# Using supervised learning algorithms as a follow-up method in the search of
gravitational waves from core-collapse supernovae

Javier M. Antelis<EMAIL_ADDRESS>Embry-Riddle Aeronautical
University, Prescott, AZ 86301, USA  Tecnologico de Monterrey, Escuela de
Ingeniería y Ciencias, Monterrey, N.L., 64849, México  Marco Cavaglia
Institute of Multi-messenger Astrophysics and Cosmology, Missouri University
of Science and Technology, Rolla, MO 65409, USA  Travis Hansen  Embry-Riddle
Aeronautical University, Prescott, AZ 86301, USA  Manuel D. Morales
Universidad de Guadalajara, Guadalajara, Jal., 44430, México  Claudia Moreno
Embry-Riddle Aeronautical University, Prescott, AZ 86301, USA  Universidad de
Guadalajara, Guadalajara, Jal., 44430, México  Soma Mukherjee  The University
of Texas Rio Grande Valley, Brownsville, TX 78520, USA  Marek J. Szczepańczyk
University of Florida, Gainesville, FL 32611, USA  Michele Zanolin  Embry-
Riddle Aeronautical University, Prescott, AZ 86301, USA

###### Abstract

We present a follow-up method based on supervised machine learning (ML) to
improve the performance in the search of gravitational wave (GW) burts from
core-collapse supernovae (CCSNe) using the coherent WaveBurst (cWB) pipeline.
The ML model discriminates noise from signal events using as features a set of
reconstruction parameters provided by cWB. Detected noise events are discarded
yielding to a reduction of the false alarm rate (FAR) and of the false alarm
probability (FAP) thus enhancing of the statistical significance. We tested
the proposed method using strain data from the first half of the third
observing run of advanced LIGO, and CCSNe GW signals extracted from 3D
simulations. The ML model is learned using a dataset of noise and signal
events, and then it is used to identify and discard noise events in cWB
analyses. Noise and signal reduction levels were examined in single detector
networks (L1 and H1) and two detector network (L1H1). The FAR was reduced by a
factor of $\sim 10$ to $\sim 100$, there was an enhancement in the statistical
significance of $\sim 1$ to $\sim 2\sigma$, while there was no impact in
detection efficiencies.

##  I Introduction

The search and characterization of gravitational wave (GW) bursts with the
network of laser interferometers LIGO Aasi  _et al._ (2015), VIRGO Acernese
_et al._ (2015) and KAGRA Aso  _et al._ (2013) need to address issues such as
discrimination between GW events and noise artifacts, reconstruction of the GW
waveforms, and localization of the source in the sky. In the case of GWs
generated by binary black holes (BBH) and binary neutron stars (BNS), the
existing algorithms benefits from having highly deterministic signal models,
and thus, searches are based on match-filtering detector strain data with
available template signals (see for example Abbott  _et al._ (2019a, 2020a)).

Core-collapse supernovae (CCSNe) are also a primary detection target in the
upcoming LIGO and VIRGO observing runs. CCSNe are of special interest because
the electromagnetic radiation and emission of neutrinos along with GWs will
provide new hints to understand their formation mechanism and dynamic, and
also will lead to novel insights in multimessenger astronomy. The morphology
of GWs from CCSNe is predominantly stochastic with some deterministic
components like the growing trend of the central frequency of the fundamental
g-f mode or the characteristic waveform during the core bounce emission in
rapidly rotating progenitors. Furthermore, the production of templates from
three-dimensional (3D) state-of-the-art numerical simulations is computational
extremely expensive, including the fact that multiple run simulations for same
progenitor might produce slightly different morphologies, even if this
limitation does not apply to the core bounce component of rapidly rotating
progenitors that could be described by deterministic template banks Richers
_et al._ (2017). These limitations are the main reasons why unmodeled or
weakly modeled searches are so far the only approaches considered for CCSNe
GWs Abbott  _et al._ (2020b); Szczepańczyk  _et al._ (2021).

Coherent WaveBurst (cWB) is a standard method for the search and
characterization of GWs using data collected by the LIGO and VIRGO detectors
without imposing assumptions about the signal morphology Drago  _et al._
(2021). To detect unmodelled GW transients, cWB identifies coincident excess-
power between the strain data in the network of detectors using wavelet-based
analyses Necula  _et al._ (2012). Such coincidence between multiple detectors
allows to identify and reject noise events since they are present in only one
of the detectors. The method also reconstructs the waveform of the detected GW
and estimates some signal parameters Klimenko  _et al._ (2005, 2008, 2016).
cWB has been an essential computational tool in the detection of many GW
transients from binary systems discovered so far Abbott  _et al._ (2016a, b,
2020c); Szczepanczyk  _et al._ (2020); Abbott  _et al._ (2020d), and has been
a core method in all-sky and targeted searches of burst GW signals in the
previous LIGO and VIRGO observing runs Abbott  _et al._ (2016c, 2018, 2017,
2019b, 2020b). Furthermore, cWB will play a critical role in the detection of
CCSNe GWs in the upcoming fourth and fifth observing runs (O4 and O5) with the
LIGO, VIRGO, and KAGRA (LVK) network Szczepańczyk  _et al._ (2021).

The search of GWs emitted by CCSNe possesses other difficulties in addition to
the inherent uncertainties in the waveform models. The production of candidate
events is mostly driven by excess energy instances that can be related to
stationary or non-stationary noise components. For small signal-to-noise ratio
(SNR) the stationary ones produce most of the events, while non-stationary
ones (usually termed non-Gaussian glitches) dominate the large SNR values.
Morphologically both type of noise events tend to carry specific signatures of
the physical causes that generated them. The rate of more rare glitches has
been largely reduced (see for example ref. Abbott  _et al._ (2020b)) by
requiring a temporal coincidence and some morphological similarity between
different interferometers (as encoded in the so-called $cc$ coefficient of
cWB). However, if we have only one interferometer collecting data, temporal
coincidence and morphological consistency are not available. But even in the
case of a network of detectors, the population of non-Gaussian glitches can
have a rate sufficiently large to be a limiting factor in obtaining a large
statistical confidence in the detection.

