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Information transfer which reveals the state variation of variables usually plays a vital role in big data analytics and processing. In fact, the measures for information transfer could reflect the system change by use of the variable distributions, similar to KL divergence and Renyi divergence. Furthermore, in terms of the information transfer in big data, small probability events usually dominate the importance of the total message to some degree. Therefore, it is significant to design an information transfer measure based on the message importance which emphasizes the small probability events. In this paper, we propose a message importance transfer measure (MITM) and investigate its characteristics and applications on three aspects. First, the message importance transfer capacity based on MITM is presented to offer an upper bound for the information transfer process with disturbance. Then, we extend the MITM to the continuous case and discuss the robustness by using it to measuring information distance. Finally, we utilize the MITM to guide the queue length selection in the caching operation of mobile edge computing.

State Variation Mining: On Information Divergence with Message Importance in Big Data