Original: Identifying witnesses to Noise Transients in Ground-based Gravitational-wave Observations using Auxiliary Channels with Matrix and Tensor Factorization Techniques
Revised: Identifying Witnesses to Noise Transients in Ground-based Gravitational-wave Observations using Auxiliary Channels with Matrix and Tensor Factorization Techniques

Original: Abstract
Revised: Abstract

Original: Ground-based gravitational-wave (GW) detectors are a frontier large-scale experiment in experimental astrophysics.
Revised: Ground-based gravitational-wave (GW) detectors are a frontier large-scale experiment in experimental astrophysics.

Original: Given the elusive nature of GWs, theground-based detectors have complex interacting systems made up of exquisitelysensitive instruments which makes them susceptible to terrestrial noise sources.
Revised: Given the elusive nature of GWs, theground-based detectors have complex interacting systems made up of exquisitelysensitive instruments which makes them susceptible to terrestrial noise sources.

Original: As these noise transients - termed as glitches - appear in the detector’s main datachannel, they can mask or mimic real GW signals resulting in false alarms in thedetection pipelines.
Revised: As these noise transients - termed as glitches - appear in the detector’s main datachannel, they can mask or mimic real GW signals resulting in false alarms in thedetection pipelines.

Original: Given their high rate of occurrence compared to astrophysicalsignals, it is vital to examine these glitches and probe their origin in the detector’senvironment and instruments in order to possibly eliminate them from the sciencedata.
Revised: Given their high rate of occurrence compared to astrophysicalsignals, it is vital to examine these glitches and probe their origin in the detector’senvironment and instruments in order to possibly eliminate them from the sciencedata.

Original: In this paper we present a tensor factorization-based data mining approach,based on irregular tensor mining, to finding witness events to these glitches in thenetwork of heterogeneous sensors that monitor the detectors and build a catalogwhich can aid human operators in diagnosing the sources of these noise transients.
Revised: In this paper we present a tensor factorization-based data mining approach,based on irregular tensor mining, to finding witness events to these glitches in thenetwork of heterogeneous sensors that monitor the detectors and build a catalogwhich can aid human operators in diagnosing the sources of these noise transients.

Original:  Introduction
Revised:  Introduction

Original: Noise coupling into a large-scale, complex instrument’s main channel(s) is a typical issue in bigscientific experiments that push the limits of technology towards ground-breaking discoveries.
Revised: Noise coupling into a large-scale, complex instrument’s main channel(s) is a typical issue in bigscientific experiments that push the limits of technology towards ground-breaking discoveries.

Original: Totackle this issue, along with constant engineering improvements, these complex frontier experimentsdeploy a large array of monitoring systems for day-to-day diagnostics and calibration, producing vastquantities of raw data-streams about the overall state of the detectors.
Revised: Totackle this issue, along with constant engineering improvements, these complex frontier experimentsdeploy a large array of monitoring systems for day-to-day diagnostics and calibration, producing vastquantities of raw data-streams about the overall state of the detectors.

Original: This raw data, if strategicallymined for latent patterns of interest, can potentially point to origins of noise couplings and aid theoperators in their diagnostics.
Revised: This raw data, if strategicallymined for latent patterns of interest, can potentially point to origins of noise couplings and aid theoperators in their diagnostics.

Original: The raw data is often heterogeneous temporal data from which weneed to engineer datasets suitable for data mining and the authors of this paper wish to explore theend-to-end matrix and tensor factorization based data mining pipeline in the context of complexscientific instruments like the ground-based gravitational wave detectors at LIGO.
Revised: The raw data is often heterogeneous temporal data from which weneed to engineer datasets suitable for data mining and the authors of this paper wish to explore theend-to-end matrix and tensor factorization based data mining pipeline in the context of complexscientific instruments like the ground-based gravitational wave detectors at LIGO.

Original: The ground-based gravitational-wave (GW) detectors like advanced LIGO Aasi et al.
Revised: The ground-based gravitational-wave (GW) detectors like advanced LIGO Aasi et al.

Original: [2015] areone such frontier complex instrument that have successfully reached the state-of-the-art sensitivityneeded to detect astrophysical signals.
Revised: [2015] areone such frontier complex instrument that have successfully reached the state-of-the-art sensitivityneeded to detect astrophysical signals.

Original: Given their exquisite sensitivity, these detectors are plaguedby various sources of transient terrestrial noise which affects the searches for GWs.
Revised: Given their exquisite sensitivity, these detectors are plaguedby various sources of transient terrestrial noise which affects the searches for GWs.

Original: Glitches are non-Gaussian noise transients appearing in the main channel of the detector which measures the amount of strain 1 , h ( t ) , produced by a passing gravitational wave.
Revised: Glitches are non-Gaussian noise transients appearing in the main channel of the detector which measures the amount of strain 1 , h ( t ) , produced by a passing gravitational wave.

Original: Their origins are environmentaland instrumental in nature.
Revised: Their origins are environmentaland instrumental in nature.

Original: These noise transients stand out from the expected stationary Gaussiannoise as transient power excesses which trigger GW search pipelines leading to false alarms and,along with the stationary noise, limit the detector’s sensitivity.
Revised: These noise transients stand out from the expected stationary Gaussiannoise as transient power excesses which trigger GW search pipelines leading to false alarms and,along with the stationary noise, limit the detector’s sensitivity.

Original: Hence, glitch characterization isa crucial problem and has been studied at LIGO in two important ways - 1.
Revised: Hence, glitch characterization isa crucial problem and has been studied at LIGO in two important ways - 1.

Original: the time-frequencymorphology of the glitches in the main channel, 2. presence of triggers in auxiliary diagnosticchannels that are coincident with the glitches.
Revised: the time-frequencymorphology of the glitches in the main channel, 2. presence of triggers in auxiliary diagnosticchannels that are coincident with the glitches.

