Original: Supervised change-point detection with dimension reduction, applied to physiological signals
Revised: Supervised change-point detection with dimension reduction, applied to physiological signals

Original: Abstract
Revised: Abstract

Original: This paper proposes an automatic method to calibrate change point detectionalgorithms for high-dimensional time series.
Revised: This paper proposes an automatic method to calibrate change point detection algorithms for high-dimensional time series.

Original: Our procedure builds on the abilityof an expert (e.g. a medical researcher) to produce approximate segmentationestimates, called partial annotations, for a small number of signal examples.
Revised: Our procedure builds on the ability of an expert (e.g. a medical researcher) to produce approximate segmentation estimates, called partial annotations, for a small number of signal examples.

Original: Thiscontribution is a supervised approach to learn a diagonal Mahalanobis metric,which, once combined with a detection algorithm, is able to reproduce the expert’ssegmentation strategy on out-of-sample signals.
Revised: This contribution is a supervised approach to learn a diagonal Mahalanobis metric, which, once combined with a detection algorithm, is able to reproduce the expert’s segmentation strategy on out-of-sample signals.

Original: Unlike previous works for changedetection, our method includes a sparsity-inducing regularization which performsupervised dimension selection, and adapts to partial annotations.
Revised: Unlike previous works for change detection, our method includes a sparsity-inducing regularization which perform supervised dimension selection, and adapts to partial annotations.

Original: Experiments onactivity signals collected from healthy and neurologically impaired patients support the fact that supervision markedly ameliorate detection accuracy
Revised: Experiments on activity signals collected from healthy and neurologically impaired patients support the fact that supervision markedly ameliorate detection accuracy

Original:  Introduction
Revised:  Introduction

Original: The task of change-point detection, or signal segmentation, is a crucial step in numerous machinelearning pipelines that handle time series.
Revised: The task of change-point detection, or signal segmentation, is a crucial step in numerous machine learning pipelines that handle time series.

Original: Roughly, it consists in finding the temporal boundaries ofthe successive regimes of a multivariate signal.
Revised: Roughly, it consists in finding the temporal boundaries of the successive regimes of a multivariate signal.

Original: There are a great deal of applications, from sleepmonitoring [8], DNA sequences [4], study of neurological disorders [2], etc.
Revised: There are a great deal of applications, from sleep monitoring [8], DNA sequences [4], study of neurological disorders [2] etc.

Original: Practically, the expert(e.g. an medical researcher or a biologist) must choose by themself the most suitable change-pointdetection procedure from the vast associated literature [12].
Revised: Practically, the expert (e.g. an medical researcher or a biologist) must choose by themself the most suitable change-point detection procedure from the vast associated literature [12].

Original: One particularly important parameter toselect is the kind of change to detect, which is related to the signal representation or, similarly, themetric to measure the distance between samples.
Revised: One particularly important parameter to select is the kind of change to detect, which is related to the signal representation or, similarly, the metric to measure the distance between samples.

Original: This calibration step is complex, time-consumingand often achieved by a trial and error.
Revised: This calibration step is complex, time-consuming and often achieved by a trial and error.

Original: However, more often than not, the expert is able to manuallysegment a few signals, at least partially (i.e. give approximate change locations).
Revised: However, more often than not, the expert is able to manually segment a few signals, at least partially (i.e. give approximate change locations).

Original: For instance,
Revised: For instance,

Original: Figure 1 shows the partial annotation of an expert: on a signal collected by monitoring, with aninertial sensor, a subject performing a sequence of simple activities (stand, walk, turn around, walk,stop) [2], a medical researcher has indicated a rough estimation for the activity changes.
Revised: Figure 1 shows the partial annotation of an expert: on a signal collected by monitoring, with an inertial sensor, a subject performing a sequence of simple activities (stand, walk, turn around, walk, stop) [2], a medical researcher has indicated a rough estimation for the activity changes.

