# Video Camera Identification from Sensor Pattern Noise with a Constrained
ConvNet

Derrick Timmerman* 1 , Guru Swaroop Bennabhaktula*1 , Enrique Alegre2 , and
George Azzopardi1
1Bernoulli Institute for Mathematics, Computer Science and Artificial
Intelligence,
University of Groningen, The Netherlands
2 Group for Vision and Intelligent Systems, Universidad de León, Spain
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
https://orcid.org/0000-0002-9797-8261 https://orcid.org/0000-0002-8434-9271
https://orcid.org/0000-0003-2081-774X https://orcid.org/0000-0001-6552-2596

###### Abstract

The identification of source cameras from videos, though it is a highly
relevant forensic analysis topic, has been studied much less than its
counterpart that uses images. In this work we propose a method to identify the
source camera of a video based on camera specific noise patterns that we
extract from video frames. For the extraction of noise pattern features, we
propose an extended version of a constrained convolutional layer capable of
processing color inputs. Our system is designed to classify individual video
frames which are in turn combined by a majority vote to identify the source
camera. We evaluated this approach on the benchmark VISION data set consisting
of $1539$ videos from $28$ different cameras. To the best of our knowledge,
this is the first work that addresses the challenge of video camera
identification on a device level. The experiments show that our approach is
very promising, achieving up to $93.1\%$ accuracy while being robust to the
WhatsApp and YouTube compression techniques. This work is part of the EU-
funded project 4NSEEK focused on forensics against child sexual abuse.

##  1 INTRODUCTION

††*Derrick Timmerman and Guru Swaroop Bennabhaktula are both first authors.

Source camera identification of digital media plays an important role in
counteracting problems that come along with the simplified way of sharing
digital content. Proposed solutions aim to reverse-engineer the acquisition
process of digital content to trace the origin, either on a model or device
level. Whereas the former aims to identify the brand and model of a camera,
the latter aims at identifying a specific instance of a particular model.
Detecting the source camera that has been used to capture an image or record a
video can be crucial to point out the actual owner of the content, but could
also serve as additional evidence in court.

Proposed techniques typically aim to identify the source camera by extracting
noise patterns from the digital content. Noise patterns can be thought of as
an invisible trace, intrinsically generated by a particular device. These
traces are the result of imperfections during the manufacturing process and
are considered unique for an individual device (Lukáš et al.,, 2006). By its
unique nature and its presence on every acquired content, the noise pattern
functions as an instrument to identify the camera model.

Within the field of source camera identification a distinction is made between
image and video camera identification. Though a digital camera can capture
both images and videos, in a recent study it is experimentally shown that a
system designed to identify the camera model of a given image cannot be
directly applied to the problem of video camera model identification (Hosler
et al.,, 2019). Therefore, separate techniques are required to address both
problems.

Though great effort is put into identifying the source camera of an image,
significantly less research has been conducted so far on a similar task using
digital videos (Milani et al.,, 2012). Moreover, to the best of our knowledge,
only a single study addresses the problem of video camera model identification
by utilizing deep learning techniques (Hosler et al.,, 2019). Given the
potential of such techniques in combination with the prominent role of digital
videos in shared digital media, the main goal of this work is to further
explore the possibilities of identifying the source camera at device level of
a given video by investigating a deep learning pipeline.

In this paper we present a methodology to identify the source camera device of
a video. We train a deep learning system based on the constrained
convolutional neural network architecture proposed by Bayar and Stamm, (2018)
for the extraction of noise patterns, to classify individual video frames.
Subsequently, we identify the video camera device by applying the simple
majority vote after aggregating frame classifications per video.

With respect to current state-of-the-art approaches, we advance with the
following contributions: i) to the best of our knowledge, we are the first to
address video camera identification on a device level by including multiple
instances of the same brand and model; ii) we evaluate the robustness of the
proposed method with respect to common video compression techniques for videos
shared on the social media platforms, such as WhatsApp and YouTube; iii) we
propose a multi-channel constrained convolutional layer, and conduct
experiments to show its effectiveness in extracting better camera features by
suppressing the scene content.

The rest of the paper is organized as follows. We start by presenting an
overview of model-based techniques in source camera identification, followed
by current state-of-the-art approaches in Section 2. In Section 3 we describe
the methodology for the extraction of noise pattern features for the
classification of frames and videos. Experimental results along with the data
set description are provided in Section 4. We provide a discussion of certain
aspects of the proposed work in Section 5 and finally, we draw conclusions in
Section 6.

##  2 RELATED WORK

In the past decades, several approaches have been proposed to address the
problem of image camera model identification (Bayram et al.,, 2005; Li,, 2010;
Bondi et al.,, 2016; Bennabhaktula. et al.,, 2020). Those methodologies aim to
extract noise pattern features from the input image or video that characterise
the respective camera model. These noise patterns or traces are the result of
imperfections during the manufacturing process and are thought to be unique
for every camera model (Lukáš et al.,, 2006). More specifically, during the
acquisition process at shooting time, camera models perform series of
sophisticated operations applied to the raw content before it is saved in
memory, as shown in Fig. 1. During these operations, characteristic traces are
introduced to the acquired content, resulting in a unique noise pattern
embedded in the final output image or video. This noise pattern is considered
to be deterministic and irreversible for a single camera sensor and is added
to every image or video the camera acquires (Caldell et al.,, 2010).