Original: Glitch’s morphology in the main channel Glitches have complex morphologies and vary induration and frequency.
Revised: Glitch’s morphology in the main channel Glitches have complex morphologies and vary induration and frequency.

Original: Therefore, LIGO scientists have been studying the glitches based on themorphological differences evident in their time-frequency spectrograms.
Revised: Therefore, LIGO scientists have been studying the glitches based on themorphological differences evident in their time-frequency spectrograms.

Original: Several different classesof glitches have been identified Zevin et al.
Revised: Several different classesof glitches have been identified Zevin et al.

Original: [2017] and given their diversity and abundance, amorphology-based glitch catalog has been built using citizen scientists to label glitch images andmachine-learning based image classification techniques.
Revised: [2017] and given their diversity and abundance, amorphology-based glitch catalog has been built using citizen scientists to label glitch images andmachine-learning based image classification techniques.

Original: However, it is important to find origins ofthese noise transients in the system and build a richer, more actionable catalog which can equip theoperators to locate sources of these noise transients, understand coupling mechanisms and possiblyeliminate these glitches with instrumental upgrades.
Revised: However, it is important to find origins ofthese noise transients in the system and build a richer, more actionable catalog which can equip theoperators to locate sources of these noise transients, understand coupling mechanisms and possiblyeliminate these glitches with instrumental upgrades.

Original: Auxiliary channels Apart from the main channel which measures the strain h
Revised: Auxiliary channels Apart from the main channel which measures the strain h

Original: ( t ) , LIGO maintains
Revised: ( t ) , LIGO maintains

Original: O (10 5 ) auxiliary channels to record the state of the instrument and its environment using a widevariety of sensors, some of which are used in calibration of the detector.
Revised: O (10 5 ) auxiliary channels to record the state of the instrument and its environment using a widevariety of sensors, some of which are used in calibration of the detector.

Original: Some of these channels maywitness noise sources induce a glitch.
Revised: Some of these channels maywitness noise sources induce a glitch.

Original: Finding correlations between glitches in the main channel andexcess power events in the auxiliary channels is therefore useful in determining the origins of theseglitches.
Revised: Finding correlations between glitches in the main channel andexcess power events in the auxiliary channels is therefore useful in determining the origins of theseglitches.

Original: Our contribution is a data mining approach for unsupervised analysis of glitches in the mainchannel and the triggers in the auxiliary diagnostic channels using matrix and tensor factorizationtechniques .
Revised: Our contribution is a data mining approach for unsupervised analysis of glitches in the mainchannel and the triggers in the auxiliary diagnostic channels using matrix and tensor factorizationtechniques .

Original: We describe some existing works in Section 2 followed by a brief background on LIGO operationsand motivate the prevalence of matrix and tensor factorization techniques for a variety of real-worldapplications in Section 3.
Revised: We describe some existing works in Section 2 followed by a brief background on LIGO operationsand motivate the prevalence of matrix and tensor factorization techniques for a variety of real-worldapplications in Section 3.

Original: We describe the end-to-end data mining pipeline in Section 4 beginningwith how we performed data collection in Section 4.1, how we did feature engineering in Section 4.2to create datasets as described in Section 4.3.
Revised: We describe the end-to-end data mining pipeline in Section 4 beginningwith how we performed data collection in Section 4.1, how we did feature engineering in Section 4.2to create datasets as described in Section 4.3.

Original: Section 5 describes the analysis results and Section 6concludes the paper with some future directions for this line of work.
Revised: Section 5 describes the analysis results and Section 6concludes the paper with some future directions for this line of work.

Original:  Background
Revised:  Background

Original: Gravitational-wave Astronomy with LIGO LIGO detectors are state-of-the-art laser interferometers, which, in absence of a gravitational wave are designed to register no signal at the outputphoto-diode.
Revised: Gravitational-wave Astronomy with LIGO LIGO detectors are state-of-the-art laser interferometers, which, in absence of a gravitational wave are designed to register no signal at the outputphoto-diode.

Original: When a gravitational wave passes through the earth, a relative change in arm lengths isinduced which is measured in terms of strain h ( t ) , which is the main data product of LIGO.
Revised: When a gravitational wave passes through the earth, a relative change in arm lengths isinduced which is measured in terms of strain h ( t ) , which is the main data product of LIGO.

Original: Unfortunately, however, transient terrestrial disturbances originating in the environment or the instrumentcan also cause a brief power excess and result in a signal being registered at the output photo-diode.
Revised: Unfortunately, however, transient terrestrial disturbances originating in the environment or the instrumentcan also cause a brief power excess and result in a signal being registered at the output photo-diode.

Original: This coupling of noise into the main channel, h ( t ) , is, in essence, a glitch.
Revised: This coupling of noise into the main channel, h ( t ) , is, in essence, a glitch.

Original: LIGO data analystsuse the auxiliary channels as veto generators to remove time segments contaminated with glitchesand generate clean segments of h ( t ) that are then searched for GW signals.
Revised: LIGO data analystsuse the auxiliary channels as veto generators to remove time segments contaminated with glitchesand generate clean segments of h ( t ) that are then searched for GW signals.

Original: Thus, as described in
Revised: Thus, as described in

Original: Essick et al.
Revised: Essick et al.

Original: [2013] it is useful to determine important auxiliary channels which can act as vetogenerators .
Revised: [2013] it is useful to determine important auxiliary channels which can act as vetogenerators .

Original: Given the large number of auxiliary channels, only some of which may witness a glitch,it is conducive to use machine learning-based techniques to find correlation between the main andauxiliary channel power excesses in an attempt to determine what type of mechanical couplingsproduces a certain type of glitch.
Revised: Given the large number of auxiliary channels, only some of which may witness a glitch,it is conducive to use machine learning-based techniques to find correlation between the main andauxiliary channel power excesses in an attempt to determine what type of mechanical couplingsproduces a certain type of glitch.

