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Entropy 2018, 20(1), 33; https://doi.org/10.3390/e20010033

Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection

1
Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Buenos Aires C1428EGA, Argentina
2
Department of Statistics, Universidad Carlos III de Madrid, 28903 Getafe, Spain
3
Department of Computer Science and Statistics, University Rey Juan Carlos, 28933 Móstoles, Spain
*
Authors to whom correspondence should be addressed.
Received: 5 December 2017 / Revised: 29 December 2017 / Accepted: 2 January 2018 / Published: 11 January 2018
(This article belongs to the Special Issue Entropy in Signal Analysis)
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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. View Full-Text
Keywords: entropy; stochastic process; minimum-entropy sets; anomaly detection; functional data entropy; stochastic process; minimum-entropy sets; anomaly detection; functional data
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Martos, G.; Hernández, N.; Muñoz, A.; Moguerza, J.M. Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection. Entropy 2018, 20, 33.

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