  We develop a mapping between the factorial moments of the second order $F_2$
and the correlation integral $C$. We formulate a fast computation technique for
the evaluation of both, which is more efficient, compared to conventional
methods, for data containing number of pairs per event which is lower than the
estimation points. We find the effectiveness of the technique to be more
prominent as the dimension of the embedding space increases. We are able to
analyse large amount of data in short computation time and access very low
scales in $C$ or extremely high partitions in $F_2$. The technique is an
indispensable tool for detecting a very weak signal hidden in strong noise.