Original: There have been several efforts at LIGO that use these auxiliary channels for glitch analysis.
Revised: There have been several efforts at LIGO that use these auxiliary channels for glitch analysis.

Original: Notably,iDQ Essick et al.
Revised: Notably,iDQ Essick et al.

Original: [2020] is a machine learning-based low-latency glitch prediction pipeline whichuses auxiliary channels information to train a binary classifier to compute the probability of presenceof glitches in the main channel.
Revised: [2020] is a machine learning-based low-latency glitch prediction pipeline whichuses auxiliary channels information to train a binary classifier to compute the probability of presenceof glitches in the main channel.

Original: Similarly, in Cavaglia et al.
Revised: Similarly, in Cavaglia et al.

Original: [2018] the authors use auxiliary channelinformation and binary classification as a tool to study 2 sets of well-understood glitches from thefirst two observing runs of LIGO.
Revised: [2018] the authors use auxiliary channelinformation and binary classification as a tool to study 2 sets of well-understood glitches from thefirst two observing runs of LIGO.

Original: Data Mining using Matrix and Tensor Factorization Techniques There is a wealth of worksthat leverage matrix and tensor factorization especially for exploratory unsupervised data mining ofmulti-modal data in a wide and seemingly disparate number of real-world applications.
Revised: Data Mining using Matrix and Tensor Factorization Techniques There is a wealth of worksthat leverage matrix and tensor factorization especially for exploratory unsupervised data mining ofmulti-modal data in a wide and seemingly disparate number of real-world applications.

Original: Examplesinclude brain network discovery Davidson et al.
Revised: Examplesinclude brain network discovery Davidson et al.

Original: [2013] and Electronic Health Record mining andextraction of disease phenotypes Ho et al.
Revised: [2013] and Electronic Health Record mining andextraction of disease phenotypes Ho et al.

Original: The motivation behind the choice of using matrixand tensor factorization to do these types of analysis is the computational efficiency and the simpleand interpretable nature of these techniques.
Revised: The motivation behind the choice of using matrixand tensor factorization to do these types of analysis is the computational efficiency and the simpleand interpretable nature of these techniques.

Original:  Proposed Data Mining Pipeline
Revised:  Proposed Data Mining Pipeline

Original: The task at hand is to find co-clusters of glitch events and their witness channels from a set of glitchevents ( G ) occurring in the main channel ( h ( t ) ) with respect to the set of auxiliary channels ( A )selected for the analysis.
Revised: The task at hand is to find co-clusters of glitch events and their witness channels from a set of glitchevents ( G ) occurring in the main channel ( h ( t ) ) with respect to the set of auxiliary channels ( A )selected for the analysis.

Original: In this paper, we formulate this task as a soft co-clustering problem whichis discussed in brief in Section 3.3.
Revised: In this paper, we formulate this task as a soft co-clustering problem whichis discussed in brief in Section 3.3.

Original: Figure 1 shows a diagrammatic representation of the completedata mining pipeline.
Revised: Figure 1 shows a diagrammatic representation of the completedata mining pipeline.

Original: We begin by choosing an analysis time interval in which we collect a set ofglitch events that occurred in the main channel ( G ) and corresponding loud triggers that occurred ina set of auxiliary channels ( A ) around the time of the glitch events.
Revised: We begin by choosing an analysis time interval in which we collect a set ofglitch events that occurred in the main channel ( G ) and corresponding loud triggers that occurred ina set of auxiliary channels ( A ) around the time of the glitch events.

Original: We represent this informationfirst as a 2-mode tensor, i.e a matrix, where each element represents the occurrence of a trigger in anauxiliary channel for each glitch event.
Revised: We represent this informationfirst as a 2-mode tensor, i.e a matrix, where each element represents the occurrence of a trigger in anauxiliary channel for each glitch event.

Original: We can later expand the matrix into a tensor to featurize thematrix elements with a set of features ( F ) related to the channels or the triggers in the channels.
Revised: We can later expand the matrix into a tensor to featurize thematrix elements with a set of features ( F ) related to the channels or the triggers in the channels.

Original: Theconstructed tensor is then factorized and the latent patterns resulting from the factors are examinedusing various validation tests that are specific to certain downstream applications.
Revised: Theconstructed tensor is then factorized and the latent patterns resulting from the factors are examinedusing various validation tests that are specific to certain downstream applications.

Original: 3.1 Data Collection
Revised: 3.1 Data Collection

Original: A channel is typically a raw data-readout over time from a monitoring sensor (or some useful derivedquantity).
Revised: A channel is typically a raw data-readout over time from a monitoring sensor (or some useful derivedquantity).

Original: Each channel can be tagged with certain features (properties) like - 1. which subsystemin the complex system it belongs to (for example, a temperature sensor belonging to the physicalenvironment monitoring subsystem or an inertial sensor measuring ground motion belonging to theinternal seismic isolation subsystem), 2. where it is located in the observatory’s infrastructure.
Revised: Each channel can be tagged with certain features (properties) like - 1. which subsystemin the complex system it belongs to (for example, a temperature sensor belonging to the physicalenvironment monitoring subsystem or an inertial sensor measuring ground motion belonging to theinternal seismic isolation subsystem), 2. where it is located in the observatory’s infrastructure.

Original: A trigger refers to a transient power excess event in a channel - h ( t ) or any a ( t ) - detected by an eventtrigger generator (ETG) like Omicron Robinet [2016] which runs continually in real-time at LIGOduring its operational runs.
Revised: A trigger refers to a transient power excess event in a channel - h ( t ) or any a ( t ) - detected by an eventtrigger generator (ETG) like Omicron Robinet [2016] which runs continually in real-time at LIGOduring its operational runs.

