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Attention to the Variation of Probabilistic Events: Information Processing with Message Importance Measure

Beijing National Research Center for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China
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Entropy 2019, 21(5), 439; https://doi.org/10.3390/e21050439
Received: 10 March 2019 / Revised: 9 April 2019 / Accepted: 23 April 2019 / Published: 26 April 2019
(This article belongs to the Special Issue Information Theoretic Measures and Their Applications)
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Abstract

Different probabilities of events attract different attention in many scenarios such as anomaly detection and security systems. To characterize the events’ importance from a probabilistic perspective, the message importance measure (MIM) is proposed as a kind of semantics analysis tool. Similar to Shannon entropy, the MIM has its special function in information representation, in which the parameter of MIM plays a vital role. Actually, the parameter dominates the properties of MIM, based on which the MIM has three work regions where this measure can be used flexibly for different goals. When the parameter is positive but not large enough, the MIM not only provides a new viewpoint for information processing but also has some similarities with Shannon entropy in the information compression and transmission. In this regard, this paper first constructs a system model with message importance measure and proposes the message importance loss to enrich the information processing strategies. Moreover, the message importance loss capacity is proposed to measure the information importance harvest in a transmission. Furthermore, the message importance distortion function is discussed to give an upper bound of information compression based on the MIM. Additionally, the bitrate transmission constrained by the message importance loss is investigated to broaden the scope for Shannon information theory. View Full-Text
Keywords: message importance measure; information theory; probabilistic events processing; message transmission and compression message importance measure; information theory; probabilistic events processing; message transmission and compression
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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She, R.; Liu, S.; Fan, P. Attention to the Variation of Probabilistic Events: Information Processing with Message Importance Measure. Entropy 2019, 21, 439.

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