be a memoryless uniform Bernoulli source and
be the output of it through a binary symmetric channel. Courtade and Kumar conjectured that the Boolean function
that maximizes the mutual information
is a dictator function, i.e.,
for some i
. We propose a clustering problem, which is equivalent to the above problem where we emphasize an information geometry aspect of the equivalent problem. Moreover, we define a normalized geometric mean of measures and interesting properties of it. We also show that the conjecture is true when the arithmetic and geometric mean coincide in a specific set of measures.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited