  Dimension reduction is a technique used to transform data from a
high-dimensional space into a lower-dimensional space, aiming to retain as much
of the original information as possible. This approach is crucial in many
disciplines like engineering, biology, astronomy, and economics. In this paper,
we consider the following dimensionality reduction instance: Given an
n-dimensional probability distribution p and an integer m<n, we aim to find the
m-dimensional probability distribution q that is the closest to p, using the
Kullback-Leibler divergence as the measure of closeness. We prove that the
problem is strongly NP-hard, and we present an approximation algorithm for it.
