Tuning Parameters For the HACR Algorithm R. Balasubramanian, Gareth - PowerPoint PPT Presentation

Tuning Parameters For the HACR Algorithm R. Balasubramanian, Gareth Jones, B. S. Sathyaprakash Cardiff University GWDAW 2003

HACR Algorithm ● Hierarchical Algorithm for Curves and Ridges ● A Time Frequency Approach – Compute Spectrogram – Identify (TF) pixels which have extra power – Group pixels into clusters. Clustering algorithm is almost the same algorithm as in Julien's TFClusters. – Classification of events ● Suitable for detecting unmodelled bursts of gravitational waves

Constructing the Spectrogram t T secs Parameters ● Segment size (T) ● Subsegment size (t) ● Window function ● Overlap fraction

Selecting Black Pixels ● For each frequency bin we compute the mean and variance after dropping outliers. ● For each pixel we then compute the ratio of the power (after subtracting the mean) to the rms value. If this is greater than a user defined threshold it is marked as a black pixels. ● Therefore the parameters for this stage are – The threshold (we call this the lower threshold) – The fraction of points to be dropped as outliers.

Clustering of Pixels ● Clustering algorithm is the same as defined in Julien's TFClusters. All contiguous pixels which cross the lower threshold are grouped as one cluster. ● A cluster is accepted as an event only if at least one pixel in the cluster crosses an upper threshold. The number of pixels in the cluster must also excced a preset value. ● Thus the parameters for this stage are – The upper threshold – The number of pixels in the cluster

HACR Parameters How do we choose them? ● Spectrogram parameters – Segment Size – Subsegment size – Window (Window parameters) – Overlap ● Identifying Black Pixels – Outlier fraction – lower threshold – upper threshold – number of pixels

Tuning HACR Parameters Main Strategy ● Tune the spectrogram parameters which are the subsegment size, window function and the overlap to the kinds of signals that we expect to see. Can construct multiple spectrograms with different sets of parameters if a single set cannot be found. ● Choose the other parameters including the thresholds to control the false alarm rate

Window function A window is necessary to prevent leakage of power across ● frequencies. Have been using Hann window by default. t T secs

Spectrogram parameters ● The segment size (T) can simply be chosen as T >> (typical burst_length) ● The subsegment size (t) is the most important parameter. ● There is a tradeoff between time and frequency localization. ● We take several kinds of signals such as sine Gaussians, spinning BH binaries etc. and compute spectrograms for several values of t. ● For a particular class of signals use that value of t for which the pixel power is maximum.

Clustering Parameters ● The remaining parameters are chosen emperically through Monte Carlo Simulations. ● These parameters are – Upper threshold – Lower threshold – Number of pixels – Outlier fraction ● These will depend on the nature of the data/noise. ● Simulation are in progress.