Abstract:
We propose a definition of entropy for stochastic processes. We provide a reproducing kernel Hilbert space model to estimate entropy from a random sample of realizations of a stochastic process, namely functional data, and introduce two approaches to estimate minimum entropy sets. These sets are relevant to detect anomalous or outlier functional data. A numerical experiment illustrates the performance of the proposed method; in addition, we conduct an analysis of mortality rate curves as an interesting application in a real-data context to explore functional anomaly detection. © 2018 by the authors.
Registro:
Documento: |
Artículo
|
Título: | Entropy measures for stochastic processes with applications in functional anomaly detection |
Autor: | Martos, G.; Hernández, N.; Muñoz, A.; Moguerza, J.M. |
Filiación: | Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Buenos Aires, C1428EGA, Argentina Department of Statistics, Universidad Carlos III de Madrid, Getafe, 28903, Spain Department of Computer Science and Statistics, University Rey Juan Carlos, Móstoles, 28933, Spain
|
Palabras clave: | Anomaly detection; Entropy; Functional data; Minimum-entropy sets; Stochastic process |
Año: | 2018
|
Volumen: | 20
|
Número: | 1
|
DOI: |
http://dx.doi.org/10.3390/e20010033 |
Título revista: | Entropy
|
Título revista abreviado: | Entropy
|
ISSN: | 10994300
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_10994300_v20_n1_p_Martos |
Referencias:
- Rényi, A., On measures of entropy and information (1961) Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, 1, pp. 547-561. , Contributions to the Theory of Statistics University of California Press: Berkeley, CA, USA
- Bosq, D., (2012) Linear Processes in Function Spaces: Theory and Applications, , Springer Science & Business Media: New York, NY, USA
- Ramsay, J.O., (2006) Functional Data Analysis, , Wiley: New York, NY, USA
- Ferraty, F., Vieu, P., (2006) Nonparametric Functional Data Analysis: Theory and Practice, , Springer: New York, NY, USA
- Berlinet, A., Thomas-Agnan, C., (2011) Reproducing Kernel Hilbert Spaces in Probability and Statistics, , Springer: New York, NY, USA
- Kimeldorf, G., Wahba, G., Some results on Tchebycheffian spline functions (1971) J.Math. Anal. Appl, 33, pp. 82-94
- Cucker, F., Smale, S., On the mathematical foundations of learning (2002) Bull. Am. Math. Soc, 39, pp. 1-49
- Muñoz, A., González, J., Representing functional data using support vector machines (2010) Pattern Recognit. Lett, 31, pp. 511-516
- Zhu, H., Williams, C., Rohwer, R., Morciniec, M., (1997) Gaussian Regression and Optimal Finite Dimensional Linear Models, , Aston University: Birmingham, UK
- López-Pintado, S., Romo, J., On the concept of depth for functional data (2009) J. Am. Stat. Assoc, 104, pp. 718-734
- Cuevas, A., Febrero, M., Fraiman, R., Robust estimation and classification for functional data via projection-based depth notions (2007) Comput. Stat, 22, pp. 481-496
- Sguera, C., Galeano, P., Lillo, R., Spatial depth-based classification for functional data (2014) Test, 23, pp. 725-750
- Cuesta-Albertos, J.A., Nieto-Reyes, A., The random Tukey depth (2008) Comput. Stat. Data Anal, 52, pp. 4979-4988
- Hero, A., Geometric entropy minimization (GEM) for anomaly detection and localization (2007) Proceedings of the Advances in Neural Information Processing Systems, pp. 585-592. , Vancouver, BC, Canada, 3-6 December
- Xie, T., Narabadi, N., Hero, A.O., (2016) Robust training on approximated minimal-entropy set
- Hyndman, R.J., Computing and graphing highest density regions (1996) Am. Stat, 50, pp. 120-126
- Maronna, R., Martin, R., Yohai, V., (2006) Robust Statistics, , John Wiley & Sons: Hoboken, NJ, USA
- Beirlant, J., Dudewicz, E., Györfi, L., Van der Meulen, E., Nonparametric entropy estimation: An overview (1997) Int. J. Math. Stat. Sci, 6, pp. 17-39
- Cano, J., Moguerza, J.M., Psarakis, S., Yannacopoulos, A.N., Using statistical shape theory for the monitoring of nonlinear profiles. Applied Stochastic Models in Business and Industry (2015) Appl. Stoch. Models Bus. Ind, 31, pp. 160-177
- Febrero-Bande, M., De la Fuente, M.O., Statistical computing in functional data analysis: The R package fda.usc (2012) J. Stat. Softw, 51, pp. 1-28
- Hyndman, R.J., (2017) Demography Package, , R Foundation for Statistical Computing: Vienna, Austria
- Muñoz, A., Moguerza, J.M., Estimation of high-density regions using one-class neighbor machines (2006) IEEE Trans. Pattern Anal. Mach. Intell, 28, pp. 476-480
Citas:
---------- APA ----------
Martos, G., Hernández, N., Muñoz, A. & Moguerza, J.M.
(2018)
. Entropy measures for stochastic processes with applications in functional anomaly detection. Entropy, 20(1).
http://dx.doi.org/10.3390/e20010033---------- CHICAGO ----------
Martos, G., Hernández, N., Muñoz, A., Moguerza, J.M.
"Entropy measures for stochastic processes with applications in functional anomaly detection"
. Entropy 20, no. 1
(2018).
http://dx.doi.org/10.3390/e20010033---------- MLA ----------
Martos, G., Hernández, N., Muñoz, A., Moguerza, J.M.
"Entropy measures for stochastic processes with applications in functional anomaly detection"
. Entropy, vol. 20, no. 1, 2018.
http://dx.doi.org/10.3390/e20010033---------- VANCOUVER ----------
Martos, G., Hernández, N., Muñoz, A., Moguerza, J.M. Entropy measures for stochastic processes with applications in functional anomaly detection. Entropy. 2018;20(1).
http://dx.doi.org/10.3390/e20010033