Original: The objectiveof this work is to formulate a procedure to automatically learn from segmentation examples (i.e.signals and their partial annotations) an appropriate metric.
Revised: The objective of this work is to formulate a procedure to automatically learn from segmentation examples (i.e. signals and their partial annotations) an appropriate metric.

Original: Combining the learned metric with achange-point detection algorithm could then replicate the expert’s segmentation strategy.
Revised: Combining the learned metric with a change-point detection algorithm could then replicate the expert’s segmentation strategy.

Original: The change point detection problem.
Revised: The change point detection problem.

Original: Consider a R d -valued signal y =
Revised: Consider a R d -valued signal y =

Original: [ y 1 , y 2 , . . .
Revised: [ y 1 , y 2 , . . .

Original: , y T ] with Tsamples.
Revised: , y T ] with T samples.

Original: Formally, change-point detection with an fixed number K of changes consists in solving thefollowing discrete optimization problem
Revised: Formally, change-point detection with an fixed number K of changes consists in solving the following discrete optimization problem

Original: [Equation]
Revised: [Equation]

Revised: [Figure]

Original: where y a..b is the empirical mean of the sub-signal { y t } b − 1 t = a and t 0 :
Revised: where y a..b is the empirical mean of the sub-signal { y t } b − 1 t = a and t 0 :

Original: = 1 and t K +1 =
Revised: = 1 and t K +1 =

Original: T +1 are dummyindexes and ∥·∥ is a user-defined norm on R d (e.g. the Euclidean norm).
Revised: T +1 are dummy indexes and ∥·∥ is a user-defined norm on R d (e.g. the Euclidean norm).

Original: The indexes { ˆ t 1 , ˆ t 2 , . .
Revised: The indexes { ˆ t 1 , ˆ t 2 , . .

Original: , ˆ t ˆ K }[Figure] are the instants when the signal has the most significant mean-shifts.
Revised: , ˆ t ˆ K } are the instants when the signal has the most significant mean-shifts.

Original: A number of methods have beendeveloped to optimize this sum of residuals (see [12] for a review).
Revised: A number of methods have been developed to optimize this sum of residuals (see [12] for a review).

Original: Algorithms based on dynamicprogramming solves Problem 1 exactly with a complexity of O ( dKT 2 ) .
Revised: Algorithms based on dynamic programming solves Problem 1 exactly with a complexity of O ( dKT 2 ) .

Original: This is the method thatwill be adopted.
Revised: This is the method that will be adopted.

Original: Any faster but approximate methods such as window-based procedures and binarysegmentation could be used instead, depending on the operational constraints.
Revised: Any faster but approximate methods such as window-based procedures and binary segmentation could be used instead, depending on the operational constraints.

Original: Learning a relevant metric.
Revised: Learning a relevant metric.

Original: This article focuses on the calibration of the norm ∥·∥ , which is relatedto the type of change that can be detected.
Revised: This article focuses on the calibration of the norm ∥·∥ , which is related to the type of change that can be detected.

Original: The chosen norm is a Mahalanobis-type (pseudo-)norm∥·∥ M such that ∥ x ∥ 2 M := x ⊺ Mx ( ∀ x ∈ R d ) where M ∈ R d × d a positive semi-definite (psd) matrix.
Revised: The chosen norm is a Mahalanobis-type (pseudo-)norm ∥·∥ M such that ∥ x ∥ 2 M := x ⊺ Mx ( ∀ x ∈ R d ) where M ∈ R d × d a positive semi-definite (psd) matrix.

Original: In this work, only diagonal matrix are considered, i.e. M = diag( w ) for a vector w ∈ R d + of positiveweights.
Revised: In this work, only diagonal matrix are considered, i.e. M = diag( w ) for a vector w ∈ R d + of positive weights.

Original: Calibration reduces to finding an appropriate w , which can be seen as a scaling of eachdimension p by w p .
Revised: Calibration reduces to finding an appropriate w , which can be seen as a scaling of each dimension p by w p .

Original: If w is sparse, the learn metric even performs variable selection.
Revised: If w is sparse, the learn metric even performs variable selection.

