In the original DENCLUE algorithm ( Hinneburg, Alexander, and Daniel A. Keim. "An efficient approach to clustering in large multimedia databases with noise." KDD. Vol. 98. 1998. ) , where they define "center defined" cluster (Definition 4 in the paper) , they write " A center defined cluster (wrt σ, ξ ) for a density attractor x* is a subset C ⊆ D , with x ∈ C being density attracted by x* and fBD (x*) >= ξ. Points x ⊆ D are called outliers if they are density attracted by a local maximum x*0 , with fBD (x*0) < ξ.

My question is:

In a center defined cluster, is the density attractor x* somehow the center of the cluster C? If yes then the (bold part in the) definition should be x ∈ C being density attracted TO (instead of density attracted by ) x* and fBD (x*) >= ξ.