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  <front>
    <journal-meta>
      <issn pub-type="ppub">1613-0073</issn>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Spatio-temporal Event Transformer on Versatile Tasks for Human Behavior Analysis</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Kejing Xia</string-name>
          <email>xiakejing.lesia@whu.edu.cn</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lixuan Wei</string-name>
          <email>weilx_selina@whu.edu.cn</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Lei Yu</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Electronic Information School, Wuhan University</institution>
          ,
          <addr-line>Wuhan, Hubei Province</addr-line>
          ,
          <country>P.R.</country>
          <addr-line>China. 430072</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Human behavior</institution>
          ,
          <addr-line>Event-based, Multi-task, rPPG, Micro-expression, Micro-gesture</addr-line>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2024</year>
      </pub-date>
      <abstract>
        <p>Human behavior encompasses a range of physical actions and changes exhibited by individuals, including gesture variations, facial expressions, and physiological state changes. Given the diversity and complexity of these behaviors, a versatile and robust analytical method is highly necessary. We introduce the Spatio-temporal Event Transformer (STET), the first approach to leverage event streams for multi-task human behavior analysis. By utilizing the unique characteristics of events, we can efectively extract features across diferent time scales (ranging from 1 μs to extended sequences). Specifically, we employ an E-Voxel Guided Multi-head Transformer (EVGMH) module to fuse event information at various scales, enhancing the representation of spatio-temporal features. Our experimental results on multiple task datasets demonstrate the eficacy of the STET method, establishing a new benchmark for event-based human behavior analysis.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>-</title>
      <p>CEUR
ceur-ws.org</p>
    </sec>
    <sec id="sec-2">
      <title>1. Introduction</title>
      <p>
        The field of human behavior analysis has deepened with the continuous development of
computer vision [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. This expansion not only enhances our understanding of human behavior,
emotions, and physiological states but also drives advancements in areas such as healthcare,
security, and human-computer interaction. However, due to the diversity and complexity of
human behavior, various analysis techniques (e.g. heartbeat detection [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ], facial expression
recognition [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ], and gesture understanding [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]) exhibit significant diferences in their
representation methods. For instance, heartbeat is characterized by periodicity, facial expressions
by idiosyncratic and subtle variations, and gestures by idiosyncratic and large movements.
Additionally, existing methods [
        <xref ref-type="bibr" rid="ref5 ref6 ref7 ref8">5, 6, 7, 8</xref>
        ] typically address only a single type of human behavior
detection.
      </p>
      <p>
        To address these issues and adopt a general approach to physiological measurements,
current research has proposed video-based methods. These methods can conveniently replace
traditional, highly specific non-visual methods with remote techniques, utilizing the learning
capabilities of networks to uncover pixel-level subtle changes caused by physiological signals
in images. In particular, some methods [
        <xref ref-type="bibr" rid="ref5 ref9">5, 9</xref>
        ] achieve remote photoplethysmography (rPPG)
measurement through end-to-end network architectures, discarding contact-based ECG and
L
      </p>
      <p>L 
Event Frame
Event Voxel
rPPG
ME
MG</p>
      <p>Attention Score Map
Multi-type Event Patch Embedding Block</p>
      <p>E-Voxel Guided Multi-head</p>
      <p>
        Transformer Block
PPG methods in the process; In the field of micro-expression research, initial studies [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]
employed high-frame-rate (200 FPS) videos to capture the requisite data, subsequently utilizing
deep networks to comprehend the micro-level facial alterations; In the field of micro-gesture,
JSSE [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] proposed a 3D-CNNs micro gesture recognition network that incorporates skeletal and
semantic embedding loss to improve classifying results.
      </p>
      <p>
        Event cameras are asynchronous visual sensors that sample brightness changes for each pixel
and generate a stream of events with timestamps when the intensity change occurs [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. Each
event contains the coordinate, timestamp, and polarity of the brightness-changed pixel. Event
cameras possess outstanding features, including high dynamic range (HDR), low latency (1 ),
and low power consumption [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]. In comparison to frame-based cameras, event cameras are
capable of capturing a greater quantity of useful behavioral information, such as facial blood
vessel pulsations, expression changes, and gesture movements.
