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Pre-print draft: arXiv:0901.3762
Journal: The Classical and Quantum Gravity, Volume 26, Issue 15, id. 155009 (2009).

Enhancing the Capabilities of LIGO Time-Frequency Plane Searches Through Clustering
Rubab Khan, Shourov Chatterji


One class of gravitational wave signals LIGO is searching for consists of short duration bursts of unknown waveforms. Potential sources include core collapse supernovae, gamma ray burst progenitors, and mergers of binary black holes or neutron stars. We present a density-based clustering algorithm to improve the performance of time-frequency searches for such gravitational-wave bursts when they are extended in time and/or frequency, and not sufficiently well known to permit matched filtering. We have implemented this algorithm as an extension to the QPipeline, a gravitational-wave data analysis pipeline for the detection of bursts, which currently determines the statistical significance of events based solely on the peak significance observed in minimum uncertainty regions of the time-frequency plane. Density based clustering improves the performance of such a search by considering the aggregate significance of arbitrarily shaped regions in the time-frequency plane and rejecting the isolated minimum uncertainty features expected from the background detector noise. In this paper, we present test results for simulated signals and demonstrate that density based clustering improves the performance of the QPipeline for signals extended in time and/or frequency.

The QPipeline

Figure 1

Fig. 1.— The QPipeline view of the inspiral phase of a simulated optimally oriented 1.4/1.4 solar mass binary neutron star merger injected into typical single detector LIGO data with an SNR of 48.2 as measured by a matched filter search targeting inspiral signal. The QPipeline projects the whitened data onto the space of time, frequency, and Q. The left panel image shows the resulting time-frequency spectrogram of normalized signal energy for the value of Q that maximizes the measured normalized energy, while the right panel image shows the time-frequency distribution of only the most significant non-overlapping triggers regardless of Q.


Figure 2

Fig. 2.— Two different clustering methods were applied to the QPipeline triggers from Figure 1. The left panel image shows the result of applying a hierarchical based clustering method, while the right panel image shows the result of applying the proposed density based clustering method. Here each combination of color and shape denotes a different cluster. Although both hierarchical and density based clustering approaches succeed in isolating most of the signal energy within a single cluster, the density based approach has the additional advantage of discarding isolated triggers due to the background detector noise.

Density Based Clustering

Figure 3

Fig. 3.— Building clusters from data-points using the density based clustering algorithm, as discussed in details in Section 4. The left panel shows the steps of building a cluster using density based clustering. The right panel shows the 4-distance graph which helps us determine the neighborhood radius. (Figures derived from concepts presented in Ester et al. 1996) .

Figure 4

Fig. 4.— Flowchart of density based clustering algorithm.


Figure 5

Fig. 5.— The false event rate of the search algorithm as a function of detection threshold when applied to typical LIGO data. The trigger rate is shown for three different trigger sets: unclustered triggers, clustered triggers, and the union of clustered and unclustered triggers.

Figure 6

Fig. 6.— Comparison of the detection efficiency vs. search threshold (left) and Receiver Operator Characteristics (ROC) (right) of the search algorithm, with and without clustering, applied to the detection of simulated inspiral (top), white noise burst (middle), and sinusoidal Gaussian (bottom) waveforms injected 200 times into typical LIGO data at fixed SNR.




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 Marka, Sharmila Kamat, Jameson Rollins, Peter Kalmus, John Dwyer, Patrick Sutton, Eirini Messeritaki, and Szabolcs Marka 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.

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