The events formed by cWB at small SNR tend to show a fairly compact time
frequency structure that would be independent of the sources, however for
increasing amplitudes the morphology can become more varied. The detector
characterization group of the LVK network operate routinely to classify the
morphology of different glitches Davis  _et al._ (2021) and some of them, like
the so-called blip glitches can strongly resemble the core bounce waveform for
rapidly rotating progenitors Szczepańczyk  _et al._ (2021). Even if cWB makes
use of internal morphological tests with multiple interferometers (especially
for extragalactic source locations), all the opportunities to improve either
the detection confidence, the detection range or both need to be taken. These
issues encourage to identify more morphological metrics to distinguish CCSNe
events from noise events, especially for loud glitches that can reduce the
statistical confidence of a detection even when they are not temporally
overlapped to the detection candidate. Machine learning (ML) methods offers
one of these opportunities and this paper is part of systematic the
explorations of its potential.

In recent times, ML along with the special class of deep learning (DL) models
have attracted a lot of attention to tackle several problems in the realm of
GWs Cuoco  _et al._ (2020), for instance, to discriminate between noise and GW
signals either from binary systems Gabbard  _et al._ (2018); George and Huerta
(2018); Morales  _et al._ (2021); Torres-Forné  _et al._ (2016); Wang  _et
al._ (2020) or from CCSNe Astone  _et al._ (2018); Chan  _et al._ (2020); Iess
_et al._ (2020); López  _et al._ (2021), and to identify and remove transient
noise events using strain data or auxiliary channels Powell  _et al._ (2017);
Biswas  _et al._ (2013); Razzano and Cuoco (2018); Vajente  _et al._ (2020).
Notably, ML models also have been used to enhance cWB performance, in
specific, to distinguish between glitches and GW signals from BBH Gayathri
_et al._ (2020), to construct a statistical veto based on the recognition of
noise events to improve the detection efficiencies of GWs from BBH Mishra  _et
al._ (2021), and to achieve higher detection sensitivity of GW signals from
CCSNe using signal enhancement Mukherjee  _et al._ (2017, 2021). ML models, in
specific genetic programming algorithms, had been previously investigated to
discriminate CCSNe GW signals from noise transients for the case of single
detector searches Cavaglià  _et al._ (2020). This is significant because it
has been shown that there are periods of time during the observing runs for
which only one detector in the network is in operational conditions and
collecting science-quality data Cavaglià  _et al._ (2020). Indeed, $\sim$30%
of the collected strain data during the first observing runs has been from one
detector only Vallisneri  _et al._ (2015). Along this line, this paper
investigates the benefits of supervised ML as a follow-up method of cWB that
discriminates between noise and signal events in searches of GWs from CCSNe.
We extended the previous approach Cavaglià  _et al._ (2020) by investigating
the noise reduction in two detector network and assessing its effects in the
detection range for extragalactic CCSNe; using classification algorithms that
rely on a discriminant function that do not require stochastic initialization
of parameters and iterative executions thus avoiding to perform several
training repetitions or the selection of a sub-optimal solution, as in the
case of classifiers based on genetic approaches.

To discriminate between noise and signal triggers, we used as features a set
of cWB reconstruction parameters such as duration and central frequency, and
the supervised classification models linear discriminant analysis (LDA) and
support vector machines (SVM). Detected noise events are discarded, thus
reducing the rate of false detections. We carried out systematic studies to
assess to quantify the effective improvement in the false alarm rate (FAR) and
in the statistical significance with networks of one or two detectors using
strain data from the O3a observing run, and with several recent CCSNe GW
waveforms from 3D simulations. These studies considered robustness tests where
the ML is tuned with a distribution of noise and signal triggers extracted
from a stretch of data and then it is applied and tested in a different
stretch of data. The manuscript is organized as follows. Section II describes
the cWB analyses carried out to generate distributions of noise and signals
triggers and the LDA and SVM classification models used to recognize between
noise and CCSNe GW signal events. Section III presents the results of the
studies devoted, first to assess the noise reduction and signal lost rates
produced by the classification models, and second to ascertain the actual
improvement in the FAR and the statistical significance. Section IV presents
conclusions and future directions.

##  II Methods

###  II.1 cWB analysis

Table 1:  Total time and the background (non-zero lag) time of each network of detectors (L1, H1 and L1H1) for the three stretches of open O3a LIGO data. Time window | TW1 | TW2 | TW3
---|---|---|---
Initial time | 2019-06-17T00:00:01 | 2019-06-25T00:00:01 | 2019-08-26T00:00:01
Final time | 2019-06-19T23:59:59 | 2019-06-27T23:59:59 | 2019-08-28T23:59:59
Network | Total time | Background time | Total time | Background time | Total time | Background time
L1 | 1.73 days | - | 1.62 days | - | 2.18 days | -
H1 | 1.77 days | - | 1.66 days | - | 2.38 days | -
L1H1 | 1.50 days | 4.6 years | 1.06 days | 3.3 years | 1.96 days | 6.2 years

In this study we used LIGO strain data from the first half of the third
observing run (O3a). cWB analyses were carried out independently in three
stretches of open data (i.e., three time windows named TW1, TW2 and TW3) with
a duration of three days each. For the case of CCSNe GWs, the search is
typically driven by optical observations where the time window ranges from
hours to days, while it is a few seconds in the potential case of neutrino
flux driven searches. Hence, three days was chosen as a representative window
duration of how much we would be able to constrain the GW emission from
electromagnetic observations and a relatively rapid discovery of the CCSNe.
All cWB analyses were carried out separatelly with one and two detectors
network (L1, H1, and L1H1) with the aim of studying the rate of false
detection (background analysis), the detectability of CCSNe GWs (sensitivity
analysis), and to generate datasets of noise and signal events to train and to
test the classification algorithms. Table 1 shows the total time of the three
time windows for each network of detectors used in this study.

####  II.1.1 cWB Background

With more that one detector, the data from one detector is shifted with
respect to the other in a time length that has to be longer than the GW travel
time between detectors ($\sim$10ms between L1 and H1). This time-shift
procedure is repeated multiple times to obtain a total background search time
(also called non-zero lag time) long enough to attach a certain statistical
significance. All detected events from this analysis are of non-astrophysical
origin and therefore correspond to false detections or noise events. Then, the
FAR can be estimated simply as the ratio between the number of detected events
and the total background time. Table 1 also shows the total background time of
the three time windows considered in this study. Note that with only one
detector available in the network the time-shifting is not possible, neither
coincident test to remove glitches can be performed. This drastically worsen
the FAR in comparison with networks of two or more operational detectors.

In the cWB background analysis, the FAR is produced for different values of
the network SNR or $\rho$, yielding to the FAR versus $\rho$ curves. Note that
for the case of a single interferometer, $\rho$ is equivalent to the SNR of
the available detector. The statistical significance is computed in terms of
the false alarm probability (FAP) as follows Abbott  _et al._ (2020b):

$FAP=1-e^{T_{on}\times FAR},$ (1)

where $T_{on}$ is the on-source window where a GW signal is searched for.