      </p>
      <p>In light of these distinctive characteristics of event cameras, we are the first to propose
an event-based method for human behavior analysis, i.e. STET. As shown in Figure 1, the
end-to-end STET includes a Multi-type Event Patch Embedding (MTE) module, an E-Voxel
Guided Multi-head Transformer (EVGMH) module, and task-specific prediction heads. The
MTE module extracts event features from event formations to tokens. The EVGMH module is
designed to enhance the feature and facilitate spatio-temporal feature representations, efectively
decomposing the idiosyncratic and periodic features in the original input events. Finally, the
feature representations are fed to the task-specific prediction heads for diferent tasks.</p>
      <p>In summary, our contributions are as follows:
• We propose an end-to-end STET method, the first approach presenting a general
framework utilizing events for multi-task human behavior analysis.
• We introduce an E-Voxel Guided Multi-head Transformer Block to make use of features
from event frames that focus on global compressed information and event voxels that
focus on local temporal information.
• We build a simulated event dataset, E-Human Behaviour (EHB) dataset, for multiple
human behavior analysis tasks. Additionally, we conduct multiple experiments and
provide an event-based experimental benchmark.</p>
    </sec>
    <sec id="sec-3">
      <title>2. Related Works</title>
      <sec id="sec-3-1">
        <title>2.1. Human Behaviour Analysis</title>
        <p>
          Remote photoplethysmography measurement. The minute variations in light reflections
from human facial skin can be utilized to extract heart rate [
          <xref ref-type="bibr" rid="ref11">11</xref>
          ]. Various HR estimation
techniques have utilized information from diferent color channels and regions of interest (ROI)
to recover rPPG signals, employing techniques like blind signal separation (e.g., independent
component analysis (ICA) [
          <xref ref-type="bibr" rid="ref12">12, 13</xref>
          ]), matrix completion [14], and optimal space transformation
[15]. Building on these foundations, several deep learning-based approaches have been
developed [16, 17, 18, 19, 20, 21]. Špetlík et al. [20] introduced a two-stage, two-dimensional CNN
method, while Chen et al. further advanced the field with convolutional attention networks for
physiological measurement [21]. To better utilize spatio-temporal information in facial videos,
several end-to-end spatio-temporal attention methods have been developed to directly recover
rPPG signals from these videos [
          <xref ref-type="bibr" rid="ref5 ref9">5, 9, 22, 23, 24, 25</xref>
          ].
        </p>
        <p>
          Micro-expression recognition. In micro-expression recognition, various methods based
on optical flow, such as Main Directional Mean Optical Flow (MDMO) [ 26] and its improved
versions like Facial Dynamics Map [27], Sparse MDMO [28], and Bi-Weighted Oriented Optical
Flow [29], extract micro-expression features by calculating the average optical flow of facial
regions. Additionally, some CNN and LSTM methods analyze micro-expressions by extracting
spatio-temporal features from frames [30, 31, 32]. Due to the short duration and subtlety of
micro-expressions, Yang proposed MERTA [33], which employs three attention mechanisms
to construct feature maps. To further leverage the temporal and spatial features of
microexpressions, Micron-BERT [
          <xref ref-type="bibr" rid="ref6">6</xref>
          ] introduced a self-supervised framework  -BERT consistently
achieves State-of-the-Art result in various ME benchmarks.
        </p>
        <p>
          Micro-gesture understanding. Body gestures can convey a wide range of emotions and
mental states [34, 35, 36, 37]. For the classification task of pre-segmented body gestures,
traditional RGB-based methods such as 2D CNN [38, 39, 40] and 3D CNN [41, 42] utilize frame
sequence depth and optical flow for classification. Additionally, some approaches directly extract
gestures by leveraging spatio-temporal relationships within frame sequences. The SlowFast
model [43] captures both long-term and short-term temporal information through dual pathways.
