Generalized DBSCAN is an abstraction of the original DBSCAN idea, that allows the use of arbitrary "neighborhood" and "core point" predicates.
For each object, the neighborhood as defined by the "neighborhood" predicate is retrieved - in original DBSCAN, this is the objects within an epsilon sphere around the query object. Then the core point predicate is evaluated to decide if the object is considered dense. If so, a cluster is started (or extended) to include the neighbors as well.
Jörg Sander, Martin Ester, Hans-Peter Kriegel, Xiaowei Xu
Density-Based Clustering in Spatial Databases: The Algorithm GDBSCAN and Its Applications
Data Mining and Knowledge Discovery, 1998.
Class Summary Class Description DBSCAN<O>Density-Based Clustering of Applications with Noise (DBSCAN), an algorithm to find density-connected sets in a database. DBSCAN.Par<O>Parameterization class. GeneralizedDBSCANGeneralized DBSCAN, density-based clustering with noise. GeneralizedDBSCAN.Instance<T>Instance for a particular data set. GeneralizedDBSCAN.ParParameterization class GriDBSCAN<V extends NumberVector>Using Grid for Accelerating Density-Based Clustering. GriDBSCAN.Instance<V extends NumberVector>Instance, for a single run. LSDBC<O extends NumberVector>Locally Scaled Density Based Clustering. LSDBC.Par<O extends NumberVector>Parameterization class