Figure 1: Acquisition pipeline of an image. Adapted from Chen and Stamm,
(2015).

###  2.1 Model-based Techniques

Based on the hypothesis of unique noise patterns, many image camera model
identification algorithms have been proposed aiming at capturing these
characteristic traces which can be divided into two main categories: hardware
and software based techniques. Hardware techniques consider the physical
components of a camera such as the camera’s CCD (Charge Coupled Device) sensor
(Geradts et al.,, 2001) or the lens (Dirik et al.,, 2008). Software techniques
capture traces left behind by internal components of the acquisition pipeline
of the camera, such as the sensor pattern noise (SPN) (Lukas et al.,, 2006) or
demosaicing strategies (Milani et al.,, 2014).

###  2.2 Data-driven Technologies

Although model-based techniques have shown to achieve good results, they all
rely on manually defined procedures to extract (parts of) the characteristic
noise patterns. Better results are achieved by applying deep learning
techniques, also known as data-driven methodologies. There are a few reasons
why these methods work so well. First, these techniques are easily scalable
since they learn directly from data. Therefore, adding new camera models does
not require manual effort and is a straightforward process. Second, these
techniques often perform better when trained with large amounts of data,
allowing us to take advantage of the abundance of digital images and videos
publicly available on the internet.

Given their ability to learn salient features directly from data,
convolutional neural networks (ConvNets) are frequently incorporated to
address the problem of image camera model identification. To further improve
the feature learning process of ConvNets, tools from steganalysis have been
adapted that suppress the high level scene content of an image (Qiu et al.,,
2014). In their existing form, convolutional layers tend to extract features
that capture the scene content of an image as opposed to the desired
characteristic camera detection features, i.e. the noise patterns. This
behavior was first observed by Chen et al., (2015) in their study to detect
traces of median filtering. Since the ConvNet was not able to learn median
filtering detection features by feeding images directly to the input layer,
they extracted the median filter residual (i.e. a high dimensional feature
set) from the image and provided it to the ConvNet’s input layer, resulting in
an improvement in classification accuracy.

Following the observations of Chen et al., (2015), two options for the ConvNet
have emerged that suppress the scene content of an image: using a
predetermined high-pass filter (HPF) within the input layer (Pibre et al.,,
2016) or the adaptive constrained convolutional layer (Bayar and Stamm,,
2016). Whereas the former requires human intervention to set the predetermined
filter, the latter is able to jointly suppress the scene content and to
adaptively learn relationships between neighbouring pixels. Initially designed
for image manipulation detection, the constrained convolutional layer shows to
achieve state-of-the-art results in other digital forensic problems as well,
including image camera model identification (Bayar and Stamm,, 2017).

Although deep learning techniques are commonly used to identify the source
camera of an image, it was not until very recently that these techniques were
applied to video camera identification. Therefore, the work of Hosler et al.,
(2019) is one of the few ones closely related to the ideas we propose. Hosler
et al., adopted the constrained ConvNet architecture proposed by Bayar and
Stamm, (2018), although they removed the constrained convolutional layer due
to its incompatibility with color inputs. To identify the camera model of a
video, in their work they train the ConvNet to produce classification scores
for patches extracted from video frames. Subsequently, individual patch scores
are combined to produce video-level classifications, as single-patch
classifications showed to be insufficiently reliable.

The ideas we propose in this work differ from Hosler et al., (2019) in the
following ways. Instead of removing the constrained convolutional layer, we
propose an extended version of it by making it suitable for color inputs.
Furthermore, instead of using purely different camera models, we include $28$
camera devices among which $13$ are of the same brand and model, allowing us
to investigate the problem in a device-based manner. Lastly, we provide the
network with the entire video frame to extract noise pattern features, whereas
Hosler et al., use smaller patches extracted from frames.

##  3 METHODOLOGY

In Fig. 2 we illustrate a high level overview of our methodology, which mainly
consists of the following steps: i) extraction of frames from the input video;
ii) classification of frames by the trained ConstrainedNet, and iii)
aggregation of frame classifications to produce video-level classifications.

In the following sections, the frame extraction process is explained, as well
as the voting procedure. Furthermore, architectural details of the
ConstrainedNet are provided.

Figure 2: High level overview of our methodology. During the training process,
highlighted in red, $N$ frames are extracted from a video $V$, inheriting the
same label $y$ to train the ConstrainedNet. During evaluation, highlighted in
black, the ConstrainedNet produces $\hat{y}_{n}$ labels for $N$ frames to
predict the label $\hat{y}$ of the given video.

