I am reading a paper on information gathering by autonomous robot and it discusses submodularity of objective function as follows:
The submodularity of the objective function arises from the spatial (and potentially temporal) correlation of the measurement locations.
Submodularity pertains to diminishing returns, so if we start with nothing any sampling will provide us with higher knowledge compared to if we have prior information about the subject.
So in brief if the 2d space is correlated then the objective function is submodular. I am trying to understand how does spacial correlation yields submodularity?