  In this paper we introduce and study the online consistent $k$-clustering
with outliers problem, generalizing the non-outlier version of the problem
studied in [Lattanzi-Vassilvitskii, ICML17].
  We show that a simple local-search based online algorithm can give a
bicriteria constant approximation for the problem with $O(k^2 \log^2 (nD))$
swaps of medians (recourse) in total, where $D$ is the diameter of the metric.
When restricted to the problem without outliers, our algorithm is simpler,
deterministic and gives better approximation ratio and recourse, compared to
that of [Lattanzi-Vassilvitskii, ICML17].
