  SpectralNet is a graph clustering method that uses neural network to find an
embedding that separates the data. So far it was only used with $k$-nn graphs,
which are usually constructed using a distance metric (e.g., Euclidean
distance). $k$-nn graphs restrict the points to have a fixed number of
neighbors regardless of the local statistics around them. We proposed a new
SpectralNet similarity metric based on random projection trees (rpTrees). Our
experiments revealed that SpectralNet produces better clustering accuracy using
rpTree similarity metric compared to $k$-nn graph with a distance metric. Also,
we found out that rpTree parameters do not affect the clustering accuracy.
These parameters include the leaf size and the selection of projection
direction. It is computationally efficient to keep the leaf size in order of
$\log(n)$, and project the points onto a random direction instead of trying to
find the direction with the maximum dispersion.
