Title: Coresets for Vector Summarization with Applications to Network Graphs,
Abstract: We provide a deterministic data summarization algorithm that approximates the
mean $\bar{p}=\frac{1}{n}\sum_{p\in P} p$ of a set $P$ of $n$ vectors in
$\REAL^d$, by a weighted mean $\tilde{p}$ of a \emph{subset} of $O(1/\eps)$
vectors, i.e., independent of both $n$ and $d$. We prove that the squared
Euclidean distance between $\bar{p}$ and $\tilde{p}$ is at most $\eps$
multiplied by the variance of $P$. We use this algorithm to maintain an
approximated sum of vectors from an unbounded stream, using memory that is
independent of $d$, and logarithmic in the $n$ vectors seen so far. Our main
application is to extract and represent in a compact way friend groups and
activity summaries of users from underlying data exchanges. For example, in the
case of mobile networks, we can use GPS traces to identify meetings, in the
case of social networks, we can use information exchange to identify friend
groups. Our algorithm provably identifies the {\it Heavy Hitter} entries in a
proximity (adjacency) matrix. The Heavy Hitters can be used to extract and
represent in a compact way friend groups and activity summaries of users from
underlying data exchanges. We evaluate the algorithm on several large data
sets.