Results for the background analysis in the time window TW1 are presented in
figure 1. Note how the FAR (figure 1a) is considerably higher with one
detector than with two detectors. Likewise, the corresponding values of the
FAP (figure 1b, where the $\rho$ threshold was set to 5) for the case of a
search in a on-source window of 1s reveals a statistical significance barely
close to $3\sigma$, and a quite higher significance close to $5\sigma$ for the
two detector network. This illustrates the need of a follow-up method to
identify and discard noise events (not only in single detector based searches
but also in searches with two detectors) which reduces the FAR and improves
the statistical significance of the search.

|  |
---|---|---
(a) | (b) | (c)
Figure 1:  cWB search results for the cases of single detector network (L1 and
H1) and two detectors network (L1H1) using strain data in the time window TW1.
(a) False Alarm Rate (FAR) versus the $\rho$ statistic from the background
analysis. (b) False alarm rate (FAR) versus False Alarm Probability (FAP) for
the case of a on-source window of 1 second. (c) Detection efficiency (DE) with
respect to the source distance achieved with the CCSNe GW “he3.5” from Powell
et al. 2019 for a corresponding FAR of $2.74\times 10^{-2}$, $2.47\times
10^{-2}$ and $9.30\times 10^{-6}$ Hz for L1, H1, and L1H1, respectively.

####  II.1.2 cWB sensitivity

The goal in this analysis is to determine the sensitivity in the search of
known CCSNe GWs, and to obtain a distribution of signal events. Here,
waveforms are systematically added into detector noise data, rescaled to
different amplitudes corresponding to diverse source distances, and at
different time delays between detectors corresponding to diverse source sky
locations. For the case of single detector network, the injection is carried
out only in the available detector and thus no time delay is required.
Subsequently, the search of GWs is carried out and the detection efficiency
(DE) is simply measured as the fraction of successfully detected GWs. DE is
computed for each injected type of GW and for each distance to construct DE
versus source distance curves.

All simulation analyses were done at different source distances from 0.1 up to
10kpc. Furthermore, several families of CCSNe GWs were used (see next
subsection). Results for the analysis around time window TW1 are presented in
figure 1c for the case of the waveform named “he3.5” from Powell and Müller
(2019). These DE curves are for a FAR of $2.74\times 10^{-2}$, $2.47\times
10^{-2}$ and $9.30\times 10^{-6}$ Hz for L1, H1, and L1H1, respectively. This
result shows how the efficiency reduces as the distance increases, and quite
similar performance for all network of detectors. Despite the good and steady
sensitivity irrespective of the number of detectors, the low statistical
significance imply not only to recognize the noise events with high accuracy,
but also to not to affect these detection efficiencies.

####  II.1.3 CCSNe GW waveforms

To carry out simulation analyses, freely-available CCSNe GWs from recent 3D
simulations were selected to be added into noise data. We selected recent
families of CCSNe GW waveforms that were used in the all-sky search of short
GW bursts in O3 Abbott  _et al._ (2021), and that were part of the recent
study devoted to investigate the detectability of GWs from CCSNe in the
upcoming fourth and fifth observing runs Szczepańczyk  _et al._ (2021). In
specific, we used the following waveform families representing a wide variety
of physical phenomena and modeling methods:

  * •

Scheidegger et al. 2010. This a large set of GWs obtained in 3D-simulations of
magnetohydrodynamic (MHD) driven explosions with diverse rotating progenitors
Scheidegger  _et al._ (2010). For this work we considered three representative
GWs generated by a progenitor start of 15$M_{\odot}$ with different rotational
speeds and with neutrino leakage scheme, R1E1CA_L (slowly rotating), R3E1AC_L
(moderate rotating), and R4E1FC_L (rapidly rotating).

  * •

O’Connor et al. 2018. This is a family of seven GWs generated by a
20$M_{\odot}$ progenitor star mass O’Connor and Couch (2018). The simulations
considered neutrino physics and the resulting GW signatures exhibit strong
g-modes and SASI components. The name of the seven waveforms are mesa20,
mesa20_LR, mesa20_pert, mesa20_pert_LR, mesa20_v_LR, mesa20_2D, and
mesa20_2D_pert.

  * •

Powell et al. 2019. This is set of two GWs (named he3.5 and sl8) that were
computed from simulations considering low to regular energies in the explosion
mechanisms Powell and Müller (2019). They are non-rotating models with 3.5
helium core solar masses after the star has lost its outer layers due to
binary interactions for model he3.5 and with a a zero age main sequence (ZAMS)
of 18$M_{\odot}$ for model sl8. The GW waveforms exhibit the typical frequency
rise associated with emission of g-modes.

  * •

Powell et al. 2020. This family of three GWs were obtained from simulations
including explosion properties of the progenitor star Powell and Müller
(2020). The name of the waveforms are m39, s18np, y20. The first model is from
a rapidly rotating progenitor of 39$M_{\odot}$, while the other two are from
non-rotating progenitors of 18 and 20$M_{\odot}$. The model s18np has the same
progenitor as the model s18 in Powell et al. 2019, but it does not include
perturbations (np).

  * •

Mezzacappa et al. 2020. This is a single GW named C15-3D generated by a
15$M_{\odot}$ progenitor start that includes a neutrino-driven convection
mechanisms Mezzacappa  _et al._ (2020). The GW signature presents low- and
high-frequency components and SASI emission.

###  II.2 Features

The features used to feed the classification algorithms to be able to
discriminate between noise and signal events are reconstruction parameters
provided by cWB for each event. We used the same set of parameters proposed in
Cavaglià  _et al._ (2020) which are representative to describe the duration,
frequency and time-frequency characteristics of the reconstructed GW burst
transients:

  * •

$\rho$: cWB detection statistic.

  * •

Volume: number of time-frequency pixels composing the event.

  * •

Duration 1 and Duration 2: time length of the event computed from the energy-
weighted and from the reconstructed waveform.

  * •

Frequency 0 and Frequency 1: central frequency of the event computed from the
energy-weighted and from the reconstructed waveform.

  * •

Low and High: minimum and maximum frequency of the time-frequency map pixels.

  * •

Bandwidth 1 and Bandwidth 2: bandwidth estimated from the energy-weighted and
from the time-frequency map.

  * •

Norm: effective number of time-frequency resolutions used for GW
reconstruction.