Shah et al. [44] employ graph-encoding convolutional networks to identify semantic features,
while Huang et al. [
          <xref ref-type="bibr" rid="ref8">8</xref>
          ] propose a deep framework with an ensemble hypergraph-convolution
Transformer. Recently, the JSSE model [
          <xref ref-type="bibr" rid="ref7">7</xref>
          ] introduced a 3D-CNNs micro-gesture recognition
network that incorporates skeletal and semantic embedding loss to enhance classification results.
        </p>
      </sec>
      <sec id="sec-3-2">
        <title>2.2. Event Camera in Computer Vision</title>
        <p>
          Event cameras are bio-inspired visual sensors that generate asynchronous event streams [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]
by responding to changes in brightness [45]. Each event consists of pixel location, timestamp,
and polarity, distinguishing them from conventional RGB-based data. Due to the paradigm
shift in visual information acquisition, event cameras possess unique characteristics such as
extremely low latency, high dynamic range (HDR), and low power consumption [
          <xref ref-type="bibr" rid="ref10">10</xref>
          ]. These
features drive research in various fields, including occlusion removal [
          <xref ref-type="bibr" rid="ref13 ref14">46, 47</xref>
          ], super-resolving
[
          <xref ref-type="bibr" rid="ref15 ref16">48, 49</xref>
          ], and motion deblurring [
          <xref ref-type="bibr" rid="ref17 ref18">50, 51</xref>
          ]. In our task, event cameras have significant advantages
in capturing subtle behaviors, including rPPG signals, micro-expression, and micro-gesture. The
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        <sec id="sec-3-2-1">
          <title>Event Stream</title>
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E-Voxel Guided Multi-head
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        </sec>
        <sec id="sec-3-2-2">
          <title>Event Frame</title>
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(b) Temporal Attention Module (TAM)</p>
        </sec>
        <sec id="sec-3-2-3">
          <title>Multi-head</title>
        </sec>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>3. Methods</title>
      <p>This section presents a comprehensive overview of our Spatio-temporal Event Transformer
(STET) network, which is depicted in Fig.2.</p>
      <p>Our model processes raw event streams as input. Specifically, the  -th event, e = (x ,   ,   ) is
triggered at pixel coordinate x and time   whenever the log-scale brightness change exceeds a
threshold  &gt; 0 ,
log( (, x)) − log( ( +  , x)) =  ⋅ ,
(1)
where  (, x) and  ( +  ,</p>
      <p>x) are the brightness intensity of position x at time  and  +  . The
polarity  ∈ {+1, −1} indicates the direction of brightness change.</p>
      <p>First, a Multi-type Event Patch Embedding (MTE) module is developed to extract event features
as tokens, utilizing both global-local and spatio-temporal event information. Furthermore, an
EVoxel Guided Multi-head Transformer (EVGMH) module is employed to enhance event features
and facilitate spatio-temporal feature representations.Finally, the feature representations are
fed into task-specific prediction heads for diferent tasks. Further details will be provided in the
subsequent sections.</p>
      <sec id="sec-4-1">
        <title>3.1. Multi-type Event Patch Embedding Block</title>
        <p>
          Multi-type Event Patch Embedding Block (MTE) can be divided into two parts: spatial and
temporal (frame and temporal-voxel). First, the long event stream is partitioned into short
sequences  = { S1, S2, ..., S }. The event points in each short sequence are projected onto
the pixel coordinate system according to their coordinates x = (x1, x2) and accumulated
sequentially, resulting in a sequence of k event frames ℱ = {F1, F2, ..., F }. Next, the feature
dimensions are expanded through a coarsely-to-finely downsample 3D temporal adaptive
convolution layer [
          <xref ref-type="bibr" rid="ref19">52</xref>
          ], achieving patch embedding to obtain the token   . Additionally,
to preserve the temporal information in the event frames, the event points in the  short
sequences are projected onto the voxel coordinate system based on v = (, x1, x2), producing an
event voxel sequence. However, event voxels are extremely sparse and not suitable for direct
representation. Inspired by CEUTrack [
          <xref ref-type="bibr" rid="ref20">53</xref>
          ] and typical 3D perceptual models [
          <xref ref-type="bibr" rid="ref21 ref22 ref23">54, 55, 56</xref>
          ], we
perform a sparse representation of event voxels. The event voxels are converted into interval
voxels V
 = (V , V , V , V ). Here, V and V
 represent the coordinates x = (x1, x2), V
represents the time dimension  , and V is the feature representation of the event voxel V . V
has a dimension of 19, consisting of three coordinate values and voxel features of length 1 ×
16. We then sort the voxel grids by event density and select the top 1024 grids to sparsify the
input dimensions, obtaining sparse event voxel  . Moreover, we use the 3D temporal adaptive
convolution layer for its patch embedding and get the token   .
