  Motivated by this, we study the problem of obtaining persistent homology based summaries of time-dependent metric data.
<meaning-changed>   Motivated by this, we study the problem of obtaining persistent homology based summaries of time-dependent metric data.
 In a similar vein, studying the dynamics of social networks leads to the problem of characterizing groups/communities as they form and disperse throughout time. Motivated by this, we study the problem of obtaining persistent homology based summaries of time-dependent metric data.