Hence, the vector of features is $\textbf{x}\in\mathbb{R}^{N_{f}\times 1}$
where $N_{f}$ is the number of reconstruction parameters extracted from each
event.

###  II.3 Classification algorithms

The classifier is a computational model that takes as input a vector of
features extracted from a cWB event, and assigns to it one class label
indicating “noise” or “signal”. Common and robust classification models used
in diverse applications are Linear Discriminant Analysis (LDA) and Support
Vector Machines (SVM). These classifiers allow to identify a linear or non-
linear separation hyper-surface in such a way that the class assigned to a
input vector of features depends on which region the vector is located Duda
_et al._ (2001). They consist of a discriminant function defined by
$\textbf{w}^{T}\cdot f(\textbf{x})=0$, where
$\textbf{x}\in\mathbb{R}^{N_{f}\times 1}$ is the vector of $N_{f}$ features,
$f(\cdot)$ is a transformation function, and
$\textbf{w}\in\mathbb{R}^{N_{f}\times 1}$ is a vector of classification
weights (i.e., discriminant vector) that have to be calculated from a training
dataset $\\{\textbf{x}_{i},y_{i}\\},i=1,...,N$, where $y_{i}$ indicates
whether $\textbf{x}_{i}$ is a feature vector extracted from a noise or a
signal event, and $N$ in the number of instances.

LDA defines the transformation function as $f(\textbf{x})=\textbf{x}$, thus it
is only able to construct linear separation surfaces since the discriminant
function becomes $\textbf{w}^{T}\cdot\textbf{x}=0$ Bishop (2006) . In this
classifier, the discriminant vector w is estimated by seeking the projection
that maximizes the difference between the means of the classes while minimizes
their variance (leading to a classification model that is optimal when the two
classes are Gaussian with equal co-variance). Thus, the hyper-surface is found
by solving this optimization problem:

$\widehat{\textbf{w}}=\stackbin[\textbf{w}]{}{arg\,max}\frac{\textbf{w}^{T}\,\textbf{S}_{B}\,\textbf{w}}{\textbf{w}^{T}\,\textbf{S}_{W}\,\textbf{w}},$
(2)

where $\textbf{S}_{B}$ is the between-class co-variance matrix and
$\textbf{S}_{W}$ is the within-class co-variance matrix Bishop (2006).

SVM is able to compute linear or non-linear separation surfaces in such a way
that maximizes the separation between the hyper-surface and the nearest data
points of each class which are called support vectors Cortes and Vapnik
(1995). This involves solving the following optimization problem:

$\widehat{\textbf{w}}=\stackbin[\textbf{w},\xi]{}{arg\,min}\frac{1}{2}\|\textbf{w}\|^{2}+C\sum_{i=1}^{n}\xi_{i},$
(3)

subject to the condition
$y_{i}\left(\textbf{w}^{T}f(\textbf{x}_{i})\right)\geq 1-\xi_{i},\forall
i=1,...,N$, where $\xi_{i}\geq 0$ measure the error in the misclassification
of $\textbf{x}_{i}$. The separation hyper-plane is linear when
$f(\textbf{x})=\textbf{x}$, leading to the linear SVM (or SVML). On the
contrary, non-linear separation boundaries are obtained through a kernel
function. The most common kernel is the radial basis function (RBF), which
leads to a non-linear SVM with RBF (or SVMR),

In this work, we first used LDA, SVML and SVMR to test the discrimination
between noise and signal events, and then, we selected the one with the higher
performance in order to assess the actual improvement produced by
classification model as a follow-up method in offline cWB searches.

##  III Results

|
---|---
(a) | (b)
Figure 2:  Classification results from the cross-validation analysis obtained with the dataset of triggers extracted from the time window TW1 in detector networks H1, L1, and L1H1. (a) Distribution of classification rates (TNR and FNR) for the case of signal triggers from all families of GW and from all distances combined. (b) Mean and standard deviation values of classification rates (TNR and FNR) for the case of signal triggers from all families of GW and for each distance individually. All these results were obtained when using the classification algorithm SVMR.  |  |
---|---|---
|  |
|  |
(a) | (b) | (c)
Figure 3:  Distribution of classification metrics (TNR and FNR) obtained with
(a) the three different CCSNe time windows, (b) each family of CCSNe GW, and
(c) the three classification algorithms. These results are for the case of the
single detector network L1 (upper panel), H1 (central panel) and L1H1 (lower
panel).

###  III.1 Training/Testing with data from the same time window

As a first step to investigate the classification between noise and signal
triggers we perform both the training and testing with information from the
same stretch of strain data, i.e., noise and signal triggers used to train and
test the classification model are from the same background and simulation
analyses. To do so, a cross-validation process was employed to assess
classification performance. The process was implemented as follows: $(i)$
randomly split the dataset of noise and signal triggers into $K$ non-
overlapping subsets or folds; $(ii)$ use the data from $K-1$ subsets for
training and the data from the remaining subset for testing (note that data
for training and testing are always mutually exclusive); $(iii)$ use the
training set to calculate the parameters of the classification model; $(iv)$
fed the classification model with all the triggers from the test set and
compute performance metrics by comparing the output labels provided by the
classifier with the corresponding true labels; $(v)$ repeat steps $(ii)$ to
$(iv)$ until all the $K$ combinations of train and test data are exhausted.

This cross-validation process with $K=5$ was repeated 10 times to be able to
compute distributions of the classification performance metrics. Prior to the
training of the classification model, the number of noise and signal triggers
in the training set is balanced to avoid overfitting to one of the classes,
moreover, the training data was normalized according to
$x_{i}=(x_{i}-\mu_{i})/\sigma_{i}$, $(i=1,2,\cdots,N_{f})$ where $\mu_{i}$ and
$\sigma_{i}$ are the mean and standard deviation of the $i$-th feature which
are computed exclusively from training data. The normalization is later
applied to to each feature vector in the test set.

To assess performance the following metrics were computed: true negative rate
(TNR) or specificity (i.e., correct classification percentage of noise events)
and false negative rate (FNR) (i.e., percentage of signal triggers incorrectly
classified as noise triggers). TNR is expected to be large to reduce the FAR,
while FNR is expected to be small to not affect the efficiency. Classification
analyses were carried out separately for each variant of:

  * •

Detector network: L1, H1 and L1H1.

  * •

Time window of strain data: TW1, TW2, and TW3 (see table 1).

  * •

Distance: 1.00, 1.33, 1.78, 2.37, 3.16, 4.22, 5.62, 7.5, 10kpc, and all those
distances together.