        </p>
        <p>,  
=   (  ( )),
(2)
where   ,   ∈ ℝ× ×</p>
        <p>, here  ,  and  denote batch size, short sequences numbers, and token
dimension, respectively. Finally, fully connected projection layers are applied to   and   ,
before inputting them into the transformer architecture.</p>
      </sec>
      <sec id="sec-4-2">
        <title>3.2. E-Voxel Guided Multi-head Transformer Block</title>
        <p>
          Inspired by Physformer [
          <xref ref-type="bibr" rid="ref9">9</xref>
          ], we propose the Temporal Attention Module (TAM). The E-Voxel
Guided Multi-head Transformer Block (EVGMH) consisting of multiple TAMs that compute the
attention between the frame token   and the voxel token   as well as self-attention of the
frame token   itself, as shown in Fig.2, Temporal Attention Module.
        </p>
        <p>
          Based on the self-attention mechanism [
          <xref ref-type="bibr" rid="ref24 ref25">57, 58</xref>
          ], we utilize 3D temporal adaptive convolution
(C3DAda) layer instead of point linear projection for query (Q) and keyword (K) projections,
which captures fine-grained local temporal features. For the value (V) projection, we utilize
linear projection.
        </p>
        <p>{
,  ,  =
,  ,  =</p>
        <p>C3DAda(  ), C3DAda(  ),     ,    ℎ</p>
        <p>,</p>
        <p>C3DAda(  ), C3DAda(  ),     ,    ℎ   ,
Afterwards, the flattened sequences of
 ,  , and  , denoted as ,  ,  ∈ ℝ
× ×
, are split into
ℎ heads (with  ℎ = /ℎ for each head). For the  -th head ( ≤ ℎ ), the self-attention score ( ) can
be calculated using the following formulas:
  ,  
 = Softmax (      ), Softmax (  ⋅   ).</p>
        <p>√ ℎ</p>
        <p>The output of E-Voxel Guided Multi-head Transformer Block (EVGMH) is obtained by
concatenating   from all heads and then applying a linear (full connected layer) projection ∈ ℝ× .
The first layer and following layers of EVGMH operation can be represented as:</p>
        <p>= MLP(Concate(Att1; Att2; ...; Attℎ)).</p>
        <p>As depicted in Fig.2, a residual connection and layer normalization are applied after the
attention operation. Subsequently, the result is fed into the feed-forward network, which
comprises two convolution layers with batch normalization and nonlinear activation to refine
local inconsistencies and reduce noise in the features.
(3)
(4)
(5)</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>4. Experiments</title>
      <sec id="sec-5-1">
        <title>4.1. Experimental Settings</title>
        <p>
          Datasets. SMIC: SMIC [
          <xref ref-type="bibr" rid="ref28">61</xref>
          ] is made up of 164 samples. Lacking apex frame and action unit
labels, the samples span 16 participants of 3 ethnicities. The recordings are taken with a
resolution of 640 × 480 at 100 fps. UBFC: UBFC [
          <xref ref-type="bibr" rid="ref29">62</xref>
          ] is a dataset comprised of RGB video
recordings (30fps). Participants are seated and lit with ambient light. The dataset includes
ground truth obtained through contact-sensor-based PPG measurements. iMiGUE: iMiGUE
[
          <xref ref-type="bibr" rid="ref30">63</xref>
          ] collected 359 videos of post-match press conferences from Grand Slam tournaments via
        </p>
      </sec>
      <sec id="sec-5-2">
        <title>3.3. Prediction Head</title>
        <p>Based on diferent prediction tasks, we designed simple prediction heads. We firstly downsample
the output token to obtain a sequence of feature representations. For the rPPG task, a fully
connected layer outputs PPG signal results as a time series. For micro-expression or
microgesture recognition, the feature sequence passes through an LSTM block, followed by a fully
connected layer projecting to the classification categories.</p>
      </sec>
      <sec id="sec-5-3">
        <title>3.4. Loss Function</title>
        <p>
          For rPPG prediction, we use PhysFormer’s label distribution method [
          <xref ref-type="bibr" rid="ref26">59</xref>
          ] and frame HR
estimation as a multi-label classification task [
          <xref ref-type="bibr" rid="ref27">60</xref>
          ] with ℒLD. We also examine the correlation
between the predicted rPPG signal and ground truth with ℒtime. For micro-expression and
micro-gesture classification, we use the cross-entropy loss function as ℒ . More details for
loss function are provided in the Appendix. The final loss function is defined as:
where the  and  are hyperparameters that can be adjusted to balance ℒLD and ℒtime.