Original: Thus, glitches are simply loud triggers in h ( t ) that are not astrophysical in origin.
Revised: Thus, glitches are simply loud triggers in h ( t ) that are not astrophysical in origin.

Original: Omicron infers certain features (properties) of the generated triggers viz.
Revised: Omicron infers certain features (properties) of the generated triggers viz.

Original: signal-to-noiseratio (SNR), peak frequency, bandwidth, amplitude, duration, phase, etc. 

Revised: signal-to-noiseratio (SNR), peak frequency, bandwidth, amplitude, duration, phase, etc.

Original: We can do a systematic trigger collection inspired by Cavaglia et al.
Revised: We can do a systematic trigger collection inspired by Cavaglia et al.

Original: [2018] as follows:
Revised: [2018] as follows:

Original: Obtain a set, G , of loud triggers, i.e. trigger with peak SNR > 7.5, that occurred in h ( t )
Revised: Obtain a set, G , of loud triggers, i.e. trigger with peak SNR > 7.5, that occurred in h ( t )

Original: between t start and t end .
Revised: between t start and t end .

Original: For all t g ∈ G , find triggers from a set, A , of safe auxiliary channels in a fixed window[ t g − γ, t g + γ ] around each t g where, t g ∈ G is the peak SNR time of the glitch trigger.
Revised: For all t g ∈ G , find triggers from a set, A , of safe auxiliary channels in a fixed window[ t g − γ, t g + γ ] around each t g where, t g ∈ G is the peak SNR time of the glitch trigger.

Original: γis window parameter to center the glitch trigger around its peak SNR time.
Revised: γis window parameter to center the glitch trigger around its peak SNR time.

Original: In this analysisγ ranges from 0.1 to 1 second.
Revised: In this analysisγ ranges from 0.1 to 1 second.

Original: If no trigger is present in the window, a default null trigger is stored for that channel corresponding tothat t g .
Revised: If no trigger is present in the window, a default null trigger is stored for that channel corresponding tothat t g .

Original: In case of multiple loud triggers in the window, we pick the loudest trigger.
Revised: In case of multiple loud triggers in the window, we pick the loudest trigger.

Original: 3.2 Feature Engineering and Dataset Construction
Revised: 3.2 Feature Engineering and Dataset Construction

Original: Matrix Construction:
Revised: Matrix Construction:

Original: The matrix X ∈ R | G |×| A | encodes the presence or absence of a loud triggerin each auxiliary channel for every glitch in G weighted by peak SNR.
Revised: The matrix X ∈ R | G |×| A | encodes the presence or absence of a loud triggerin each auxiliary channel for every glitch in G weighted by peak SNR.

Original: Each | A | -length row of Xcorresponds to a glitch and each element X ( i, j ) is the peak SNR of i th trigger in j th auxiliarychannel if trigger present, zero otherwise.
Revised: Each | A | -length row of Xcorresponds to a glitch and each element X ( i, j ) is the peak SNR of i th trigger in j th auxiliarychannel if trigger present, zero otherwise.

Original: Tensor Construction:
Revised: Tensor Construction:

Original: The matrix described in the previous section can be extended into a tensor 4 toadditionally encode the features (properties) of the 2 entities in the matrix i.e. the events and/or thechannels.
Revised: The matrix described in the previous section can be extended into a tensor 4 toadditionally encode the features (properties) of the 2 entities in the matrix i.e. the events and/or thechannels.

Original: Structurally, we can create 2 types of the tensor as follows -
Revised: Structurally, we can create 2 types of the tensor as follows -

Original: “Regular” 3-mode cuboid tensor: X ∈ R | G |×| A |×| P | where, |
Revised: “Regular” 3-mode cuboid tensor: X ∈ R | G |×| A |×| P | where, |

Original: P
Revised: P

Original: | = number of features.
Revised: | = number of features.

Original: Thus,
Revised: Thus,

Original: each element X ( i, j, k ) is the peak SNR of i th trigger in j th auxiliary channel the has the
Revised: each element X ( i, j, k ) is the peak SNR of i th trigger in j th auxiliary channel the has the

Original: k th feature (property) if trigger present, zero otherwise.
Revised: k th feature (property) if trigger present, zero otherwise.

Original: “Irregular” tensor / Collection of matrices: X i ∈ R | G |×|
Revised: “Irregular” tensor / Collection of matrices: X i ∈ R | G |×|

Original: A i | where, i is the i th feature
Revised: A i | where, i is the i th feature

Original: (property), i = 1 , ..., | P | .
Revised: (property), i = 1 , ..., | P | .

Original: Thus, each element X i ( m, n ) is the peak SNR of m th trigger in
Revised: Thus, each element X i ( m, n ) is the peak SNR of m th trigger in

Original: n th auxiliary channel that has the i th feature (property) if trigger present, zero otherwise.
Revised: n th auxiliary channel that has the i th feature (property) if trigger present, zero otherwise.

Original: array.
Revised: array.

Original: 3.3 Co-clustering glitches, channels and their features
Revised: 3.3 Co-clustering glitches, channels and their features

Original: Consider the traditional clustering problem where, a data matrix D ∈ R m × n has m data-points(or observations) each of which has n features.
Revised: Consider the traditional clustering problem where, a data matrix D ∈ R m × n has m data-points(or observations) each of which has n features.

Original: Clustering methods, like the popular k-meansalgorithm, partition the data-points to discover k subsets called clusters such that data-points in acluster are similar to each other and distinct from data-points in other clusters.
Revised: Clustering methods, like the popular k-meansalgorithm, partition the data-points to discover k subsets called clusters such that data-points in acluster are similar to each other and distinct from data-points in other clusters.

Original: Co-clustering refersto simultaneous clustering of multiple modes of the data.
Revised: Co-clustering refersto simultaneous clustering of multiple modes of the data.

