Some edits.

Author: astamm

_02_Material.qmd

@@ -206,7 +206,7 @@ smoothed_qts |>
 Smoothed version of a centered QTS.
 :::
 
-The code above illustrates some other nice S3 specializations implemented in the [{squat}](https://cran.r-project.org/package=squat/) package such as the `log()` and `exp()` functions to compute the logarithm and exponential of a unit QTS respectively. As mentioned in @sec-quaternions, the logarithm of a unit quaternion has a null scalar part, which is why we set the *w* coordinate to zero in the code above and only smooth the three other coordinates. @fig-smoothed-qts nicely shows the smoothing effect with subtle variations along the curves that are smoothed out.
+The code above illustrates some other nice S3 specializations implemented in the [{squat}](https://cran.r-project.org/package=squat/) package such as the `log()` and `exp()` functions to compute the logarithm and exponential of a unit QTS respectively. As mentioned in @sec-quaternions, the logarithm of a unit quaternion has a null scalar part, which is why we set the *w* coordinate to zero in the code above and only smooth the three other coordinates. The function `squat::qts2sqts()` is dedicated to performing this exact computation. @fig-smoothed-qts nicely shows the smoothing effect with subtle variations along the curves that are smoothed out.
 
 ### Pressure mat data
 

_03_Methods.qmd

@@ -6,15 +6,15 @@ Gait event detection is performed by evaluating and comparing two strategies to
 
 Strategy E: Predicting gait [E]{.underline}vents
 
-: The strategy E pertains to directly predicting the gait events occuring when walking. Specifically, we classify the observations into five categories:
+: The strategy E pertains to directly predicting the gait events occuring when walking. Specifically, time points are viewed as statistical units (observations) and we aim at classifying them into five categories:
 
 - *Right Heel Strike*,
 - *Left Toe Off*,
 - *Left Heel Strike*,
 - *Right Toe Off*,
 - *None* (all other times not corresponding to a certain event).
 
-This strategy aims at directly predicting the occurrence of gait events of interest. However, it inherits by construction of a severe class imbalance  effect, with the *None* class widely over-represented. Indeed, the class that represents all the times that do not belong to an event is clearly larger than the four other ones (see @tbl-class-imbalance). It is clearly represented on @fig-event-timeserie where we can see the event times from the GAITRite® mat overlaid on the QTS recorded by the IMU. Each colored point represents a different event and all other times belong to the *None* class.
+The first four events  (RHS, LTO, LHS and RTO) are coined *events of interest* while the last one encodes the so-called *negative* class. While conveniently aiming at directly predicting the occurrence of gait events of interest, this strategy suffers from a severe class imbalance issue, with the *None* (negative) class being widely over-represented as summarized in @tbl-class-imbalance.
 
 ::: {#tbl-class-imbalance tbl-pos="H"}
 
@@ -48,6 +48,8 @@ Strategy E: Count and proportion of observations in each class.
 
 :::
 
+Another way of showing this issue is to overlay the occurence of the events of interest detected by the GAITRite® mat on a QTS recorded by the IMU device (see @fig-event-timeserie). Each colored point represents an event of interest and all other times belong to the *None* class.
+
 ![Gait event occurences overlaid on a unit QTS.](images/events_on_time_serie_MSI_N_R2.png){#fig-event-timeserie width=350}
 
 To mitigate this effect, when the mat records the occurence of a gait event of interest at a specific time point, we also label surrounding time points with the same event. The size of this window is controlled by a parameter $k$ which sets the number of preceding points labelled as the event of interest. It also allows to account for some uncertainty as the time range between two points is only 10 ms. For instance, if we set $k = 1$, we label $3$ observations as part of the event rather than just one. In this case, we consider that the event happens in a window of $20$ ms.