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

Chasing 5-sigma: Prospects for searches for long-duration gravitational-waves without time slides