  In recent years, persistent homology (PH) has been successfully applied to
real-world data in many different settings. When attempting to study large and
noisy data sets, however, many of the currently available algorithms for PH
fail due to computational complexity preventing interesting applications. One
approach to address computational issues posed by PH is to select a set of
landmarks by subsampling from the data. Currently, these landmark points are
chosen either at random or using the so called maxmin algorithm. Neither is
ideal as random selection tends to favour dense areas of the data while the
maxmin algorithm is very sensitive to noise. We propose a novel approach to
select landmarks specifically for PH that preserves topological properties of
the original data set. Our method is motivated by the Mayer-Vietoris sequence
and requires only local PH computation thus enabling efficient computation. We
test our landmarks on artificial data sets which contain different levels of
noise and compare them to standard landmark selection techniques. We
demonstrate that our landmark selection outperforms standard methods as well as
a subsampling technique based on an outlier-robust version of the $k$- means
algorithm for low sampling densities in noisy data.