Original: In case of the 2-mode data (i.e. a datamatrix) D described above, co-clustering partitions along the n rows as well as the m columns to findsubsets.
Revised: In case of the 2-mode data (i.e. a datamatrix) D described above, co-clustering partitions along the n rows as well as the m columns to findsubsets.

Original: Co-clustering can be formulated as a multi-linear factorization as described in Papalexakisand Sidiropoulos [2011] such that D m × n ≈
Revised: Co-clustering can be formulated as a multi-linear factorization as described in Papalexakisand Sidiropoulos [2011] such that D m × n ≈

Original: [ R m × k C k × n ] where k is referred to as the rank ofthe factorization.
Revised: [ R m × k C k × n ] where k is referred to as the rank ofthe factorization.

Original: In this paper, to co-cluster the 2-mode data matrix, we use Non-negative Matrix
Revised: In this paper, to co-cluster the 2-mode data matrix, we use Non-negative Matrix

Original: Factorization (NMF).
Revised: Factorization (NMF).

Original: The choice of NMF is dictated by the non-negative values (the SNRs of thetriggers) in X .
Revised: The choice of NMF is dictated by the non-negative values (the SNRs of thetriggers) in X .

Original: Imposing the non-negativity constraint can potentially yield more interpretable factorsthat prove useful for further analysis.
Revised: Imposing the non-negativity constraint can potentially yield more interpretable factorsthat prove useful for further analysis.

Original: To co-
Revised: To co-

Original: cluster the 3-mode data tensors which add triggeror channel related features to the event-channel pairs, we will use variants of PARAFAC tensorfactorization.
Revised: cluster the 3-mode data tensors which add triggeror channel related features to the event-channel pairs, we will use variants of PARAFAC tensorfactorization.

Original: We describe these factorization methods formally in the following sections.
Revised: We describe these factorization methods formally in the following sections.

Original: 3.3.1 Non-negative Matrix Factorization (NMF)
Revised: 3.3.1 Non-negative Matrix Factorization (NMF)

Original: The formulation of NMF is stated as follows.
Revised: The formulation of NMF is stated as follows.

Original: Given X ∈ R | G |×| A | + and desired number of components(rank)
Revised: Given X ∈ R | G |×| A | + and desired number of components(rank)

Original: k << min ( | G | , | A | ) , find E ∈ R | G |× k + and C ∈ R
Revised: k << min ( | G | , | A | ) , find E ∈ R | G |× k + and C ∈ R

Original: k ×| A | + such that M ≈ EC .
Revised: k ×| A | + such that M ≈ EC .

Original: In our case,each row of E and C T is a k -length latent space representation of triggers and channels respectively.
Revised: In our case,each row of E and C T is a k -length latent space representation of triggers and channels respectively.

Original: For computation of NMF, we used the implementation from Scikit-Learn library available for Python.
Revised: For computation of NMF, we used the implementation from Scikit-Learn library available for Python.

Original: 3.3.2 Non-negative CP/PARAFAC Tensor Factorization
Revised: 3.3.2 Non-negative CP/PARAFAC Tensor Factorization

Original: In order to incorporate features of the trigger events, we can factorize X ∈ R | G |×| A |×| P | using the
Revised: In order to incorporate features of the trigger events, we can factorize X ∈ R | G |×| A |×| P | using the

Original: CP/PARAFAC tensor factorization.
Revised: CP/PARAFAC tensor factorization.

Original: As depicted in figure 1, the CP/PARAFAC tensor factorization of 158 X is expressed as a sum of outer products of k rank-1 tensors called components or factors.
Revised: As depicted in figure 1, the CP/PARAFAC tensor factorization of 158 X is expressed as a sum of outer products of k rank-1 tensors called components or factors.

Original: Thesecomponents can be arranged as 3 factor matrices viz.
Revised: Thesecomponents can be arranged as 3 factor matrices viz.

Original: E ∈ R | G |× k
Revised: E ∈ R | G |× k

Original: + , C ∈ R |
Revised: + , C ∈ R |

Original: A |× k + , and F ∈ R | P |× k +corresponding to each mode of X , each with r columns.
Revised: A |× k + , and F ∈ R | P |× k +corresponding to each mode of X , each with r columns.

Original: Formally stated as, X ≈ k (cid:88) r
Revised: Formally stated as, X ≈ k (cid:88) r

Original: = e r ◦ c r ◦ f r ,where e r , c r and f r are the r th column in factor matrices E , C and F respectively.
Revised: = e r ◦ c r ◦ f r ,where e r , c r and f r are the r th column in factor matrices E , C and F respectively.

Original: The true rank kof the tensor is defined as the minimum number of rank-1 components required to exactly reconstructthe original tensor.
Revised: The true rank kof the tensor is defined as the minimum number of rank-1 components required to exactly reconstructthe original tensor.

Original: However, a low-rank approximation of the tensor is of interest to our analysissince it can capture latent patterns across the modes of the tensor.
Revised: However, a low-rank approximation of the tensor is of interest to our analysissince it can capture latent patterns across the modes of the tensor.

Original: In our case, the rows of factormatrices E , C and F hold the k -length latent space representations of the glitch events, channelsand trigger features respectively.
Revised: In our case, the rows of factormatrices E , C and F hold the k -length latent space representations of the glitch events, channelsand trigger features respectively.

Original: For the computation of the PARAFAC decomposition we used theimplementation from Tensorly Kossaifi et al.
Revised: For the computation of the PARAFAC decomposition we used theimplementation from Tensorly Kossaifi et al.

Original: [2019] which uses hierarchical alternating least squaresmethod.
Revised: [2019] which uses hierarchical alternating least squaresmethod.

Original: Additionally, we impose non-negativity constraint on the factors.
Revised: Additionally, we impose non-negativity constraint on the factors.