Original: Replacing in (1),the norm ∥·∥ by ∥·∥ diag( w ) with a properly calibrated w is particularly important for high-dimensionalsignals which might contain noisy components that alter change detection algorithms.
Revised: Replacing in (1), the norm ∥·∥ by ∥·∥ diag( w ) with a properly calibrated w is particularly important for high-dimensional signals which might contain noisy components that alter change detection algorithms.

Original: While thereare many articles focused on calibrating segmentation methods in a unsupervised way [12], only afew works have tackle this problem from a supervised standpoint [7, 11] and none, to the best of ourknowledge, have added a sparsity constraints to the weight vector w .
Revised: While there are many articles focused on calibrating segmentation methods in a unsupervised way [12], only a few works have tackle this problem from a supervised standpoint [7, 11] and none, to the best of our knowledge, have added a sparsity constraints to the weight vector w .

Original: Contributions.
Revised: Contributions.

Original: We propose a procedure to learn from expert labels an appropriate norm that canboth replicate the segmentation strategy of the expert and and select important signal dimensionsfor this task, thanks to a sparsity regularization.
Revised: We propose a procedure to learn from expert labels an appropriate norm that can both replicate the segmentation strategy of the expert and and select important signal dimensions for this task, thanks to a sparsity regularization.

Original: This procedure is applied on physiological signals,collected from healthy and neurologically impaired patients to asses their gait.
Revised: This procedure is applied on physiological signals, collected from healthy and neurologically impaired patients to asses their gait.

Original:  Method
Revised:  Method

Original: The procedure consists in two steps: (i) a learning step during which, a weight vector ˆ w is learnedusing labelled signals, and (ii) a prediction step during which a change-point detection procedure isapplied to out-of-sample signals to segment them.
Revised: The procedure consists in two steps: (i) a learning step during which, a weight vector ˆ w is learned using labelled signals, and (ii) a prediction step during which a change-point detection procedure is applied to out-of-sample signals to segment them.

Original: This section formally introduces the nature of thelabels provided by the expert and the metric learning approach.
Revised: This section formally introduces the nature of the labels provided by the expert and the metric learning approach.

Original:  From annotations to constraints
Revised: 2.1 From annotations to constraints.

Original: Annotations are provided by an expert and transformed into triplet constraints, which are then fed tothe sparse metric learning algorithm.
Revised: Annotations are provided by an expert and transformed into triplet constraints, which are then fed to the sparse metric learning algorithm.

Original: Annotations can either be full or partial.
Revised: Annotations can either be full or partial.

Original: Full annotations.
Revised: Full annotations.

Original: For each training signal y ( l ) , a full label consists in the set of change points
Revised: For each training signal y ( l ) , a full label consists in the set of change points

Original: T ( l ) = { t ( l ) 1 , t ( l ) 2 , . . . } .
Revised: T ( l ) = { t ( l ) 1 , t ( l ) 2 , . . . } .

Original: The set T ( l ) includes all the changes contained in the signal y ( l ) , accordingto the expert.
Revised: The set T ( l ) includes all the changes contained in the signal y ( l ) , according to the expert.

Original: Partial labels.
Revised: Partial labels.

Original: For each training signal y ( l ) , a partial label consists in the set of intervals S ( l ) =
Revised: For each training signal y ( l ) , a partial label consists in the set of intervals S ( l ) =

Original: { [ s ( l ) 1 , e ( l ) 1 ] , [ s ( l ) 2 , e ( l ) 2 ] , . . .
Revised: { [ s ( l ) 1 , e ( l ) 1 ] , [ s ( l ) 2 , e ( l ) 2 ] , . . .

Original: } that contain a change point.
Revised: } that contain a change point.

Original: Instead of giving the exact position of a change t ( l ) k , the expert only provides an approximate position [ s ( l ) k , e ( l ) k ]
Revised: Instead of giving the exact position of a change t ( l ) k , the expert only provides an approximate position [ s ( l ) k , e ( l ) k ]

Original: such that t ( l ) k ∈
Revised: such that t ( l ) k ∈

Original: [ s ( l ) k , e ( l ) k ] .
Revised: [ s ( l ) k , e ( l ) k ] .

