  In recent years, persistent homology (PH) has been successfully applied to
real-world data in many different settings. Despite significant computational
advances, PH algorithms do not yet scale to large datasets 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 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. Here, we
propose a novel approach to select landmarks specifically for PH that preserves
coarse topological information of the original dataset. 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 datasets
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
with respect to robustness to outliers.
