  We present sDBSCAN, a scalable density-based clustering algorithm in high
dimensions with cosine distance. Utilizing the neighborhood-preserving property
of random projections, sDBSCAN can quickly identify core points and their
neighborhoods, the primary hurdle of density-based clustering. Theoretically,
sDBSCAN outputs a clustering structure similar to DBSCAN under mild conditions
with high probability. To further facilitate sDBSCAN, we present sOPTICS, a
scalable OPTICS for interactive exploration of the intrinsic clustering
structure. We also extend sDBSCAN and sOPTICS to L2, L1, $\chi^2$, and
Jensen-Shannon distances via random kernel features. Empirically, sDBSCAN is
significantly faster and provides higher accuracy than many other clustering
algorithms on real-world million-point data sets. On these data sets, sDBSCAN
and sOPTICS run in a few minutes, while the scikit-learn's counterparts demand
several hours or cannot run due to memory constraints.