###  3.1 ConstrainedNet

We propose a ConstrainedNet which we make publicly
available111https://github.com/zhemann/vcmi, that we train with deep learning
for video device identification based on recent techniques in image (Bayar and
Stamm,, 2018) and video (Hosler et al.,, 2019) camera identification. We adapt
the constrained ConvNet architecture proposed by Bayar and Stamm, (2018) and
apply a few modifications. Given the strong variation in video resolutions
within the data set that we use, we set the input size of our network equals
to the smallest video resolution of $480$ $\times$ $800$ pixels. Furthermore,
we increase the size of the first two fully-connected layers from $200$ to
$1024$, and most importantly, we extend the original constrained convolutional
layer by adapting it for color inputs.

The constrained convolutional layer was originally proposed by Bayar and
Stamm, (2016) and is a modified version of a regular convolutional layer. The
idea behind this layer is that relationships exist between neighbouring pixels
independent of the scene content. Those relationships are characteristic of a
camera device and are estimated by jointly suppressing the high-level scene
content and learning connections between a pixel and its neighbours, also
referred to as pixel value prediction errors (Bayar and Stamm,, 2016).
Suppressing the high-level scene content is necessary to prevent the learning
of scene-related features. Therefore, the filters of the constrained
convolutional layer are restricted to only learn a set of prediction error
filters, and are not allowed to evolve freely. Prediction error filters
operate as follows:

  1. 1.

Predict the center pixel value of the filter support by the surrounding pixel
values.

  2. 2.

Subtract the true center pixel value from the predicted value to generate the
prediction error.

More formally, Bayar and Stamm, placed the following constraints on $K$
filters $\textbf{w}^{(1)}_{k}$ in the constrained convolutional layer:

$\begin{cases}\textbf{w}^{(1)}_{k}(0,0)=-1\\\ \sum_{m,n\neq
0}\textbf{w}^{(1)}_{k}(m,n)=1\end{cases}$ (1)

where the superscript (1) denotes the first layer of the network,
$\textbf{w}^{(1)}_{k}(m,n)$ is the filter weight at position $(m,n)$ and
$\textbf{w}^{(1)}_{k}(0,0)$ the filter weight at the center position of the
filter support. The constraints are enforced during the training process after
the filter’s weights are updated in the backpropagation step. The center
weight value of each filter kernel is then set to $-1$ and the remaining
weights are normalized such that their sum equals $1$.

####  3.1.1 Extended Constrained Layer

The originally proposed constrained convolutional layer only supports gray-
scale inputs. We propose an extended version of this layer by allowing it to
process inputs with three color channels. Considering a convolutional layer,
the main difference between gray-scale and color inputs is the number of
kernels within each filter. Whereas gray-scale inputs require one kernel,
color inputs require three kernels. Therefore, we modify the constrained
convolutional layer by simply enforcing the constraints in Eq. 1 to all
kernels of each filter. The constraints enforced on $K$ $3$-dimensional
filters in the constrained convolutional layer can be formulated as follows:

$\begin{cases}\textbf{w}^{(1)}_{k_{j}}(0,0)=-1\\\ \sum_{m,n\neq
0}\textbf{w}^{(1)}_{k_{j}}(m,n)=1\end{cases}$ (2)

where $j\in\\{1,2,3\\}$. Moreover, $\textbf{w}^{(1)}_{k_{j}}$ denotes the
$j^{th}$ kernel of the $k^{th}$ filter in the first layer of the ConvNet.

Figure 3: Architecture of the proposed ConstrainedNet

###  3.2 Frame Extraction

While other studies extract the first $N$ frames of each video (Shullani et
al.,, 2017), we extract a given number of frames equally spaced in time across
the entire video. For example, to extract $200$ frames from a video consisting
of $1000$ frames, we would extract frames $[5$, $10$, .., $1000]$ whereas for
a video of $600$ frames we would extract frames $[3$, $6$, .., $600]$.
Furthermore, we did not impose requirements on a frame to be selected, in
contrast to Hosler et al., (2019).

###  3.3 Voting Procedure

The camera device of a video under investigation is identified as follows. We
first create the set $I$ consisting of $K$ frames extracted from video $v$, as
explained in Section 3.2. Then, every input $I_{k}$ is processed by the
(trained) ConstrainedNet, resulting in the probability vector
$\textbf{z}_{k}$. Each value in $\textbf{z}_{k}$ represents a camera device
$c\in C$ where $C$ is the set of camera devices under investigation. We
determine the predicted label $\hat{y}_{k}$ for input $I_{k}$ by selecting
label $y_{c}$ of the camera device that achieves the highest probability.
Eventually, we obtain the predicted camera device label $\hat{y}_{v}$ for
video $v$ by majority voting on $\hat{y}_{k}$ where $k\in[1,K]$.

##  4 EXPERIMENTS AND RESULTS

###  4.1 Data set

We used the publicly available VISION data set (Shullani et al.,, 2017). It
was introduced to provide digital forensic experts a realistic set of digital
images and videos captured by modern portable camera devices. The data set
includes a total of $35$ camera devices representing $11$ brands. Moreover,
the data set consists of $6$ camera models with multiple instances ($13$
camera devices in total), suiting our aim to investigate video camera
identification at device level.