Original: 3.3.3 PARAFAC-2 Tensor Factorization
Revised: 3.3.3 PARAFAC-2 Tensor Factorization

Original: In order to incorporate features of channels, we can jointly factorize the collection of matrices X iusing the PARAFAC-2 factorization.
Revised: In order to incorporate features of channels, we can jointly factorize the collection of matrices X iusing the PARAFAC-2 factorization.

Original: The choice of irregular tensor mining technique like PARAFAC2 is made instead of CP/PARAFAC for incorporating features of channels to avoid obtaining triviallyorthogonal slices (since each channel belongs to exactly one subsystem and location) in the thirdmode of the typical 3-mode cuboid tensor.
Revised: The choice of irregular tensor mining technique like PARAFAC2 is made instead of CP/PARAFAC for incorporating features of channels to avoid obtaining triviallyorthogonal slices (since each channel belongs to exactly one subsystem and location) in the thirdmode of the typical 3-mode cuboid tensor.

Original: As depicted in figure 1, the PARAFAC-2 factorizationof a collection of matrices where a matrix X i ∈ R | G |×|
Revised: As depicted in figure 1, the PARAFAC-2 factorizationof a collection of matrices where a matrix X i ∈ R | G |×|

Original: A i | is a frontal slice in an irregular 3-modetensor.
Revised: A i | is a frontal slice in an irregular 3-modetensor.

Original: A i is the set of auxiliary channels in the i th subsystem or at the i th location.
Revised: A i is the set of auxiliary channels in the i th subsystem or at the i th location.

Original: Formallystated as X i ≈ C
Revised: Formallystated as X i ≈ C

Original: i F i E T where k is the rank of the decomposition, C i ∈ R | A i |× k is factor matrixcorresponding to the channels belonging to the i th subsystem or at the i th location, E ∈ R | G |× kis
Revised: i F i E T where k is the rank of the decomposition, C i ∈ R | A i |× k is factor matrixcorresponding to the channels belonging to the i th subsystem or at the i th location, E ∈ R | G |× kis

Original: the factor matrix corresponding to the glitch events that is shared across all i factor matricescorresponding to channels and finally F i ∈ R
Revised: the factor matrix corresponding to the glitch events that is shared across all i factor matricescorresponding to channels and finally F i ∈ R

Original: k × k is a diagonal matrix indicating which clusters of channels in a specific subsystem or at a specific location are co-clustered with a cluster of glitchevents.
Revised: k × k is a diagonal matrix indicating which clusters of channels in a specific subsystem or at a specific location are co-clustered with a cluster of glitchevents.

Original:  Results
Revised:  Results

Original: For this analysis, we chose a 10-day time interval in the first half of the third observing run of LIGO(referred to as O3a by the LIGO community)
Revised: For this analysis, we chose a 10-day time interval in the first half of the third observing run of LIGO(referred to as O3a by the LIGO community)

Original: Tse et al.
Revised: Tse et al.

Original: There were approximately 3300loud glitches at the LIGO Hanford observatory.
Revised: There were approximately 3300loud glitches at the LIGO Hanford observatory.

Original: We used approximately 550 safe auxiliary channelsobtained from a list maintained by the Detector Characterization group at LIGO.
Revised: We used approximately 550 safe auxiliary channelsobtained from a list maintained by the Detector Characterization group at LIGO.

Original: We construct the data matrix X described in 3.3.1, the data tensor X frequency as described in 3.3.2using a feature related to the trigger events i.e. their peak frequencies and finally two variants for theirregular data tensor described in, 3.3.3 using 2 sets of features related to the auxiliary channels viz.1.
Revised: We construct the data matrix X described in 3.3.1, the data tensor X frequency as described in 3.3.2using a feature related to the trigger events i.e. their peak frequencies and finally two variants for theirregular data tensor described in, 3.3.3 using 2 sets of features related to the auxiliary channels viz.1.

Original: a set of discrete subsystems that the channels belong to: X subsystems , 2.
Revised: a set of discrete subsystems that the channels belong to: X subsystems , 2.

Original: a set of discrete locationswhere the sensors corresponding to the channels are located: X locations .
Revised: a set of discrete locationswhere the sensors corresponding to the channels are located: X locations .

Original: Clustering glitch events The | G | -length vectors in E are indicators of clusters of glitchs.
Revised: Clustering glitch events The | G | -length vectors in E are indicators of clusters of glitchs.

Original: Givensome external ground-truth labeling for the glitch events, like the Gravity Spy catalog, we canexamine whether we find homogeneous clusters for the different Gravity Spy classes w.r.t.
Revised: Givensome external ground-truth labeling for the glitch events, like the Gravity Spy catalog, we canexamine whether we find homogeneous clusters for the different Gravity Spy classes w.r.t.

Original: theauxiliary channels obtained via co-clustering.
Revised: theauxiliary channels obtained via co-clustering.

Original: More specifically, to quantify homogeneity of theclusters found in the factors w.r.t.
Revised: More specifically, to quantify homogeneity of theclusters found in the factors w.r.t.

Original: the Gravity Spy classes, we count the number of occurrences ofglitches belonging to each Gravity Spy class in the top n values of each | G | -length vector in E andaggregate this quantity across all factors.
Revised: the Gravity Spy classes, we count the number of occurrences ofglitches belonging to each Gravity Spy class in the top n values of each | G | -length vector in E andaggregate this quantity across all factors.

Original: For example, homogeneity of a co-clustering instance withrank k is defined as 1 k (cid:80) ki
Revised: For example, homogeneity of a co-clustering instance withrank k is defined as 1 k (cid:80) ki

Original: =1 1 N i where N i is the number of unique Gravity Spy classes associatedwith top n values of i th factor (column) in E .
Revised: =1 1 N i where N i is the number of unique Gravity Spy classes associatedwith top n values of i th factor (column) in E .

