  The detection of unmodeled gravitational-wave bursts by ground-based
interferometric gravitational-wave detectors is a major goal for the advanced
detector era. These searches are commonly cast as pattern recognition problems,
where the goal is to identify statistically significant clusters in
spectrograms of strain power when the precise signal morphology is unknown. In
previous work, we have introduced a clustering algorithm referred to as
"seedless clustering," and shown that it is a powerful tool for detecting weak
long-lived (10-1000s) signals in background. However, as the algorithm is
currently conceived, in order to carry out an all-sky search on a $\approx$
year of data, significant computational resources may be required in order to
carry out background estimation. Alternatively, some of the sensitivity of the
search must be sacrificed to control computational costs. The sensitivity of
the algorithm is limited by the amount of computing resources due to the
requirement of performing background studies to assign significance in
gravitational-wave searches. In this paper, we present an analytic method for
estimating the background generated by the seedless clustering algorithm and
compare the performance to both Monte Carlo Gaussian noise and time-shifted
gravitational-wave data from a week of LIGO's 5th Science Run. We demonstrate
qualitative agreement between the model and measured distributions and argue
that the approximation will be useful to supplement conventional background
estimation techniques for advanced detector searches for long-duration
gravitational-wave transients.