The VISION data set consists of $1914$ videos in total which can be subdivided
into native versions and their corresponding social media counterparts. The
latter are generated by exchanging native videos via social media platforms.
There are $648$ native videos, $622$ are shared through YouTube and $644$ via
WhatsApp. While both YouTube and WhatsApp apply compression techniques to the
input video, YouTube maintains the original resolution while WhatsApp reduces
the resolution to a size of $480$ $\times$ $848$ pixels. Furthermore, the
videos represent three different scenarios: flat, indoor, and outdoor. The
flat scenario contains videos depicting flat objects such as walls or blue
skies, and are often largely similar across multiple camera devices. The
indoor scenario comprises videos depicting indoor settings, such as stores and
offices, whereas the latter scenario contains videos showing outdoor areas
including gardens and streets. Each camera device consists of at least two
native videos for every scenario.

####  4.1.1 Camera Device Selection Procedure

Rather than including each camera device of the VISION data set, we selected a
subset of camera devices that excludes devices with very few videos. We
determined the appropriate camera devices based on the number of available
videos and the camera device’s model. More explicitly, we included camera
devices that met either of the following criteria:

  1. 1.

The camera device contains at least 18 native videos, which are also shared
through both YouTube and Whatsapp.

  2. 2.

More than one instance of the camera device’s brand and model occur in the
VISION data set.

We applied the first criterion to exclude camera devices that contained very
few videos. Exceptions are made for devices of the same brand and model, as
indicated by the second criterion. Those camera devices are necessary to
exploit video device identification. Furthermore, we excluded the Asus Zenfone
2 Laser camera model as suggested by Shullani et al., (2017), resulting in a
subset of $28$ camera devices out of $35$, shown in Table 1. The total number
of videos sum up to $1539$ of which $513$ are native and $1026$ are social
media versions. In Fig. 4 an overview of the video duration for the $28$
camera devices is provided.

Table 1: The set of $28$ camera devices we used to conduct the experiments, of which $13$ are of the same brand and model, indicated by the superscript. ID | Device |  | ID | Device
---|---|---|---|---
1 | iPhone 4 |  | 15 | Huawei P9
2 | iPhone 4s* |  | 16 | Huawei P9 Lite
3 | iPhone 4s* |  | 17 | Lenovo P70A
4 | iPhone 5** |  | 18 | LG D290
5 | iPhone 5** |  | 19 | OnePlus 3§
6 | iPhone 5c† |  | 20 | OnePlus 3§
7 | iPhone 5c† |  | 21 | Galaxy S3 Mini∥
8 | iPhone 5c† |  | 22 | Galaxy S3 Mini∥
9 | iPhone 6†† |  | 23 | Galaxy S3
10 | iPhone 6†† |  | 24 | Galaxy S4 Mini
11 | iPhone 6 Plus |  | 25 | Galaxy S5
12 | Huawei Ascend |  | 26 | Galaxy Tab 3
13 | Huawei Honor 5C |  | 27 | Xperia Z1 Compact
14 | Huawei P8 |  | 28 | Redmi Note 3

###  4.2 Frame-based Device Identification

We created balanced training and test sets in the following way. We first
determined the lowest number of native videos among the $28$ camera devices
that we included based on the camera device selection procedure. We used this
number to create balanced training and test sets of native videos in a
randomized way, maintaining a training-test split of $55\%/45\%$. Moreover, we
ensured that per camera device, each scenario (flat, indoor, and outdoor) is
represented in both the training and test set. Concerning this experiment, the
lowest number of native videos was $13$ through which we randomly picked $7$
and $6$ native videos per camera device for the training and test sets,
respectively. Subsequently, we added the WhatsApp and YouTube versions for
each native video, tripling the size of the data sets. This approach ensured
that a native video and its social media versions always belong to either the
training set or test set, but not both. Although the three versions of a video
differ in quality and resolution, they still depict the same scene content
which could possibly lead to biased results if they were distributed over both
the training set and test set. Eventually, this led to $21$ training videos
($7$ native, $7$ WhatsApp, and $7$ YouTube) and $18$ test videos ($6$ native,
$6$ WhatsApp, and $6$ YouTube) being included per camera device, resulting in
a total number of $588$ training and $504$ test videos. Due to the limited
number of available videos per camera device, we did not have the luxury to
create a validation set. We extracted $200$ frames from every video following
the procedure as described in Section 3.2, resulting in a total number of
$117,600$ training frames and $100,800$ test frames. Each training frame
inherited the same label as the camera device that was used to record the
video.

Figure 4: Boxplot showing the means and quartiles of the video durations in
seconds for the 28 camera devices. Outliers are not shown in this plot.

Furthermore, we performed this experiment in two different settings to
investigate the performance of our extended constrained convolutional layer.
In the first setting we used the ConstrainedNet as explained in Section 3.1,
whereas we removed the constrained convolutional layer in the second setting.
We refer to the network in the second setting as the UnconstrainedNet.

