A Machine Learning Pipeline for Gravitational Waves

On this work, we present how a feature extraction algorithm known as Common Spatial Patterns (CSP) used widely in electroencephalography (EEG) classifications can be used to characterize whether given (H1, L1) strain pair contains a catalouged gravitational event.

Dataset

The strains and timestamps for the catalogued events are provided by GW Open Science Collaboration (GWOSC). For a baseline, we will use the same strains, except at random, non-overlapping timestamps.

>>> len(event_epochs)
88
>>> len(noise_epochs)
88
>>> X = event_epochs + noise_epochs

X[0] contains H1 strain cropped to [-16s, +16s] around catalouged timestamp. X[1] contains L1 strain cropped to [-16s, +16s] around catalouged timestamp.

>>> X[0][0].sample_rate
4096Hz
>>> len(X[0][0])
131072

Procedure

On Notebook 1, we download these events from H1 (LIGO Hanford) and L1 (LIGO Livingston) interferometers at 4096 Hz and trim them to [-16s, 16s] around their event timestamps.

On Notebook 2, we will generate noise strains.

On Notebook , we will build a machine learning pipeline involving signal processing (Whitening + bandpass at 30-400 Hz), feature extraction using CSP, and different classifier pipelines and run them using 10x5 cross-validation over 21 sliding windows (start=-1.0s, length=0.3s, jump=0.1s). We compute the classification accuracy.

On Notebook , we analyze the classification accuracy and evaluate the performance of our best classifier.

Result

Finally, we will evaluate the performance of multiple classification pipelines.

1. csp_svm (Signal Filter + CSP + Support Vector Machine)
2. csp_svm_nosigfilt (CSP + SVM)
3. csp_lda (Signal Filter + CSP + Linear Descriminant Analysis)
4. csp_lda_nosigfilt (CSP + Linear Descriminant Analysis)

Comparison

Peak classification accuracy using csp_svm: 0.8529365079365079
Peak classification accuracy using csp_svm_nosigfilt: 0.53
Peak classification accuracy using csp_lda: 0.8398571428571429
Peak classification accuracy using csp_lda_nosigfilt: 0.46750793650793654

The peak classification accuracy was given by csp_svm at 85.29%.

Analyzing down classification accuracy

When plotting the SNRs and prediction of the events (coalescenses), we get the following diagram.

Clearly, the errors of our classifier are for events with SNR <= 11. This will the continuated line of study in our work.

Plotting the sensitivity against SNRs

We plot the sensitivity of the csp_svm classifier against SNRs for catalouged events provided by GWOSC, rounded to nearest integer.

Packages used

• sklearn
• gwpy
• gwosc
• mne (for CSP)
• pandas
• numpy
• matplotlib

Authorship/Credits

Damodar Dahal damodar.dahal@selu.edu damodar.dahal@anthem.com

LIGO Strain Data provided by GWOSC (https://gw-openscience.org)