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Functional Principal Components direction to cluster earthquake
Type
Conference paper
Language
English
Status
Published
Conference Name
Issued date
May 2, 2010
Conference Location
Vienna (Austria)
Keywords
Abstract
Looking for curves similarity could be a complex issue characterized by subjective choices related to continuous
transformations of observed discrete data (Chiodi, 1989).
In this paper we combine the aim of finding clusters from a set of individual curves to the functional nature of data,
applying a variant of a k-means algorithm based on the principal component rotation of data. We apply a classical
clustering method to rotated data, according to the direction of maximum variance.
A k-means clustering algorithm based on PCA rotation of data is proposed, as an alternative to methods that
require previous interpolation of data based on splines or linear fitting (García-Escudero and Gordaliza (2005),
Tarpey (2007), Sangalli et al. (2008)).
transformations of observed discrete data (Chiodi, 1989).
In this paper we combine the aim of finding clusters from a set of individual curves to the functional nature of data,
applying a variant of a k-means algorithm based on the principal component rotation of data. We apply a classical
clustering method to rotated data, according to the direction of maximum variance.
A k-means clustering algorithm based on PCA rotation of data is proposed, as an alternative to methods that
require previous interpolation of data based on splines or linear fitting (García-Escudero and Gordaliza (2005),
Tarpey (2007), Sangalli et al. (2008)).
References
[1] Chiodi, M. (1989). The clustering of longitudinal data when time series are short. Multivariate data analysis,
pages 445–453.
[2] García-Escudero, L. A. and Gordaliza, A. (2005). A proposal for robust curve clustering. Journal of classification,
22, 185–201.
[3] Gillard, D., R. A. and Okubom, P. (1996). Highly concentrated seismicity caused by deformation of kilauea’s
depp magma system. Nature, 384, 343–346.
[4] Hastie, T. J. (1997). Generalized additive models. Chapman and Hall, London.
[5] Menke, W. (1999). Using waveform similarity to constrain earthquake locations. Bull.Seismol. Soc. Am., 89,
1143–1146.
[6] Mezcua, J. and Rueda, J. (1994). Earthquake relative location based on waveform similarity. Tectonophysics,
233, 253–263.
[7] Phillips, W. S., H. L. F. J. (1997). Detailed joint structure in a geothermal reservoir from studies of induced
microearthquake studies. Journal of Geophysical Research, 102, 745–763.
[8] Ramsey, J. O. and Silverman, B. W. (2006). Functional Data Analysis. Springer, New York.
[9] Sangalli, L. M., Secchi, P., Vantini, S., and Vitelli, V. (2008). K-means alignment for curve clustering. MOX
(Modeling and Scientific Computing)-Report, 13.
[10] Tarpey, T. (2007). Linear transformations and the k-means clustering alghoritm: applications to clustering
curves. American statistician, 61(1), 34–40.
pages 445–453.
[2] García-Escudero, L. A. and Gordaliza, A. (2005). A proposal for robust curve clustering. Journal of classification,
22, 185–201.
[3] Gillard, D., R. A. and Okubom, P. (1996). Highly concentrated seismicity caused by deformation of kilauea’s
depp magma system. Nature, 384, 343–346.
[4] Hastie, T. J. (1997). Generalized additive models. Chapman and Hall, London.
[5] Menke, W. (1999). Using waveform similarity to constrain earthquake locations. Bull.Seismol. Soc. Am., 89,
1143–1146.
[6] Mezcua, J. and Rueda, J. (1994). Earthquake relative location based on waveform similarity. Tectonophysics,
233, 253–263.
[7] Phillips, W. S., H. L. F. J. (1997). Detailed joint structure in a geothermal reservoir from studies of induced
microearthquake studies. Journal of Geophysical Research, 102, 745–763.
[8] Ramsey, J. O. and Silverman, B. W. (2006). Functional Data Analysis. Springer, New York.
[9] Sangalli, L. M., Secchi, P., Vantini, S., and Vitelli, V. (2008). K-means alignment for curve clustering. MOX
(Modeling and Scientific Computing)-Report, 13.
[10] Tarpey, T. (2007). Linear transformations and the k-means clustering alghoritm: applications to clustering
curves. American statistician, 61(1), 34–40.
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