Original: Here, n is adaptively chosen to be 90% of the normof the factor.
Revised: Here, n is adaptively chosen to be 90% of the normof the factor.

Original: Thus if we find highly homogeneous clusters for the Gravity Spy classes this quantityis close to 1.
Revised: Thus if we find highly homogeneous clusters for the Gravity Spy classes this quantityis close to 1.

Original: To quantify how many Gravity Spy classes a factorization instance covers, we definecoverage as the fraction of unique Gravity Spy classes represented across all factors (columns) of Eover the total number of classes in the dataset.
Revised: To quantify how many Gravity Spy classes a factorization instance covers, we definecoverage as the fraction of unique Gravity Spy classes represented across all factors (columns) of Eover the total number of classes in the dataset.

Original: We expect coverage to approach 1 as we increase thefactorization rank.
Revised: We expect coverage to approach 1 as we increase thefactorization rank.

Original: Selecting veto-generator channels The | A | -length vectors in C are indicators of clusters ofchannels.
Revised: Selecting veto-generator channels The | A | -length vectors in C are indicators of clusters ofchannels.

Original: More specifically, each vector encodes the contribution of a subset of channels to thecorresponding subset of glitches.
Revised: More specifically, each vector encodes the contribution of a subset of channels to thecorresponding subset of glitches.

Original: We used these vectors to obtain a set of candidate channels S ⊂ A ,to test as witnesses of occurrences of glitches.
Revised: We used these vectors to obtain a set of candidate channels S ⊂ A ,to test as witnesses of occurrences of glitches.

Original: We pick the channel corresponding to the maximummagnitude value in the vector, i.e. the highest contribution, and add it to S .
Revised: We pick the channel corresponding to the maximummagnitude value in the vector, i.e. the highest contribution, and add it to S .

Original: For each channel s i ∈ S ,if there is a glitch in h ( t ) and a corresponding trigger in s i in a window around the glitch, we says i witnessed the glitch.
Revised: For each channel s i ∈ S ,if there is a glitch in h ( t ) and a corresponding trigger in s i in a window around the glitch, we says i witnessed the glitch.

Original: For each channel s i ∈ S , we count the number of glitches in h ( t ) that itwitnessed to test whether s i can be used as a veto generator and remove segments of h ( t ) beforesearching for real GW signals and reduce the number of false alarms.
Revised: For each channel s i ∈ S , we count the number of glitches in h ( t ) that itwitnessed to test whether s i can be used as a veto generator and remove segments of h ( t ) beforesearching for real GW signals and reduce the number of false alarms.

Original: Channels-based glitch catalog Using factor matrices E and C we can label each glitch event withthe channels that witness it.
Revised: Channels-based glitch catalog Using factor matrices E and C we can label each glitch event withthe channels that witness it.

Original: Since each row i in E is an embedding of i th glitch event ( e i ) in the 218 R k latent space discovered by the rank- k factorization, we can choose factor j from the k availablefactors which has the highest magnitude value for e i and associate the channels in the j th factor of Cwith e i .
Revised: Since each row i in E is an embedding of i th glitch event ( e i ) in the 218 R k latent space discovered by the rank- k factorization, we can choose factor j from the k availablefactors which has the highest magnitude value for e i and associate the channels in the j th factor of Cwith e i .

Original: 4.1 Analysis
Revised: 4.1 Analysis

Original: Figure 2 shows factors discovered by a rank-5 Non-negative CP/PARAFAC instance for the datatensor X frequency .
Revised: Figure 2 shows factors discovered by a rank-5 Non-negative CP/PARAFAC instance for the datatensor X frequency .

Original: We can observe that the two factors (out of 5) shown in the figure have highhomogeneity and find clusters of glitch events belonging to class #

Revised: We can observe that the two factors (out of 5) shown in the figure have highhomogeneity and find clusters of glitch events belonging to class #

Original: and we can find the diagnosticchannels that strongly witnesses this cluster is channel #281 in the first factor and channels #367 and
Revised: and we can find the diagnosticchannels that strongly witnesses this cluster is channel #281 in the first factor and channels #367 and

Original: #369 in the second factor.
Revised: #369 in the second factor.

Original: We can also observe that the first factor finds higher frequency witnesstriggers compared to the second factor.
Revised: We can also observe that the first factor finds higher frequency witnesstriggers compared to the second factor.

Original: Testing homogeneity of glitch clusters Although we can examine individual factors to discoversuch patterns, as shown in figure 3, the overall homogeneity of factors discovered by NMF acrossvarious choices of factorization rank ( k ) and coincidence window sizes ( γ ) for the glitch events inour dataset with respect to the external ground-truth (Gravity Spy) labels is low.
Revised: Testing homogeneity of glitch clusters Although we can examine individual factors to discoversuch patterns, as shown in figure 3, the overall homogeneity of factors discovered by NMF acrossvarious choices of factorization rank ( k ) and coincidence window sizes ( γ ) for the glitch events inour dataset with respect to the external ground-truth (Gravity Spy) labels is low.

Original: This suggests thatmorphological similarity in the time-frequency spectrograms of glitches as they appear in the mainchannel does not necessarily translate to having a common set of witness channels for the widevariety of Gravity Spy classes.
Revised: This suggests thatmorphological similarity in the time-frequency spectrograms of glitches as they appear in the mainchannel does not necessarily translate to having a common set of witness channels for the widevariety of Gravity Spy classes.

Original: This finding matches the one in Gurav et al.
Revised: This finding matches the one in Gurav et al.

Original: [2020] made about a setof glitch events in a different analysis period and w.r.t.
Revised: [2020] made about a setof glitch events in a different analysis period and w.r.t.

Original: a superset of auxiliary channels than ours.
Revised: a superset of auxiliary channels than ours.