Original: All the changes contained in the signal y ( l ) , according to the expert, are in one of the intervals ofthe set S ( l ) .
Revised: All the changes contained in the signal y ( l ) , according to the expert, are in one of the intervals of the set S ( l ) .

Original: Each interval [ s ( l ) k , e ( l ) k ] contains only one change and the intervals do not overlap.
Revised: Each interval [ s ( l ) k , e ( l ) k ] contains only one change and the intervals do not overlap.

Original: Anexample of partial annotations is shown on Figure 1.
Revised: An example of partial annotations is shown on Figure 1.

Original: From label to triplets of samples.
Revised: From label to triplets of samples.

Original: The proposed metric learning procedure relies on tripletsof samples (anchor sample, positive sample, negative sample).
Revised: The proposed metric learning procedure relies on triplets of samples (anchor sample, positive sample, negative sample).

Original: Using a full label T ( l ) , a tripletcan be created as follows: for any anchor sample y t in a certain segment [ t ( l ) k , t ( l ) k +

Revised: Using a full label T ( l ) , a triplet can be created as follows: for any anchor sample y t in a certain segment [ t ( l ) k , t ( l ) k +

Original: [ , a positivesample is any element of the same segment y t + of [ t ( l ) k , t ( l ) k +

Revised: [ , a positive sample is any element of the same segment y t + of [ t ( l ) k , t ( l ) k +

Original: [ (except the anchor sample) and anegative sample y t − is any element of the previous segment [ t ( l ) k − 1 , t ( l ) k
Revised: [ (except the anchor sample) and a negative sample y t − is any element of the previous segment [ t ( l ) k − 1 , t ( l ) k

Original: [ or the following segment[ t ( l ) k +1 , t ( l ) k +2 [ .
Revised: [ or the following segment [ t ( l ) k +1 , t ( l ) k +2 [ .

Original: Using a partial label S ( l ) , a triplet can be created similarly: for any anchor sampley t in a certain segment [ e ( l ) k , s ( l ) k +1 ] , a positive sample is any element of the same segment y t + of[ e ( l ) k , s ( l ) k +1 ] (except the anchor sample) and a negative sample y t − is any element of the previoussegment [ e ( l ) k − 1 , s ( l ) k ] or the following segment [ e ( l ) k
Revised: Using a partial label S ( l ) , a triplet can be created similarly: for any anchor sample y t in a certain segment [ e ( l ) k , s ( l ) k +1 ] , a positive sample is any element of the same segment y t + of [ e ( l ) k , s ( l ) k +1 ] (except the anchor sample) and a negative sample y t − is any element of the previous segment [ e ( l ) k − 1 , s ( l ) k ] or the following segment [ e ( l ) k

Original: +1 , s ( l ) k +2 ] .
Revised: +1 , s ( l ) k +2 ] .

Original: Intuitively, two samples that belong tothe same homogeneous segment (i.e. without change) are from the same class, while two samplesthat belong to two consecutive segments (i.e. separated by a change point) are from different classes.
Revised: Intuitively, two samples that belong to the same homogeneous segment (i.e. without change) are from the same class, while two samples that belong to two consecutive segments (i.e. separated by a change point) are from different classes.

Original: 2.2 Sparse metric learning
Revised: 2.2 Sparse metric learning

Original: Let D ( l ) be the set of triplets generated from the labels (full T ( l ) or partial S ( l ) ).
Revised: Let D ( l ) be the set of triplets generated from the labels (full T ( l ) or partial S ( l ) ).

Original: The sparse metriclearning procedure for change-point detection consists in solving the following optimization problemmin
Revised: The sparse metric learning procedure for change-point detection consists in solving the following optimization problem

Original: [Equation]
Revised: [Equation]

Original: where [ · ] + = max(0 , · ) and λ > 0 controls the trade-off between the sparsity of w and the tripletconstraints.
Revised: where [ · ] + = max(0 , · ) and λ > 0 controls the trade-off between the sparsity of w and the triplet constraints.

