Message Importance Measure and Its Application to Minority Subset   Detection in Big Data
  Message importance measure (MIM) is an important index to describe the message importance in the scenario of big data. Similar to the Shannon Entropy and Renyi Entropy, MIM is required to characterize the uncertainty of a random process and some related statistical characteristics. Moreover, MIM also need to highlight the importance of those events with relatively small occurring probabilities, thereby is especially applicable to big data. In this paper, we first define a parametric MIM measure from the viewpoint of information theory and then investigate its properties. We also present a parameter selection principle that provides answers to the minority subsets detection problem in the statistical processing of big data. 
Pingyi Fan, Yunquan Dong, Jiaxun Lu, Shanyun Liu
cs.IT math.IT