  Distances to the $k$-nearest-neighbor ($k$NN) data points from volume-filling
query points are a sensitive probe of spatial clustering. Here we present the
first application of $k$NN summary statistics to observational clustering
measurement, using the 1000 richest redMaPPer clusters ($0.1\leqslant
z\leqslant 0.3$) from the SDSS DR8 catalog. A clustering signal is defined as a
difference in the cumulative distribution functions (CDFs) of $k$NN distances
from fixed query points to the observed clusters versus a set of unclustered
random points. We find that the $k=1,2$-NN CDFs of redMaPPer deviate
significantly from the randoms' across scales of 35 to 155 Mpc, which is a
robust signature of clustering. In addition to $k$NN, we also measure the
two-point correlation function for the same set of redMaPPer clusters versus
random points, which shows a noisier and less significant clustering signal
within the same radial scales. Quantitatively, the $\chi^2$ distribution for
both the $k$NN-CDFs and the two-point correlation function measured on the
randoms peak at $\chi^2\sim 50$ (null hypothesis), whereas the $k$NN-CDFs
($\chi^2\sim 300$, $p = 1.54\times 10^{-36}$) pick up a much more significant
clustering signal than the two-point function ($\chi^2\sim 100$, $p =
1.16\times 10^{-6}$) when measured on redMaPPer. Finally, the measured 3NN and
4NN CDFs deviate from the predicted $k=3, 4$-NN CDFs assuming an ideal Gaussian
field, indicating a non-Gaussian clustering signal for redMaPPer clusters,
although its origin might not be cosmological due to observational systematics.
Therefore, $k$NN serves as a more sensitive probe of clustering complementary
to the two point correlation function, providing a novel approach for
constraining cosmology and galaxy-halo connection.
