Selfinformation - Self-information of A Partitioning

Self-information of A Partitioning

The self-information of a partitioning of elements within a set (or clustering) is the expectation of the information of a test object. I.e. if we select an element at random and observe in which partition/cluster it exists, what quantity of information do we expect to obtain. The information of a partitioning with denoting the fraction of elements within partition is