Original: This is simply the sum over the training set of the margin-based hinge loss and a sparsityinducing regularization.
Revised: This is simply the sum over the training set of the margin-based hinge loss and a sparsity inducing regularization.

Original: The learned ˆ w , which is the solution of Problem 2, is then such that thedistance between samples from the same segment is smaller than the distance between samples fromconsecutive regimes (separated by a change-point).
Revised: The learned ˆ w , which is the solution of Problem 2, is then such that the distance between samples from the same segment is smaller than the distance between samples from consecutive regimes (separated by a change-point).

Original: Because there can be a large number of possibletriplets in D ( l ) , learning a weight vector w can be computationally costly.
Revised: Because there can be a large number of possible triplets in D ( l ) , learning a weight vector w can be computationally costly.

Original: A sampling strategy isfrequently used to focus to reduce the computational burden; such a strategy is often called tripletmining [6].
Revised: A sampling strategy is frequently used to focus to reduce the computational burden; such a strategy is often called triplet mining [6].

Original: In this work, a fixed number of triplets is simply sampled at random from each set
Revised: In this work, a fixed number of triplets is simply sampled at random from each set

Original: D ( l ) .
Revised: D ( l ) .

Original: Also, Problem 2 includes a non-smooth regularization and large number of triplet constraints,stochastic composite optimization has been proposed [9].
Revised: Also, Problem 2 includes a non-smooth regularization and large number of triplet constraints, stochastic composite optimization has been proposed [9].

Original: This is an iterative minimization algorithmwhere each step is a stochastic gradient step followed by the application of a proximal operator (forthe ℓ 1 norm).
Revised: This is an iterative minimization algorithm where each step is a stochastic gradient step followed by the application of a proximal operator (for the ℓ 1 norm).

Original: This work uses the implementation of [3].
Revised: This work uses the implementation of [3].

Original:  Applications on physiological signals
Revised:  Applications on physiological signals

Original: In the following, our method is denoted SML-CPD for Sparse Metric Learning for Change-Point
Revised: In the following, our method is denoted SML-CPD for Sparse Metric Learning for Change-Point

Original: Detection.
Revised: Detection.

Original: Data.
Revised: Data.

Original: The Gait data set contains 42 labelled time series (sampling frequency: 100 Hz) from aninertial sensor placed at the lower back of a subject performing a fixed sequence of simple activities:“Stand”, “Walk”, “Turnaround”, “Walk”, “Stop”.
Revised: The Gait data set contains 42 labelled time series (sampling frequency: 100 Hz) from an inertial sensor placed at the lower back of a subject performing a fixed sequence of simple activities: “Stand”, “Walk”, “Turnaround”, “Walk”, “Stop”.

Original: The objective is to detect the time indexes at whichthe activity of the subject changes (each signal has 4 change-points).
Revised: The objective is to detect the time indexes at which the activity of the subject changes (each signal has 4 change-points).

Original: The time series have d = 6dimensions: the accelerations (m/s 2 ) along three axes ( X , Y and Z ) and the angular velocities(deg/s) around the same three axes.
Revised: The time series have d =dimensions: the accelerations (m/s 2 ) along three axes ( X , Y and Z ) and the angular velocities (deg/s) around the same three axes.

Original: Figure 1 shows an example (only two dimensions are displayed).
Revised: Figure 1 shows an example (only two dimensions are displayed).

Original: The time-frequency representation is the short-term Fourier transform (STFT), computed with 300samples per segment and an overlap of 299 samples, of each dimension; the concatenation of all
Revised: The time-frequency representation is the short-term Fourier transform (STFT), computed withsamples per segment and an overlap of 299 samples, of each dimension; the concatenation of all

Original: STFT yields a d = 906 -dimensional signal.
Revised: STFT yields a d = 906 -dimensional signal.

