A density based method for clustering the measurements from neighboring or overlapping basis functions has been employed to more efficiently detect GWB signals that are extended in time and/or frequency, and not well represented by QPipeline's particular choice of basis. The method is capable of identifying an arbitrary number of clusters of arbitrary shape and size, while also rejecting spurious noise triggers, and does not significantly increase the computational cost of the overall QPipeline search.
The proposed clustering algorithm itself is not specific to the QPipeline. Similar improvements are expected when applied to other time-frequency searches for gravitational wave bursts. In particular, the algorithm described here has already been applied to the search for bursts from the soft gamma repeaters using the flare pipeline [27,28,29]. For estimating upper limits, the flare pipeline initially performed a simple sum over all frequency bins to measure the total signal energy of a trigger. The use of density based clustering instead improved the flare pipeline's upper limit estimate for 100 ms long white noise bursts in the frequency band from 64 to 1024 Hz by 42%. No improvement was observed for 22 ms long white noise bursts in the band from 100 to 200 Hz, but such signals are fairly localized in the time-frequency plane. These results are consistent with our conclusion that density based clustering is only beneficial when searching for extended signals.
Our implementation of density based clustering is already implemented
as part of the QPipeline, which has now been incorporated into the
-Pipeline [30] for use in future GWB searches.
A number of issues remain open for future investigation. This paper has focused only on single detector data. We have left a study of the effect of density based clustering on multi-detector GWB searches as a subject for future investigation. In Equation 4, we have proposed one possible distance metric. A study of other distance metrics, in particular ones based on the mismatch metric of Equation 2 is also possible. A more in depth study of hierarchical clustering methods, and comparison with the proposed density based method, as well as previously proposed methods [31,32,33] is also recommended. Finally, the application of clustering to astrophysical parameter estimation in the event of a detection also warrants further investigation.
The authors are grateful for the support of the United States National Science Foundation under cooperative agreement PHY-04-57528, California Institute of Technology, and Columbia University in the City of New York. We are grateful to the LIGO Scientific collaboration for their support. We are indebted to many of our colleagues for frequent and fruitful discussion. In particular, we'd like to thank Albert Lazzarini for his valuable suggestions regarding this project, and Luca Matone, Zsuzsa Márka, Sharmila Kamat, Jameson Rollins, Peter Kalmus, John Dwyer, Patrick Sutton, Eirini Messeritaki, and Szabolcs Márka for their thoughtful comments on the manuscript. The authors gratefully acknowledge the LIGO Scientific Collaboration hardware injection team for providing the data used in figures 1 and 2. We gratefully acknowledge the contributions of all the software developers and programmers in the broader scientific community without whose incremental achievements over many decades we would not be able to reach this point where implementing this project has become possible.
The authors gratefully acknowledge the support of the United States National Science Foundation for the construction and operation of the LIGO Laboratory and the Particle Physics and Astronomy Research Council of the United Kingdom, the Max-Planck-Society and the State of Niedersachsen / Germany for support of the construction and operation of the GEO600 detector. The authors also gratefully acknowledge the support of the research by these agencies and by the Australian Research Council, the Natural Sciences and Engineering Research Council of Canada,the Council of Scientific and Industrial Research of India, the Department of Science and Technology of India, the Spanish Ministerio de Educaciony Ciencia, The National Aeronautics and Space Administration, the John Simon Guggenheim Foundation, the Alexander von Humboldt Foundation,the Leverhulme Trust, the David and Lucile Packard Foundation, the Research Corporation, and the Alfred P. Sloan Foundation. The LIGO Observatories were constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation under cooperative agreement PHY-9210038. The LIGO Laboratory operates under cooperative agreement PHY-0107417. This document has been assigned LIGO document number LIGO-P070041-01-Z.