online video-sharing platforms. The videos have a resolution of 1280×720 and a frame rate of
25 fps. A total of 18,499 MG samples are labeled and assigned to 32 categories, along with one
non-MG category, resulting in an average of approximately 51 MG samples per video.
        </p>
        <p>
          Our E-Human Behaviour dataset is from simulation. First of all, the dataset is produced from
the public rPPG datasets UBFC, micro-expression datasets SMIC, and a part of micro-gesture
understanding datasets iMiGUE (because of space constraints), in which we input the reshaped
gray (from RGB) channel images into the event simulator DVS-voltmeter [
          <xref ref-type="bibr" rid="ref31">64</xref>
          ]. In total, our
proposed E-Human Behaviour dataset consists of 584 face region (164 from SMIC and 420 from
UBFC) and 3500 upper body region (from iMiGUE) event streams with a resolution of 128×128
and the corresponding PPG signals as well as micro-expression and micro-gesture categories.
Implementation details. We implement the network using PyTorch [
          <xref ref-type="bibr" rid="ref32">65</xref>
          ] and the ADAM
optimizer [
          <xref ref-type="bibr" rid="ref33">66</xref>
          ] with an initial learning rate of 4e-4 and a weight decay of 5e-5. The model is
trained for 200 epochs on a NVIDIA TITAN Xp 12G. For ℒ , like Physformer, a fixed  is
set to 0.1, while the parameter  for frequency loss grew exponentially. For EVGMH, we used
the settings block number  = 6 , multi-head ℎ = 4,  = 96,   ′  = 512. The targeted token
patch size Ts × Hs × Ws is set to 1 × 4 × 4. During the training phase, we randomly select event
streams from the dataset corresponding to a constant duration and input these streams into
the network via the MTE module with a temporal size of 160, corresponding to the subsequent
segment inputs.
        </p>
      </sec>
      <sec id="sec-5-4">
        <title>4.2. Comparison with the State-of-the-arts</title>
        <p>For the three tasks, we perform 9-fold cross-validation on the UBFC, SMIC, and iMiGUE datasets.
We use the experimental metrics from other methods and present the test results for the UBFC,
SMIC, and iMiGUE datasets in Table 1, Table 2, and Table 3, respectively. Although our
eventbased approach does not show a distinct advantage in the evaluated metrics, it demonstrates
the feasibility of our method.</p>
        <p>Notably, the training set accuracy reaches nearly 100% during training on the SMIC datasets,
but the model performs poorly on the test set, indicating overfitting due to the small dataset
size. This issue is less significant for the larger iMiGUE dataset, where there is no significant
gap between training and test set performance.</p>
        <p>The event data in this experiment is simulated from the original image data. The quality of
this simulation depends on the original data, and the information in the simulated events cannot
exceed that of the original images. Additionally, our simulation produces a one-channel event
stream, resized to 128 × 128 for network bandwidth considerations. Despite these constraints,
the event-based method has proven efective in the three human behavior analysis tasks,
demonstrating its potential in this field.</p>
      </sec>
      <sec id="sec-5-5">
        <title>4.3. Ablation Study</title>
        <p>In this section, we provide the results of ablation studies for micro-gesture on the 9-fold
crossvalidation of the iMiGUE dataset.</p>
        <p>Analysis of network hyperparameters. We perform ablation experiments on the network
hyperparameters, specifically investigating the number of feature dimensions in the TAM and
the number of EVGMHs. As presented in Table.4, the evaluation metrics exhibit improvement
with an increase in feature dimensions and a higher number of EVGMHs. This enhancement
can be attributed to the larger network model’s superior capability to capture spatio-temporal
features within the event stream, resulting in more precise predictions.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>5. Conclusion</title>
      <p>This paper introduces STET, a novel event-based multi-task architecture for rPPG measurement,
micro-expression recognition, and micro-gesture understanding. Our approach combines
events compressed into frames and transformed into voxel representations, fully leveraging
the potential of events to capture the spatio-temporal features of human behavior. The results
demonstrate that our method efectively models spatially and temporally diverse event signals.