Original: Testing channels for veto generation A veto generator is a channel used by LIGO data analyststo iteratively remove segments of h ( t ) that are contaminated with glitches before searching forastrophysical signals in it.
Revised: Testing channels for veto generation A veto generator is a channel used by LIGO data analyststo iteratively remove segments of h ( t ) that are contaminated with glitches before searching forastrophysical signals in it.

Original: If a channel has coincident triggers with h ( t ) glitches, the data segmentaround the trigger time is removed from h ( t ) .
Revised: If a channel has coincident triggers with h ( t ) glitches, the data segmentaround the trigger time is removed from h ( t ) .

Original: Thus an ideal veto generator will only have triggers thatcoincide with h ( t ) glitch events (true positives) to avoid removing valuable science data segmentsthat don’t have a coincident glitch (false positives).
Revised: Thus an ideal veto generator will only have triggers thatcoincide with h ( t ) glitch events (true positives) to avoid removing valuable science data segmentsthat don’t have a coincident glitch (false positives).

Original: Figure 3 shows 2 candidate witness channelsselected by an NMF instance.
Revised: Figure 3 shows 2 candidate witness channelsselected by an NMF instance.

Original: Channel #281 can be a good veto generator as the true positive rateexceeds the false positive rate above an SNR threshold of 25.
Revised: Channel #281 can be a good veto generator as the true positive rateexceeds the false positive rate above an SNR threshold of 25.

Original: This is not true for channel #300 whichappears to a noisy channels with high rate of spurious loud triggers.
Revised: This is not true for channel #300 whichappears to a noisy channels with high rate of spurious loud triggers.

Original: Building a channels-based glitch catalog Figure 4 show how we can build a glitch catalog basedon witness channels.
Revised: Building a channels-based glitch catalog Figure 4 show how we can build a glitch catalog basedon witness channels.

Original: A rank 5 NMF instance selected the same 2 witness channels (out of approx.550 available channels) for 2 different glitch events occurring in h ( t ) .
Revised: A rank 5 NMF instance selected the same 2 witness channels (out of approx.550 available channels) for 2 different glitch events occurring in h ( t ) .

Original: We can see these two channelshave loud triggers in them around the time of these glitches but the morphology of the loud triggersdiffer for each glitch event as evident in the spectrograms of the trigger signals.
Revised: We can see these two channelshave loud triggers in them around the time of these glitches but the morphology of the loud triggersdiffer for each glitch event as evident in the spectrograms of the trigger signals.

Original: The data analysispipeline described in this paper enables us to systematically label each glitch event with a small subsetof channels that witness it and further examine the morphology of the triggers in the witness channels.
Revised: The data analysispipeline described in this paper enables us to systematically label each glitch event with a small subsetof channels that witness it and further examine the morphology of the triggers in the witness channels.

Original: Thus far the morphology of only the glitches in the main channel ( h ( t ) ) have been exhaustivelystudied and cataloged by Gravity Spy since doing so for hundreds of auxiliary diagnostic channels isnot feasible.
Revised: Thus far the morphology of only the glitches in the main channel ( h ( t ) ) have been exhaustivelystudied and cataloged by Gravity Spy since doing so for hundreds of auxiliary diagnostic channels isnot feasible.

Original: The proposed data analysis pipeline addresses this feasibility issue by systematicallyclustering the glitch events w.r.t.
Revised: The proposed data analysis pipeline addresses this feasibility issue by systematicallyclustering the glitch events w.r.t.

Original: their witness channels instead of resorting to a brute force search.
Revised: their witness channels instead of resorting to a brute force search.

Original:  Conclusions and Future Directions
Revised:  Conclusions and Future Directions

Original: In this paper, we present an end-to-end data mining pipeline using unsupervised matrix and tensorfactorization techniques to build a more comprehensive, data-driven catalog of noise transient eventsoccurring in large-scale, complex scientific instruments like the ground-based gravitational wavedetectors at LIGO.
Revised: In this paper, we present an end-to-end data mining pipeline using unsupervised matrix and tensorfactorization techniques to build a more comprehensive, data-driven catalog of noise transient eventsoccurring in large-scale, complex scientific instruments like the ground-based gravitational wavedetectors at LIGO.

Original: Such catalogs can aid operators to study sources of noise events, investigatemechanisms through which noise gets coupled into the detector’s highly sensitive main channel andultimately push the detectors towards their design sensitivity to achieve the scientific goal of observinglarger volumes of spacetime to detect gravitational waves emanating from merging black holes andneutron stars.
Revised: Such catalogs can aid operators to study sources of noise events, investigatemechanisms through which noise gets coupled into the detector’s highly sensitive main channel andultimately push the detectors towards their design sensitivity to achieve the scientific goal of observinglarger volumes of spacetime to detect gravitational waves emanating from merging black holes andneutron stars.

Original: The procedures described to build useful datasets using hundreds of raw data-streamsfrom a complex instrument’s infrastructure and the unsupervised machine learning techniques usedto systematically mine this data are fairly generic and can be generalized to any similarly large-scalecomplex scientific instruments that are becoming prevalent in modern experimental physics.
Revised: The procedures described to build useful datasets using hundreds of raw data-streamsfrom a complex instrument’s infrastructure and the unsupervised machine learning techniques usedto systematically mine this data are fairly generic and can be generalized to any similarly large-scalecomplex scientific instruments that are becoming prevalent in modern experimental physics.

Original: Theauthors of this paper will test the proposed methods to build comprehensive catalog of noise eventsoccurring in LIGO data at scale and extend the utility of this catalog for discovering and modellingthe mechanisms of noise couplings in order to subtract them from the science data.
Revised: Theauthors of this paper will test the proposed methods to build comprehensive catalog of noise eventsoccurring in LIGO data at scale and extend the utility of this catalog for discovering and modellingthe mechanisms of noise couplings in order to subtract them from the science data.