  In this paper, we consider the problem of estimating the distance between any
two large data streams in small- space constraint. This problem is of utmost
importance in data intensive monitoring applications where input streams are
generated rapidly. These streams need to be processed on the fly and accurately
to quickly determine any deviance from nominal behavior. We present a new
metric, the Sketch \star-metric, which allows to define a distance between
updatable summaries (or sketches) of large data streams. An important feature
of the Sketch \star-metric is that, given a measure on the entire initial data
streams, the Sketch \star-metric preserves the axioms of the latter measure on
the sketch (such as the non-negativity, the identity, the symmetry, the
triangle inequality but also specific properties of the f-divergence).
Extensive experiments conducted on both synthetic traces and real data allow us
to validate the robustness and accuracy of the Sketch \star-metric.