Original: As for the partial annotations, a medical researcher usedan annotation tool to provide portions of 50 samples (0.5 s) around activity’s changes.
Revised: As for the partial annotations, a medical researcher used an annotation tool to provide portions of 50 samples (0.5 s) around activity’s changes.

Original: Detection algorithms.
Revised: [Figure]

Original: Our method SML-CPD is compared to two common change-point detectionalgorithms: EUC-CPD which is equivalent to SML-CPD without the sparse metric learning step
Revised: [Figure]

Original: [Figure]
Revised: [Figure]

Original:  u r a c y
Revised: A cc u r a c y

Original: SML-CPD EUC-CPD
Revised: SML-CPD EUC-CPD

Original: RBF [Figure] CPD ([Figure]
Revised: RBF-CPD (

Original: Accuracy

Original: [Figure]
Revised: [Figure]

Original: margin
Revised: margin

Original: D e n s i t y ( % )
Revised: D e n s i t y ( % )

Original: Acc.
Revised: Acc.

Original: X
Revised: X

Original: Acc.
Revised: Acc.

Original: Y
Revised: Y

Original: Acc.
Revised: Acc.

Original: Z   3 Frequency (Hz)
Revised: Z   3 Frequency (Hz)

Original: D e n s i t y ( % )
Revised: D e n s i t y ( % )

Original: Rot.
Revised: Rot.

Original: X   3 Frequency (Hz)
Revised: X   3 Frequency (Hz)

Original: Rot.
Revised: Rot.

Original: Y   3 Frequency (Hz)
Revised: Y   3 Frequency (Hz)

Original: Rot.
Revised: Rot.

Original: Z
Revised: Z

Original: [Figure]
Revised: [Figure]

Original:  (i.e. the norm ∥·∥ w reduces to the Euclidean norm ∥·∥ ) and RBF-CPD which is a kernel-basedsegmentation procedure that can detect general changes in the distribution of the samples [1].
Revised: Detection algorithms. Our method SML-CPD is compared to two common change-point detection algorithms: EUC-CPD which is equivalent to SML-CPD without the sparse metric learning step (i.e. the norm ∥·∥ w reduces to the Euclidean norm ∥·∥ ) and RBF-CPD which is a kernel-based segmentation procedure that can detect general changes in the distribution of the samples [1].

Original: Thechosen kernel is the radial basis function (RBF).
Revised: The chosen kernel is the radial basis function (RBF).

Original: Note that both SML-CPD and EUC-CPD are appliedon the time-frequency representation of the signal, while RBF-CPD is applied on the original data 1 .
Revised: Note that both SML-CPD and EUC-CPD are applied on the time-frequency representation of the signal, while RBF-CPD is applied on the original data 1 .

Original: Evaluation metrics.
Revised: Evaluation metrics.

Original: The detection power is evaluated with the accuracy which is the proportionof correctly detected changes.
Revised: The detection power is evaluated with the accuracy which is the proportion of correctly detected changes.

Original: For a given margin M > 0 , a true change t is considered detectedif the estimated change-point ˆ t is such that | t − ˆ t | < M .
Revised: For a given margin M > 0 , a true change t is considered detected if the estimated change-point ˆ t is such that | t − ˆ t | < M .

Original: All scores are computed with a 5-foldcross-validation.
Revised: All scores are computed with a 5-fold cross-validation.

Original: Results A number of observations can be made from the results:
Revised: A number of observations can be made from the results:

Original: • Supervision improves detection accuracy.
Revised: • Supervision improves detection accuracy.

Original: The cross-validated accuracy is shown on Figure 
Revised: The cross-validated accuracy is shown on Figure 2a.

Original: a. The accuracy curve can be read like a ROC curve: here, SML-CPD has the highest curve and outperforms other methods, meaning that supervision markedly improves the detection at all margins.
Revised: The accuracy curve can be read like a ROC curve: here, SML-CPD has the highest curve and outperforms other methods, meaning that supervision markedly improves the detection at all margins.