  * •

Family of CCSNe GW: Scheidegger et al. 2010, O’connor et al. 2018, Powell et
al. 2019, Powell et al. 2020, and Mezzacappa et al. 2020) and from all those
families together.

  * •

Classification models: LDA, SVML, SVMR.

Table 2:  Percentage of noise and signal reduction obtained by the three detector networks for each familiy of CCSNe GW waveforms and for several distances of signal triggers. These results are dataset of noise and signal triggers extracted from the time window TW1. For the two detector network there are missing results because it was not possible to train and test the classification model since no signal triggers were obtained in the simulation analysis. | 1kpc | 2.37kpc | 4.22kpc | 7.5kpc | 10kpc | All
---|---|---|---|---|---|---
| Noise | Signal | Noise | Signal | Noise | Signal | Noise | Signal | Noise | Signal | Noise | Signal
L1 |
Scheidegger at al. 2010 | $99.6$ | $5.4$ | $99.6$ | $9.5$ | $99.4$ | $13.4$ | $99.0$ | $16.5$ | $98.7$ | $18.5$ | $99.0$ | $7.0$
O’connor at al. 2018 | $97.0$ | $20.9$ | $93.4$ | $35.7$ | $91.9$ | $39.0$ | $90.9$ | $39.3$ | $91.5$ | $39.0$ | $97.5$ | $24.3$
Powell at al. 2019 | $99.4$ | $16.2$ | $98.4$ | $18.5$ | $96.7$ | $22.1$ | $93.7$ | $29.6$ | $92.5$ | $34.5$ | $99.5$ | $15.8$
Powell at al. 2020 | $98.8$ | $8.2$ | $97.5$ | $12.8$ | $96.7$ | $16.5$ | $95.8$ | $20.3$ | $95.5$ | $22.4$ | $97.9$ | $10.4$
Mezzacappa at al. 2020 | $99.2$ | $18.1$ | $97.2$ | $23.7$ | $94.0$ | $35.8$ | $93.5$ | $39.5$ | $93.0$ | $39.1$ | $98.9$ | $20.8$
All | $97.6$ | $16.1$ | $96.7$ | $23.0$ | $95.3$ | $25.7$ | $93.4$ | $29.7$ | $93.8$ | $32.2$ | $97.5$ | $16.6$
H1 |
Scheidegger at al. 2010 | $99.0$ | $4.3$ | $98.9$ | $9.1$ | $98.8$ | $12.6$ | $98.5$ | $15.2$ | $98.2$ | $16.5$ | $98.6$ | $6.4$
O’connor at al. 2018 | $96.6$ | $23.3$ | $93.4$ | $32.7$ | $93.8$ | $33.2$ | $93.5$ | $33.0$ | $93.8$ | $33.7$ | $97.8$ | $22.9$
Powell at al. 2019 | $99.4$ | $15.1$ | $97.8$ | $18.7$ | $96.2$ | $24.5$ | $93.5$ | $31.4$ | $92.3$ | $33.0$ | $98.9$ | $15.9$
Powell at al. 2020 | $97.9$ | $7.7$ | $96.3$ | $14.0$ | $94.4$ | $16.6$ | $93.7$ | $19.2$ | $93.7$ | $20.9$ | $97.3$ | $10.9$
Mezzacappa at al. 2020 | $99.2$ | $18.2$ | $96.2$ | $27.3$ | $93.5$ | $33.2$ | $93.8$ | $33.3$ | $93.1$ | $33.5$ | $98.6$ | $20.1$
All | $97.1$ | $17.4$ | $95.6$ | $22.1$ | $94.1$ | $25.0$ | $93.2$ | $27.4$ | $93.1$ | $28.2$ | $97.2$ | $17.2$
L1H1 |
Scheidegger at al. 2010 | $98.6$ | $2.2$ | $99.7$ | $1.0$ | $99.9$ | $0.9$ | $99.7$ | $0.1$ | $99.7$ | $0.2$ | $99.5$ | $1.9$
O’connor at al. 2018 | $98.7$ | $1.3$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $99.4$ | $1.1$
Powell at al. 2019 | $100.0$ | $0.3$ | $99.3$ | $0.3$ | $99.0$ | $0.3$ | $95.9$ | $0.8$ | $-$ | $-$ | $99.8$ | $0.1$
Powell at al. 2020 | $99.8$ | $0.1$ | $99.3$ | $1.5$ | $98.5$ | $3.2$ | $98.7$ | $5.0$ | $98.2$ | $7.0$ | $99.4$ | $1.9$
Mezzacappa at al. 2020 | $100.0$ | $0.4$ | $99.3$ | $0.5$ | $-$ | $-$ | $-$ | $-$ | $-$ | $-$ | $100.0$ | $0.4$
All | $99.5$ | $0.9$ | $99.0$ | $1.3$ | $98.7$ | $3.3$ | $98.2$ | $7.5$ | $96.1$ | $8.5$ | $99.0$ | $2.2$

Figure 2a shows the correct noise classification rate (TNR) and the incorrect
signal classification rate (FNR) obtained with the dataset from the time
window TW1 separately with detector networks H1, L1, and L1H1. These results
are for the case of signal triggers from all distances and from all families
of CCSNe GW, which represents the most difficult situation for a
classification model because they combine signal triggers with different SNR
and with different GW signatures. The percentage of noise triggers that are
correctly classified is on average $97.6\pm 0.6$, $97.2\pm 0.5$ and $99.4\pm
0.6$% for detector networks L1, H1 and L1H1, respectively. This indicates very
high specificity (nearly 100%) with very low variability (less than 0.6%)
irrespective of the number of detectors in the network. On the contrary,
signal triggers are lost, on average, $16.6\pm 1.2$, $17.2\pm 1.4$ and $2.2\pm
0.9$% for detector networks L1, H1 and L1H1, respectively. These results shows
a very high noise reduction irrespective of the detector network and low
signal lost especially for the detector network with two interferometers.

To examine the effect of the distance, figure 2b shows the classification
results obtained with signal triggers from each distance separately. As the
distance increases, correct noise classification (TNR) decreases while signal
misclassification (FNR) increases and the proportion of lost signals increases
faster than the decrease in correct noise classification. This is due to the
fact that as the distance increases the SNR of the GW signals decreases, and
therefore it becomes more difficult to discriminate between noise and signal
triggers because they tend to have similar characteristics.

