Before revision:  From the probability perspective, IC is a linear combination of the components of a directionally projected degenerated random vector. We deduct a solution to its optimization in expectation and obtain the maximum. Their closed-form expressions are given by directional statisticsin a specific condition.
After revision:  Our primary research first clearly defines IC with the high-dimensional directional statistics, discussing its first two moments. We derive the closed-form expressions are given by directional statisticsin a specific condition.