We trained both the ConstrainedNet and the UnconstrainedNet for $30$ epochs in
batches of $128$ frames. We used the stochastic gradient descent (SGD) during
the backpropagation step to minimize the categorical cross-entropy loss
function. To speed up the training time and convergence of the model, we used
the momentum and decay strategy. The momentum was set to $0.95$ and we used a
learning rate of $0.001$ with step rate decay of $0.0005$ after every training
batch. The training took roughly $10$ hours to complete for each of both
architectures222We used the deep learning library Keras on top of Tensorflow
to create, train, and evaluate the ConstrainedNet and UnconstrainedNet.
Training was performed using a Nvidia Tesla V100 GPU..

We measured the performance of the ConstrainedNet and the UnconstrainedNet by
calculating the video classification accuracy on the test set. After every
training epoch we saved the network’s state and calculated the video
classification accuracy as follows:

  1. 1.

Classify each frame in the test set.

  2. 2.

Aggregate frame classifications per video.

  3. 3.

Classify the video according to the majority vote as described in Section 3.3.

  4. 4.

Divide the number of correctly classified test videos by the total number of
test videos.

In addition to the test accuracy, we also calculated the video classification
accuracy for the different scenarios (flat, indoor, outdoor) and versions
(native, WhatsApp, YouTube). The different scenarios are used to exploit the
extraction of noise pattern features and to determine the influence of high-
level scene content. The different video versions are used to investigate the
impact of different compression techniques.

####  4.2.1 Results

In Fig. 5 we show the progress of the test accuracy for the ConstrainedNet and
the UnconstrainedNet. It can be observed that the performance significantly
improved by the introduction of the constrained convolutional layer. The
ConstrainedNet achieved its peak-performance after epoch 25 with an overall
accuracy of $66.5$%. Considering the accuracy per scenario, we observed
$89.1\%$ accuracy for flat scenario videos, $53.7\%$ for indoor scenarios, and
$55.2\%$ accuracy for the outdoor. Results for the individual scenarios are
shown in Fig. 6.

Since the flat scenario videos achieved a significantly higher classification
accuracy compared to the others, we limited ourselves to this scenario during
the investigation of how different compression techniques would affect the
results. In Fig. 7 we show the confusion matrices that the ConstrainedNet
achieved from the perspective of different compression techniques (i.e.
native, WhatsApp and YouTube). We achieved $89.7\%$ accuracy on the native
versions, $93.1\%$ on the WhatsApp versions, and $84.5\%$ on the YouTube ones.

Figure 5: Progress of the test video classification accuracy for the
ConstrainedNet and UnconstrainedNet. Figure 6: Confusion matrices for $28$
camera devices showing the normalized classification accuracies achieved for
the scenarios flat, indoor, and outdoor. Figure 7: Confusion matrices for $28$
camera devices showing the normalized classification accuracies achieved on
flat scenario videos from the perspective of the native videos and their
social media versions.

##  5 DISCUSSION

From the results in Fig. 5 it can be observed that the constrained
convolutional layer significantly contributes to the performance of our
network. This suggests this layer is worth further investigating its potential
in light of digital forensic problems on color inputs. Furthermore, in Fig. 6
it is shown that the classification accuracy greatly differs between the three
scenarios; flat, indoor, and outdoor. Whereas the indoor and outdoor scenarios
achieve accuracies of $53.7\%$ and $55.2\%$, respectively, we observe an
accuracy of $89.1\%$ for the flat scenario videos. Given the high degree of
similarity between flat scenario videos from multiple camera devices, the
results suggest that the ConstrainedNet has actually extracted characteristic
noise pattern features for the identification of source camera devices. The
results also indicate that indoor and outdoor scenario videos are less
suitable to extract noise pattern features for device identification. This
difference could lie in the absence or lack of video homogeneity. Compared to
the flat scenario videos, indoor and outdoor scenario videos typically depict
a constantly changing scene. As a consequence, the dominant features of a
video frame are primarily scene-dependent, making it significantly harder for
the ConstrainedNet to extract the scene-independent features, that is, the
noise pattern features.

Fig. 7 shows that our methodology is robust against the compression techniques
applied by WhatsApp and YouTube. While we observe an accuracy of $89.7\%$ for
the native versions of flat scenario videos, we observe accuracies of $93.1\%$
and $84.5\%$ for the WhatsApp and YouTube versions, respectively. The high
performance of WhatsApp versions could be due to the similarity in size (i.e.
resolution) between WhatsApp videos and our network’s input layer. As
explained in Section 4.1, the WhatsApp compression techniques resize the
resolution of a video to the size of $480\times 848$ pixels, becoming nearly
identical to the network’s input size of $480\times 800$ pixels. This is in
contrast to the techniques applied by YouTube, which respect the original
resolution.

These results indicate that the content homogeneity of a video frame plays an
important role in the classification process of videos. Therefore, we suggest
to search for homogeneous patches within each video frame, and only use those
patches for the classification of a video. This would limit the influence of
scene-related features, forcing the network to learn camera device specific
features.

By proposing this methodology we aim to support digital forensic experts in
order to identify the source camera device of digital videos. We have shown
that our approach is able to identify the camera device of a video with an
accuracy of $89.1\%$. This accuracy further improves to $93.1\%$ when
considering the WhatsApp versions. Although the experiments were performed on
known devices, we believe this work could be extended by matching pairs of
videos of known and unknown devices too. In that case, the ConstrainedNet may
be adopted in a two-part deep learning solution where it would function as the
feature extractor, followed by a similarity network (e.g. Siamese Networks) to
determine whether two videos are acquired by the same camera device. To the
best of our knowledge, this is the first work that addresses the task of
device-based video identification by applying deep learning techniques.