The results presented in figure 2 a and b include signal triggers from all GW
families considered herein, which represent the case with the more variability
in the characteristics of signal triggers. Similar results and observations
were drawn with analysis carried out with datasets of noise and signal
triggers obtained from time windows TW2 and TW3. Altogether, these results
shows that a better classification between noise and signal triggers with the
network of two detectors L1H1, and the lower performance with the network of
one detector H1.

Figure 3 shows the classification results from the cross-validation analysis
for the three time windows, each family of CCSNe GW, and for the three
classification algorithms. First, with regard to the three stretches of strain
data (Figure 3a), high noise detection and low signal misclassification was
obtained in the three cases, and there is a similar distribution of the
performance metrics. Second, there is some variable classification performance
considering the family of CCSNe GW (Figure 3b). In particular, using signal
triggers from O’Connor et al. 2018 yielded to a lower noise detection and
higher signal lost, while triggers from Scheidegger et al. 2010, Powell et al.
2019 and Powell et al. 2020 resulted in the best performance with the higher
TNR and lower FNR. Importantly, note that for the case of using signal
triggers from all families combined the performance metrics are distributed
within all families. Finally, regarding the comparison between classification
algorithms, all classifiers achieved similar and high rates of noise
reduction, however, the rate of signal lost varied across them, in particular,
SVMR presented the lower signal lost. In consequence, the non-linear SVMR
classifier was selected to be used is the subsequent analyses. The same
behavior of the noise reduction and signal lost is observed in all detector
networks (L1, H1 and L1H1), but the network of two detectors always presents
the best performance

A summary of the cross-validation results with the percentage of noise and
signal reduction for each network of detectors (L1, H1 and L1H1), for each
family of CCSNe GW, for different distances, and for the first time window of
data is presented in table 2. These results shows that classification
performance degrades as the distance increases, shows no large differences
across families of CCSNe GW and is higher for the two detector network.

|  |
---|---|---
|  |
(a) | (b) | (c)
Figure 4:  Distribution of noise and signal triggers before and after the
application of the classification model with CCSNe GWs from Powell et al.
2019. These results are for the cWB analysis in the time window TW2 for each
detector network (a) L1, (b) H1, and (c) L1H1. For each detector, the
classification model was tuned with the corresponding dataset of noise and
signal triggers extracted from time window TW1 with signal triggers from all
distances. Top panel shows the noise triggers while bottom panel shows the
signal triggers.

###  III.2 Training/Testing with data from different time windows

The single interferometer scenario highlight the problem of only having a
small amount of live time to tune the parameters of the ML model. This second
study aimed to assess the actual improvement (i.e., noise reduction) and the
potential drawback (i.e., signal reduction) given by the incorporation of the
ML model as a follow-up method in cWB offline searches of GWs from CCSNe.
Here, the classification model is learned with a dataset obtained from a given
cWB analysis, and then, it is used in a different cWB analysis. This allows to
effectively quantify the improvement in FAR and FAP, while also measuring the
impact in the DE. In addition, to assess the robustness to unknown GWs, the ML
model is tuned using all but one of families of GW signals, and then, it is
tested with the remaining family.

Once the classification model is applied to a offline cWB analysis, the
following performance metrics are computed: $(i)$ noise reduction rate (TNR),
and signal reduction rate (FNR); $(ii)$ FAR and FAP before and after the
application for the ML model; $(iii)$ DE before and after the application for
the ML model. Note that FAR, FAP and DE “before” refer to the original search
results provided by cWB, while FAR, FAP and DE “after” refer to the results
obtained with cWB in combination with the ML model. As in the first study,
analyses were carried out separately with each detector network (L1, H1,
L1H1), signal triggers from each distance and from all distances combined.

The results presented below are for the specific case of training the ML model
with triggers extracted from the cWB analysis in the time window TW1, whereas
the model is applied to the cWB analysis carried out in the time window TW2
using exclusively CCSNe GWs from Powell et al. 2019. Firstly, figure 4 shows
the distribution of noise and signal events before and after the application
of the ML model. Noise events are significantly reduced with only a small
proportion remaining after classification, indeed, noise reduction is 99.4%,
99.2%, and 100.0%, for L1, H1 and L1H1, respectively. At the same time, most
of the signal events remains after the application of the classifier since
there is low signal reduction of 15.7%, 14.3%, and 0.3%, for L1, H1 and L1H1,
respectively. This shows that irrespective of the detector network, a high
proportion of the noise triggers are removed while a small proportion of
signal triggers are lost. In addition, the higher noise reduction and the
lower signal lost were obtained with the two detector network.

|  |
---|---|---
|  |
(a) | (b) | (c)
Figure 5:  Results of the cWB background search in the time window TW2 before
(red) and after (green) the application of the classification model. Top panel
shows the false alarm rate (FAR) versus the signal-to-noise ratio ($\rho$),
and bottom panel shows the FAP versus false alarm rate (FAR) for the two
representative cases in the search of GWs from CCSNe (on-source of 1s
resembling a neutrino-driven search, and a on-source of 1day representing a
optical-targeted search). These results are for each detector network, (a) L1,
(b) H1, and (c) L1H1. For each detector network, the classification model was
trained with the corresponding dataset of triggers extracted from the time
window of TW1 and with signal triggers from all distances.

Secondly, figure 5 shows the FAR versus $\rho$ (or SNR for the case of single
interferometer), and the FAP versus FAP before and after the application of
the classifier. These are crucial results to determine the actual improvement
produced by the incorporation of the classifier as a follow-up method.On the
one hand, figure 5a shows a clear FAR reduction, especially in low values of
$\rho$. For the specific operating point of the cWB search (i.e., network
$\rho=5$), the FAR before/after the classification model is $2.97\times
10^{-2}$/$1.78\times 10^{-4}$, $2.53\times 10^{-2}$/$1.95\times 10^{-4}$, and
$9.76\times 10^{-6}$/$9.58\times 10^{-9}$ for L1, H1, and L1H1, respectively.
This indicates that the FAR is effectively lowered in a factor of up to $\sim
170$, $\sim 130$, and $\sim 1019$. On the other hand, figure 5b shows the
false alarm probability (FAP) before and after for on-source windows of 1s
(representing a potential neutrino driven search) and of 1day (representing a
optically targeted search). For the single detector network, the FAP
improvement is about $1.5\sigma$ in the case of a on-source window of 1s,
while no improvement was achieved in the case of a on-source window of 1day.
In contrast, with the two detector network there is FAP improvement is about
$1\sigma$. We stress that these results represent the most difficult situation
to tune and to test the classification model since it involves signal triggers
of different distances, and because, the ML model is recognizing unknown GW
waveforms that were not employed in the training.

|  |
---|---|---
(a) | (b) | (c)
Figure 6:  Results of the cWB simulation analysis for the time window TW2
before (red) and after (green) the application of the classification model.
These results are the detection efficiency (DE) versus distance for each
detector network, (a) L1, (b) H1, and (c) L1H1, obtained with the CCSNe GW
he3.5 from Powell et al. 2019. The FAR before/after the classification model
is $2.97\times 10^{-2}$/$1.78\times 10^{-4}$, $2.53\times 10^{-2}$/$1.95\times
10^{-4}$, and $9.76\times 10^{-6}$/$9.58\times 10^{-9}$ for L1, H1, and L1H1,
respectively. Again, for each detector network the classification model was
trained with the corresponding dataset of triggers extracted from the time
window DC1 and with signal triggers from all distances.

