  Graph-based clustering methods like spectral clustering and SpectralNet are
very efficient in detecting clusters of non-convex shapes. Unlike the popular
$k$-means, graph-based clustering methods do not assume that each cluster has a
single mean. However, these methods need a graph where vertices in the same
cluster are connected by edges of large weights. To achieve this goal, many
studies have proposed graph reduction methods with parameters. Unfortunately,
these parameters have to be tuned for every dataset. We introduce a graph
reduction method that does not require any parameters. First, the distances
from every point $p$ to its neighbors are filtered using an adaptive threshold
to only keep neighbors with similar surrounding density. Second, the
similarities with close neighbors are computed and only high similarities are
kept. The edges that survive these two filtering steps form the constructed
graph that was passed to spectral clustering and SpectralNet. The experiments
showed that our method provides a stable alternative, where other methods
performance fluctuated according to the setting of their parameters.