In order to further improve the performance of our methodology, we believe it
is worth investigating the potential of patch-based approaches wherein the
focus lies on the homogeneity of a video. More specifically, only homogeneous
patches would be extracted from frames and used for the classification of a
video. This should allow the network to better learn camera device specific
features, leading to an improved device identification rate. Moreover, by
using patches the characteristic noise patterns remain unaltered since they do
not undergo any resize operation. In addition, this could significantly reduce
the complexity of the network, requiring less computational effort. Another
aspect to investigate would be the type of voting procedure. Currently, each
frame always votes for a single camera device even when the ConstrainedNet is
highly uncertain about which device the frame is acquired by. To counteract
this problem, voting procedures could be tested that take this uncertainty
into account. For example, we could require a certain probability threshold to
vote for a particular device. Another example would be to select the camera
device based on the highest probability after averaging the output probability
vectors of frames aggregated per video.

##  6 CONCLUSION

Based on the results that we achieved so far, we draw the following
conclusions. The extended constrained convolutional layer contributes to
increase in performance. Considering the different types of videos, the
proposed method is more effective for videos with flat (i.e. homogeneous)
content, achieving an accuracy of $89.1\%$. In addition, the method shows to
be robust against the WhatsApp and YouTube compression techniques with
accuracy rates up to $93.1\%$ and $84.5\%$, respectively.

## ACKNOWLEDGEMENTS

We thank the Center for Information Technology of the University of Groningen
for their support and for providing access to the Peregrine high performance
computing cluster. This research has been funded with support from the
European Commission under the 4NSEEK project with Grant Agreement 821966. This
publication reflects the views only of the authors, and the European
Commission cannot be held responsible for any use which may be made of the
information contained therein.

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# Towards Robust Real-Time Hardware-based Mobile Malware Detection using
Multiple Instance Learning Formulation

Harshit Kumar, Sudarshan Sharma, Biswadeep Chakraborty, Saibal Mukhopadhyay
Electrical and Computer Engineering, Georgia Instititute of
TechnologyAtlantaGeorgiaUSA
Under peer review.

(2018)

###### Abstract.

This study introduces RT-HMD, a Hardware-based Malware Detector (HMD) for
mobile devices, that refines malware representation in segmented time-series
through a Multiple Instance Learning (MIL) approach. We address the
mislabeling issue in real-time HMDs, where benign segments in malware time-
series incorrectly inherit malware labels, leading to increased false
positives. Utilizing the proposed Malicious Discriminative Score within the
MIL framework, RT-HMD effectively identifies localized malware behaviors,
thereby improving the predictive accuracy. Empirical analysis, using a
hardware telemetry dataset collected from a mobile platform across 723 benign
and 1033 malware samples, shows a 5% precision boost while maintaining recall,
outperforming baselines affected by mislabeled benign segments.

Malware Detection, Hardware Security, Multiple Instance Learning

††copyright: acmlicensed††journalyear: 2018††doi: XXXXXXX.XXXXXXX††conference:
Make sure to enter the correct conference title from your rights confirmation
emai; June 03–05, 2018; Woodstock, NY††isbn: 978-1-4503-XXXX-X/18/06††ccs:
Security and privacy Intrusion detection systems††ccs: Security and privacy
Mobile platform security

##  1\. Introduction

Recent years have seen a surge in malicious applications challenging the
security of modern devices (fir, [n. d.]). This has shifted Endpoint Security
towards behavior analysis, using sensors across the compute stack for
continuous monitoring and data analysis (mic, [n. d.]). To address the
limitations of high performance overhead of traditional software-based
approaches, HMD has emerged, utilizing low-level hardware telemetry as a
behavioral signature for low-overhead and tamper-resistant detection of
malicious activities (Demme et al., 2013; int, [n. d.]). HMD, a vital
component in collaborative defense systems such as Endpoint Detection and
Response (EDR) (int, [n. d.]; noa, [n. d.]), enhances threat visibility and
complements software-level techniques, effectively expanding the scope of
detected threats (Kazdagli et al., 2016; Kumar et al., 2023).

HMDs offer computational efficiency through GPU offloading (int, [n. d.]) and
hardware acceleration (Ozsoy et al., 2015), allowing for real-time malware
monitoring with minimal system impact. Central to HMDs is a Machine Learning
(ML) classifier that performs binary classification on segmented time-series
data for real-time detection. Selecting the optimal window length in HMDs is
crucial, as it balances the need for capturing comprehensive malware behavior
for effective training (Küchler et al., 2021) with the necessity for early
detection during inference (Ozsoy et al., 2015)—longer windows improve
learning while shorter ones enable quicker response times. To balance these
conflicting requirements, HMDs typically segment long-duration time-series
into shorter windows for ML training, with window labels inherited from the
parent time-series (Ozsoy et al., 2015; Khasawneh et al., 2020; Kuruvila et
al., 2021; Cronin and Yang, 2018). We hypothesize that the direct inheritance
of labels from time-series to windows inaccurately represents malware due to
prevalent benign segments within malware-labeled time-series. Such labeling
inaccuracies, combined with the high base rate of benign workloads in malware
detection (Arp et al., 2022), contribute to an increase in false positives,
leading to alarm fatigue among security analysts (Alahmadi et al., 2022).