Figure 6 shows the DE versus distance before and after the application of the
classification model for the CCSNe GW he3.5 from Powell et al. 2019 which
enables to quantify the actual impact of the classifier. There is a minimum
signal reduction for single detector network and almost null effect for two
detector network. Horizontal lines allow to identify the distances with 90, 50
and 10% of efficiency. For L1 and H1, there is no effect in the distance with
10% of DE, while there is minimum reduction in the distance for 90 and 50% DE.
For L1H1, no effect in the distances is observed. We conclude that for single
detector networks there is marginal impact in the detection efficiency whereas
there is no effect at all for the two detector network.

For the cWB analysis in time window TW2, table 3 shows the noise and signal
reduction whereas table 4 shows FAR improvement factor. As in the previous
study, noise detection reduces and signal lost increases for larger distances
and varies across the families of CCSNe GW. Also, the two detector network
provides the better performance with the higher noise reduction rates and
lower signal reduction rates. Equivalently, FAR improvement factor is higher
for lower distances, and there are cases in which all noise triggers are
completely identified and therefore the FAR after the classification is
applied reaches its minimum value of the one over the background time.

##  IV Conclusions

This work investigated the use of supervised machine learning (ML) methods to
recognize between noise and signal events using a set of reconstruction
parameters from cWB outputs. This constitutes a follow-up method devised to
recognize and discard noise events while preserving signal events, which is
essential to reduce the FAR and to increase the range of detection.

Table 3:  Percentage of noise and signal reduction obtained by the three detector networks and for several distances of signal triggers. These results are for the time window TW2 and for each familiy of CCSNe GW waveforms. The classification model is trained from the dataset of noise and signal triggers obtained from the cWB analysis in the time window TW1. For the two detector network there are missing results because it was not possible to train and test the classification model since no signal triggers were obtained in the simulation analysis. | 1kpc | 2.37kpc | 4.22kpc | 7.5kpc | 10kpc | All
---|---|---|---|---|---|---
| Noise | Signal | Noise | Signal | Noise | Signal | Noise | Signal | Noise | Signal | Noise | Signal
L1 |
Scheidegger et al. 2010 | $99.6$ | $4.9$ | $99.8$ | $8.4$ | $99.8$ | $12.7$ | $99.3$ | $16.4$ | $98.7$ | $17.7$ | $99.4$ | $8.3$
O’connor at al. 2018 | $96.8$ | $19.7$ | $93.3$ | $31.7$ | $92.0$ | $35.7$ | $91.7$ | $35.3$ | $91.0$ | $35.2$ | $97.4$ | $17.8$
Powell at al. 2019 | $99.3$ | $15.3$ | $98.3$ | $18.8$ | $97.1$ | $21.7$ | $93.6$ | $28.1$ | $91.9$ | $33.1$ | $99.4$ | $15.7$
Powell at al. 2020 | $98.8$ | $8.7$ | $97.3$ | $12.5$ | $95.4$ | $15.4$ | $94.5$ | $19.2$ | $93.9$ | $21.2$ | $97.7$ | $11.2$
Mezzacappa at al. 2020 | $99.2$ | $16.9$ | $96.8$ | $21.9$ | $94.2$ | $32.3$ | $93.9$ | $36.3$ | $93.2$ | $36.0$ | $99.1$ | $16.8$
H1 |
Scheidegger at al. 2010 | $99.6$ | $4.8$ | $99.4$ | $8.2$ | $99.3$ | $11.9$ | $99.1$ | $15.9$ | $99.1$ | $16.8$ | $99.3$ | $8.0$
O’connor at al. 2018 | $97.9$ | $22.4$ | $96.2$ | $39.2$ | $95.8$ | $40.2$ | $95.5$ | $40.4$ | $95.5$ | $40.2$ | $98.4$ | $17.8$
Powell at al. 2019 | $99.7$ | $15.3$ | $98.7$ | $18.6$ | $97.8$ | $25.4$ | $95.9$ | $37.8$ | $95.3$ | $40.2$ | $99.2$ | $14.3$
Powell at al. 2020 | $98.2$ | $6.9$ | $97.3$ | $12.1$ | $96.3$ | $16.3$ | $96.3$ | $20.4$ | $96.2$ | $22.2$ | $98.1$ | $11.6$
Mezzacappa at al. 2020 | $99.4$ | $16.0$ | $97.6$ | $27.5$ | $95.4$ | $39.4$ | $95.2$ | $40.3$ | $95.5$ | $40.8$ | $99.1$ | $15.9$
L1H1 |
Scheidegger at al. 2010 | $99.3$ | $1.0$ | $100.0$ | $1.5$ | $99.9$ | $0.8$ | $99.9$ | $0.0$ | $99.9$ | $0.1$ | $99.9$ | $1.7$
O’connor at al. 2018 | $99.4$ | $0.8$ | - | - | - | - | - | - | - | - | $99.7$ | $0.7$
Powell at al. 2019 | $100.0$ | $0.1$ | $99.9$ | $0.1$ | $99.4$ | $0.6$ | $98.2$ | $0.6$ | - | - | $100.0$ | $0.3$
Powell at al. 2020 | $99.8$ | $0.1$ | $99.2$ | $0.5$ | $98.3$ | $2.8$ | $98.4$ | $6.0$ | $98.1$ | $5.9$ | $99.6$ | $1.9$
Mezzacappa at al. 2020 | $100.0$ | $0.2$ | $99.7$ | $0.3$ | - | - | - | - | - | - | $100.0$ | $0.3$
Table 4:  Improvement factor in the FAR (i.e., FAR before / FAR after) achieved for the cWB analysis in the time window TW2. The classification model is trained from the dataset of noise and signal triggers obtained from the cWB analysis in the time window TW1. Missing values indicate that no classification model was learned since no triggers were available.  | 1kpc | 2.37kpc | 4.22kpc | 7.5kpc | 10kpc | All
---|---|---|---|---|---|---
L1 |
Scheidegger at al. 2010 | $260.7$ | $595.9$ | $417.1$ | $139.0$ | $74.5$ | $173.8$
O’connor at al. 2018 | $30.9$ | $14.8$ | $12.6$ | $12.1$ | $11.1$ | $38.6$
Powell at al. 2019 | $149.0$ | $57.9$ | $34.5$ | $15.7$ | $12.4$ | $166.8$
Powell at al. 2020 | $80.2$ | $37.2$ | $22.0$ | $18.1$ | $16.4$ | $43.9$
Mezzacappa at al. 2020 | $122.7$ | $31.4$ | $17.1$ | $16.4$ | $14.7$ | $115.9$
H1 |
Scheidegger at al. 2010 | $242.7$ | $173.4$ | $140.0$ | $107.1$ | $117.5$ | $134.8$
O’connor at al. 2018 | $48.5$ | $26.2$ | $23.6$ | $22.1$ | $22.1$ | $60.7$
Powell at al. 2019 | $364.1$ | $77.5$ | $45.0$ | $24.6$ | $21.2$ | $130.0$
Powell at al. 2020 | $55.2$ | $37.2$ | $27.4$ | $27.0$ | $26.6$ | $53.5$
Mezzacappa at al. 2020 | $158.3$ | $41.4$ | $21.9$ | $20.7$ | $22.1$ | $113.8$
L1H1 |
Scheidegger at al. 2010 | $145.6$ | $1019.0$ | $1019.0$ | $1019.0$ | $1019.0$ | $1019.0$
O’connor at al. 2018 | $169.8$ | - | - | - | - | $339.7$
Powell at al. 2019 | $1019.0$ | $1019.0$ | $169.8$ | $56.6$ | - | $1019.0$
Powell at al. 2020 | $509.5$ | $127.4$ | $59.9$ | $63.7$ | $53.6$ | $254.8$
Mezzacappa at al. 2020 | $1019.0$ | $339.7$ | - | - | - | $1019.0$

