Before revision: {\cal  {\cal  _1,...,{\cal P}_m, for the data reduction purpose, one way to summarize their topological features is to compute the {\em center} {\cal C} of them .
After revision: Throughout this paper, a persistence diagram{\cal {\cal _1,...,{\cal P}_m, for the data reduction purpose, one way to summarize their topological features is to compute the {\em center} {\cal C} of them .