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Entropy Measures for Stochastic Processes with Applications in Functional Anomaly Detection.

作者信息

Martos Gabriel, Hernández Nicolás, Muñoz Alberto, Moguerza Javier M

机构信息

Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and CONICET, Buenos Aires C1428EGA, Argentina.

Department of Statistics, Universidad Carlos III de Madrid, 28903 Getafe, Spain.

出版信息

Entropy (Basel). 2018 Jan 11;20(1):33. doi: 10.3390/e20010033.

DOI:10.3390/e20010033
PMID:33265131
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC7512230/
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.

摘要
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/9ac301837b11/entropy-20-00033-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/c36095d1fd4f/entropy-20-00033-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/48fc5c75e577/entropy-20-00033-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/9ac301837b11/entropy-20-00033-g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/c36095d1fd4f/entropy-20-00033-g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/48fc5c75e577/entropy-20-00033-g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/70f5/7512230/9ac301837b11/entropy-20-00033-g003.jpg

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本文引用的文献

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Estimation of high-density regions using One-Class Neighbor Machines.
IEEE Trans Pattern Anal Mach Intell. 2006 Mar;28(3):476-80. doi: 10.1109/TPAMI.2006.52.
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Entropy (Basel). 2018 Sep 12;20(9):698. doi: 10.3390/e20090698.