While the current STET does not surpass state-of-the-art methods, event-based approaches
ofer promising new solutions for the field, indicating that further exploration into event-based
analysis of human behavior is warranted.
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      <p>
        As mentioned in [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ], the facial rPPG signals with similar HR values exhibit similar periodicity.
Motivated by this observation, we consider each event stream as an instance associated with a
label distribution. This label distribution covers a range of class labels, indicating the extent to
which each label describes the instance. By doing so, an event stream contributes not only to
its target HR value but also to its neighboring HR values. To incorporate similarity information
among HR classes during training, the rPPG-based HR estimation problem is formulated as a

specific  -class multi-label classification task, where  is 139 in our case (each integer HR value
within the range of 42 to 180 bpm is considered a class). Each event stream is assigned a label
distribution p = { 1,  2, ...,   } ∈ ℝ . We assume that each entry of p is a real value between 0
and 1, satisfying ∑
      </p>
      <p>=1   = 1. To construct the corresponding label distribution p, a Gaussian
distribution function centered at the ground truth HR label    , with a standard deviation of 
as follows was employed,
  =</p>
      <p>1
√2
exp(−
( − (</p>
      <p>− 41))2
2 2
).</p>
      <p>
        The label distribution loss, denoted as ℒLD, is formulated as the Kullback-Leibler (KL) [
        <xref ref-type="bibr" rid="ref27">60</xref>
        ]
divergence between the label distribution p and the softmax of the predicted rPPG signal’s
power spectral density (PSD), represented as p̂:
      </p>
    </sec>
    <sec id="sec-7">
      <title>6. Appendix</title>
      <sec id="sec-7-1">
        <title>6.1. Loss Function</title>
        <p>ℒLD = KL(p, Softmax (p̂)).</p>
        <p>Moreover, in the time domain, we analyze the accuracy of the response prediction by realizing
the correlation between the predicted rPPG signal and ground truth. We define the loss function
ℒtime in the time domain based on the negative Pearson loss [25]. To adapt the Pearson
correlation for use as a loss function, the loss function ℒtime can be defined as:
ℒtime = {
||,
1 − ,
if  &lt; 0,
if  ≥ 0,
where  is the Pearson correlation coeficient between the predicted rPPG signal and ground
truth. Finally, the dynamic loss ℒ</p>
        <p>is formulated as follows:
where the value of  is dynamically adjusted based on the current epoch number   and the
total number of epochs  :
 =  0 ⋅   .</p>
        <p>−1</p>
        <p>Then, in the micro-expression and micro-gesture classification task, the cross-entropy loss
function is used to measure the diference between the predicted probability distribution and
probability distribution   ̂ , the cross-entropy loss function ℒ is defined as follows:
the true distribution. Given an input sample  with its true label  , and the model’s predicted
(6)
(7)
(8)
(9)
(10)
where  (
and  ( ̂</p>
        <p>) is the true label distribution for class  (one-hot encoded for classification tasks),
) is the predicted probability for class  . Eventually, we adopt cross-entropy loss as
(micro-expression) and ℒ</p>
      </sec>
    </sec>
  </body>
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