Drawing on Demme et al.’s discussion of malware labeling challenges (Demme et
al., 2013), we evaluate the common practice of applying a single malware label
to all the windows of a segmented time-series. A malware-infected time-series
contains both malicious and benign segments, yet conventional labeling does
not distinguish between them. This labeling approach overlooks the localized
nature of malware behaviors, which are typically restricted to certain time-
series segments, evidenced by key malicious code snippets in software binaries
(e.g. Command-and-Control communication, File Discovery, etc.). Consequently,
benign-only segments are mis-labeled as malicious for training a ML
Classifier. To mitigate this, we propose a Multiple Instance Learning (MIL)
formulation (Foulds and Frank, 2010) that accurately reflects the localized
malware behaviors, thereby improving the alignment of malware representation
with the actual distribution of malicious activity within the time-series, and
improving the performance of the ML Classifier.

Figure 1. Proposed Methodology: The decision for i-th window $P_{M,W_{i}}$ is
enhanced by the Malicious Discriminative Score $\mathfrak{D}_{W_{i}}$. This
score adjustment corrects mis-classifications of benign segments within a
malware-labeled time-series, thereby improving the precision of malware
detection.

Our empirical study leverages the HMD model dataset from Kumar et al. (Kumar
et al., 2023), examining multivariate time-series data derived from SoC
components using Dynamic Voltage and Frequency Scaling (DVFS) and SYSFS
telemetry. We introduce the Malicious Discriminative Score (MDS) to evaluate
the distinctivenes of segment behaviors, assigning higher scores to segment-
behaviors uniquely observed in malware time-series. This score enhances the
classifier’s output by amplifying the signal for distinct malware behavior and
attenuating it for benign behavior, thus fine-tuning the prediction for each
time segment. Illustrated in Figure 1, the prediction for each window
($P_{M,W_{i}}$) is adjusted by its corresponding MDS ($\mathfrak{D}_{W_{i}}$),
and the overall prediction $P_{M}$ is computed as the weighted sum of these
adjusted segment predictions. To calculate the MDS, we model first-order
interactions between time-series channels using conditional histograms,
learning complex behavioral patterns as compared to single channel analysis
which treat each channel of the multivariate time-series independently. Our
key contributions are:

  * •

Introduction of MIL formulation for accurate representation of malware
behavior in segmented time-series, to reduce False Positives in real-time
HMDs.

  * •

Proposal of MDS to support the MIL assumption, calculated using a novel
statistical classifier by analyzing first-order interactions in multivariate
time-series.

The rest of the paper is organized as follows. We provide a brief background
in Section 2. Next, we explain our proposed framework in Section 3. We present
our evaluation results and discussion in Section 4 and conclude in Section 5.

##  2\. Background

###  2.1. HMD and Related Works

Demme et al. leveraged Hardware Performance Counters (HPCs) to detect a range
of malicious activities (Demme et al., 2013). Subsequent research has focused
on improving HMDs’ predictive capabilities (Khasawneh et al., 2020; Kumar et
al., 2021) and reducing their performance overhead (Patel et al., 2017; Cronin
and Yang, 2018; Ozsoy et al., 2015). Alternatives to HPCs, such as DVFS
telemetry (Chawla et al., 2021), have also been explored for their system-wide
behavior profiling across various SoC sub-devices, widening the scope of
detectable attacks beyond those with prominent architectural side-channel
effects (Kumar et al., 2023).

Efforts to address real-time detection challenges have been noted (Alam et
al., 2019; Ozsoy et al., 2015; Khasawneh et al., 2020; Kuruvila et al., 2021;
Cronin and Yang, 2018). Alam et al. used an anomaly detection approach based
on reconstruction error for real-time detection, avoiding direct benign vs.
malware classification and focusing on normal vs. anomalous behavior (Alam et
al., 2019). However, the variability in defining ”normal” often leads to high
false positives in anomaly detection. In contrast, the benign vs. malware
classification paradigm persists (Ozsoy et al., 2015; Khasawneh et al., 2020;
Kuruvila et al., 2021; Cronin and Yang, 2018). While a broad classification of
the entire time-series as malware might be justifiable (given the presence of
malicious code) as done in prior works (Demme et al., 2013), using the parent
labels for the windows is inadequate as it mislabels benign behavior. Kuruvila
et al. suggested using ensemble of classifiers operating on extended window
lengths to reduce false positives (Kuruvila et al., 2021). However, increased
window lengths delay early detection. Our method diverges by preserving the
window length, enabling timely detection, and utilizing the uniqueness of
malicious behavior to fine-tune the window predictions, reducing false
positives.

