She Rui, Liu Shanyun, Fan Pingyi
Beijing National Research Center for Information Science and Technology, Department of Electronic Engineering, Tsinghua University, Beijing 100084, China.
Entropy (Basel). 2019 Apr 26;21(5):439. doi: 10.3390/e21050439.
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.
在诸如异常检测和安全系统等许多场景中，不同的事件概率会吸引不同的关注。为了从概率角度刻画事件的重要性，提出了消息重要性度量（MIM）作为一种语义分析工具。与香农熵类似，MIM在信息表示方面有其特殊作用，其中MIM的参数起着至关重要的作用。实际上，该参数主导着MIM的性质，基于此MIM有三个工作区域，在这些区域中该度量可针对不同目标灵活使用。当参数为正但不够大时，MIM不仅为信息处理提供了新视角，而且在信息压缩和传输方面与香农熵有一些相似之处。在此方面，本文首先构建了一个带有消息重要性度量的系统模型，并提出了消息重要性损失以丰富信息处理策略。此外，提出了消息重要性损失容量来度量传输中收获的信息重要性。再者，讨论了消息重要性失真函数以给出基于MIM的信息压缩的上界。另外，研究了受消息重要性损失约束的比特率传输，以拓宽香农信息论的范围。
