  It has been insufficiently explored how to perform density-based clustering
by exploiting textual attributes on social media. In this paper, we aim at
discovering a social point-of-interest (POI) boundary, formed as a convex
polygon. More specifically, we present a new approach and algorithm, built upon
our earlier work on social POI boundary estimation (SoBEst). This SoBEst
approach takes into account both relevant and irrelevant records within a
geographic area, where relevant records contain a POI name or its variations in
their text field. Our study is motivated by the following empirical
observation: a fixed representative coordinate of each POI that SoBEst
basically assumes may be far away from the centroid of the estimated social POI
boundary for certain POIs. Thus, using SoBEst in such cases may possibly result
in unsatisfactory performance on the boundary estimation quality (BEQ), which
is expressed as a function of the $F$-measure. To solve this problem, we
formulate a joint optimization problem of simultaneously finding the radius of
a circle and the POI's representative coordinate $c$ by allowing to update $c$.
Subsequently, we design an iterative SoBEst (I-SoBEst) algorithm, which enables
us to achieve a higher degree of BEQ for some POIs. The computational
complexity of the proposed I-SoBEst algorithm is shown to scale linearly with
the number of records. We demonstrate the superiority of our algorithm over
competing clustering methods including the original SoBEst.