Original: For a reasonable margin M = 1 s, accuracies are 91.1% for SML-CPD ,86.9% for EUC-CPD , 83.9% for RBF-CPD .•
Revised: For a reasonable margin M = 1 s, accuracies are 91.1% for SML-CPD , 86.9% for EUC-CPD , 83.9% for RBF-CPD .

Original:  Our method projects the signals into a low dimension space.
Revised: • Our method projects the signals into a low dimension space.

Original: The number of non-zerocoefficients in the learned w of SML-CPD is around 15 in the different folds of the crossvalidation, meaning that only 15 dimensions are kept to perform the segmentation, comparedto the 906 dimensions of the original STFT.• SML-CPD provides useful insights on the segmentation.
Revised: The number of non-zero coefficients in the learned w of SML-CPD is around 15 in the different folds of the crossvalidation, meaning that only 15 dimensions are kept to perform the segmentation, compared to the 906 dimensions of the original STFT. • SML-CPD provides useful insights on the segmentation.

Original: The learned weight vector ˆ w inSML-CPD helps the expert understand the important dimensions to segment their signals.
Revised: The learned weight vector ˆ w in SML-CPD helps the expert understand the important dimensions to segment their signals.

Original: The distribution of the selected dimensions/frequency in the STFT is displayed on Figure 2-b {+First, even though possible frequencies range from 
+}
Revised: The distribution of the selected dimensions/frequency in the STFT is displayed on Figure 2-b {+First, even though possible frequencies range from 
+}

Original: First, even though possible frequencies range from 0 Hz to 50 Hz, no frequency above Hz was ever chosen.
Revised: Hz to 50 Hz, no frequency aboveHz was ever chosen.

Original: Second, for the accelerations, most frequencies are picked from the [1 Hz - 2.5 Hz] band; this corresponds to the frequency of the main phenomenon during the walk: the repetitions of footsteps.
Revised: Second, for the accelerations, most frequencies are picked from the [1 Hz - 2.5 Hz] band; this corresponds to the frequency of the main phenomenon during the walk: the repetitions of footsteps.

Original: A footstep lasts about 0.8 second for healthy subjects and less for neurological impaired patients (both are present in the Gait data set).
Revised: A footstep lasts about 0.8 second for healthy subjects and less for neurological impaired patients (both are present in the Gait data set).

Original: Third, for the angular velocities, most of the selected frequencies are below 0.5 Hz.
Revised: Third, for the angular velocities, most of the selected frequencies are below 0.5 Hz.

Original: This is consistent with the behaviour of the signal during the turnaround: there is a relatively smooth peak in the angular velocity (see Figure 1) which is visible at frequencies below 0.5 Hz.
Revised: This is consistent with the behaviour of the signal during the turnaround: there is a relatively smooth peak in the angular velocity (see Figure 1) which is visible at frequencies below 0.5 Hz.

Original:  Conclusion and future work
Revised:  Conclusion and future work

Original: In this paper, we have presented a procedure to integrate expert’s annotations to improve change-pointdetection algorithms, without resorting to a time-consuming calibration by trial and error.
Revised: In this paper, we have presented a procedure to integrate expert’s annotations to improve change-point detection algorithms, without resorting to a time-consuming calibration by trial and error.

Original: In addition,the learned metric performs an informative dimension selection.
Revised: In addition, the learned metric performs an informative dimension selection.

Original: In future works, we will tackle thesituation where the number of changes is unknown, by combining existing approaches [5, 10] withour own.
Revised: In future works, we will tackle the situation where the number of changes is unknown, by combining existing approaches [5, 10] with our own.

Original: Also, more complex transformations of the signal could be considered, e.g. neural networks. 
Revised: Also, more complex transformations of the signal could be considered, e.g. neural networks. segmentation algorithms.

Revised: Acknowledgments and Disclosure of Funding

Revised: Charles Truong is funded by the Industrial Data Analytics and Machine Learning (IDAML) chair of ENS Paris-Saclay.

Revised: Part of this work has been funded by Region Ile-de-France.

Revised: Part of the computations has been executed on Atos Edge computer.