models, in: Advances in Neural Information Processing Systems 18 (NIPS 2005), 5–8 December 2005, Vancouver, Canada, 1441–1448, 2006. a
Witten, D. M., Tibshirani, R., and Hastie, T.: A penalized matrix
decomposition, with applications to sparse principal components and canonical
correlation analysis, Biostatistics, 10, 515–534,
https://doi.org/10.1093/biostatistics/kxp008, 2009.
a,
b