The proposed follow-up ML method to enhance cWB searches was analyzed in two
different studies. The first aimed to ascertain the classification accuracy
between noise and signal events (i.e., noise and signal reduction rates),
while the second aimed to quantify the actual improvement in the statistical
significance (i.e., reduction in FAR and FAP for the cases of on-source
windows of 1 second and 1 day which represent a potential neutrino flux and
optically targeted searches, respectively) and the impact in the detection
efficiency. The two studies considered different conditions as the number of
detectors in the network (L1, H1, and L1H1); three stretches of open O3a train
data; diverse distances of signal events; various CCSNe GW families with
diverse characteristics; and three classification algorithms. Overall, the
results of these studies and variety of conditions showed high noise reduction
rates greater than 90% and low signal misclassification rates lower than 10%.

Importantly, in our analyses we quantified the impact bring by the ML model in
cWB offline searches. The recognition and discharging of noise triggers from
cWB outputs reduces the FAR in a factor of $\sim 10$ for one detector (or even
more for some families of GWs), and in a factor of $>100$ for two detectors in
the network. Notably, these FAR reductions are equivalent to an improvement in
the statistical significance of $\sim 1.5\sigma$ with one detector and even
more with two detectors for the case of a on-source windows of 1 second. For
the case of optically targeted searches with on-source windows of 1 day, on
the other hand, the FAR reduction yields to a $>1\sigma$ improvement with a
two detector network.

The variety of explored conditions allowed to study several important aspects.
First, comparing the classification performance when tuning the ML model with
a single or with various families of CCSNe GW showed no large differences in
performance. This shows the robustness of the ML approach with respect to
different types of CCSNe GW signatures, and points out that the morphology of
noise and signal triggers are effectively distinguishable irrespective of the
GW signals used to train and to test the classifier.vThis is noteworthy since
in practice the ML model must be tuned with a pool of synthetic GWs obtained
for example through numerical simulations (as is done in this work), but its
usage in a real situation implies correctly identifying signal events
generated by actual GWs that will not exactly match GWs used to train the
model. Secondly, there are high noise reduction rates with low signal
reduction rates irrespective of the number of detectors in the network, though
the classification performance is better with two detectors. This is simply
because with two detectors the algorithm is tuned with a uniform distribution
of noise triggers with low and moderate SNR since high SNR noise triggers do
not survive coherence tests between detectors. Also, regarding the different
classification models, the results indicated a consistent superior performance
with the support vector machine with radial basis function as kernel (SVMR).
This model provides non-linear separation surfaces allowing to account for
non-linearities in the feature space. Despite other methods can also be used
for this problem, we recommend the use of SVMR since it has been proved to be
stable and robust.

With regard to the training of the classification model, it is important to
indicate that the training data in all analyses was always balanced, hence,
there is an equal probability for each class (noise and signal). However,
during the training procedure of the classifiers there is the possibility to
assign more probability to one class. This would allow to increase the noise
reduction at the expense of the signal reduction, or vice-verse. This is an
important aspect to be able to trade off between statistical significance and
efficiency. It is also possible to train the classification model using only a
subset with loudest noise events, or with a subset of signal events with
certain characteristics (duration, bandwidth, etc.). This can be used to bias
the follow-up ML model to prioritize specific aspects during the search by
recognizing better one specific type of noise or signal event.

To sum up, this work presented a follow-up machine learning method for cWB
based searches of GWs from CCSNe which can be use with one or multiple
detectors. The method identifies and discharges non-astrophysical noise
transients allowing to reduce the false alarm rate, to improve the statistical
significance and to increase the detection range of the searches. The model is
simply tuned with a set of noise and signal triggers and then can be easily
incorporated into the search pipeline.

##  V Acknowledgements

This research has made use of data, software and/or web tools obtained from
the Gravitational Wave Open Science Center, a service of LIGO Laboratory, the
LIGO Scientific Collaboration and the Virgo Collaboration. We gratefully
acknowledge the support of LIGO and Virgo for the provision of computational
resources. This material is based upon work supported by NSF’s LIGO Laboratory
which is a major facility fully funded by the National Science Foundation.
Antelis and Moreno’s research is partially supported by CONACyT Ciencia de
Frontera Project No. 376127. Cavaglia’s research is partially supported by NSF
award number PHY 2011334 (2020). Mukherjee’s research is partially supported
by NSF award number PHY 1912630 (2019).

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