###  2.2. Multiple Instance Learning Formulation and Its Implementation
Challenges

The crux of MIL is distinguishing between ‘bags’—the entire time-series—and
‘instances’—the segmented windows within (Foulds and Frank, 2010). Our MIL
assumption assumes that a bag acquires a malware label if any instance within
exhibits malware characteristics, reflecting the locality in malicious
behavior within a malware time-series. This deviates from the current
assumption where all instances inherit the bag’s label (Ozsoy et al., 2015;
Khasawneh et al., 2020; Kuruvila et al., 2021; Cronin and Yang, 2018). A
primary challenge in MIL is the absence of segment-level labels, which would
otherwise require intensive forensic analysis to assign accurately. Such
granularity in labeling is both impractical and unscalable due to the
resources it demands. We address this by adopting a data-driven approach to
learn what constitutes a malicious segment within a time-series: it must be
unique to malware-labeled bags within the training dataset, and exhibit
significant deviation from its benign counterpart. This operational definition
aims to isolate high-discriminatory malicious segments, enhancing the fidelity
of malware detection.

Table 1. Hardware telemetry channels in the dataset (Kumar et al., 2023)

Telemetry Class | Channel # | Description
---|---|---
DVFS | 1 | GPU controller
2 | CPU controller: lower cluster
3 | CPU controller: higher cluster
4 | CPU bus bandwidth controller
5 | GPU bus bandwidth controller
6 | GPU bus bandwidth controller
7 | Latency controller L3 cache: lower cluster
8 | Latency controller L3 cache: higher cluster
9 | Last level cache controller
10 | Memory latency controller: lower cluster
11 | Memory latency controller: higher cluster
SYSFS | 12 | Network: received bytes
13 | Network: transmitted bytes
14 | Device current
15 | Device voltage

###  2.3. Dataset Information

We use the dataset from Kumar et al. (Kumar et al., 2023), consisting of
telemetry data focusing on DVFS and SYSFS states in an SoC. The telemetry is
collected on a commodity Android smartphone. The DVFS states, crucial for
power management, reflect the workload-induced activity in CPU, GPU, buses,
caches, memory, and network interfaces (see Table 1). The dataset contains
1033 malware and 723 benign Android applications sourced from AndroZoo between
December 2019 and June 2021. The malware apps span 54 families, verified by
the ESET-NOD32 AV engine on VirusTotal. Each app’s hardware telemetry
signature, collected over eight iterations, results in 2,120 signatures for
malicious and 2,143 for benign apps, with each signature being a multivariate-
time-series capturing 40 seconds of application execution. We employ a 70-30
train-test split with the test set comprising applications absent from the
training set.

###  2.4. Threat Model

RT-HMD assumes attackers can deploy malware to manipulate application-level
activities without root access, similar to (Kumar et al., 2023). Designed for
multi-core mobile devices, RT-HMD operates under the premise that users engage
with a limited number of foreground applications (1-2) simultaneously. This
assumption is due to the reliance on system-wide telemetry channels (Table 1),
capturing data from all device processes. RT-HMD’s training necessitates
malware behavior profiling within a controlled sandbox environment.
Consequently, any sandbox evasion techniques could compromise this profiling
process, impacting the quality of training data and, ultimately, malware
detection effectiveness in real-world scenarios. Additionally, RT-HMD is
vulnerable to collusion-based attacks, where attacker-controlled threads could
interfere with system-wide telemetry, potentially skewing detection
capabilities.

Figure 2. Overview of the Malicious Discriminative Score (MDS): (a) [Top]
Malware time-series with annotated benign and malicious segments [Bottom]
Segmented benign time-series; (b) hyperplane under strong supervision
assumption (current) and hyperplane under MIL assumption (proposed); (c) MDS
functionality explained.

##  3\. Proposed Framework

###  3.1. Overview

The key problem in malware detection using segmented time-series data is the
presence of benign segments in both malware and benign-labelled series,
leading to conflicting labels and noisy supervision during model training.
Figure 2.a illustrates this, depicting a malware (1) and a benign (0) time-
series, each segmented and labeled. Notably, we can observe benign segments
within the malware time-series. These segments receive conflicting labels,
blurring the classification boundary. In Figure 2.b, we visualize the
classifier’s latent space, partitioned into three regions: segments unique to
malware (lower left), common benign segments (middle), and segments unique to
benign time-series (upper right). The overlap of benign segments in both
malware and benign time-series complicates the classifier’s decision-making,
resulting in high false positives.

To address this, we introduce the Malicious Discriminative Score (MDS). MDS
evaluates the distinctiveness of segment behaviors, assigning higher scores to
behaviors uniquely observed in malware time-series. In Figure 2.c, the
effectiveness of MDS is demonstrated. The model generates a prediction,
$P_{M,W_{i}}$, for a test segment, and MDS ($\mathfrak{D}_{W_{i}}$) is
independently computed based on the observed segment behavior. The MDS is low
for malware-labelled benign segments (first row) and high for unique malicious
segments (second row). By multiplying the MDS with the model’s prediction, it
either amplifies or attenuates the segment-prediction, enhancing confidence
for uniquely malicious behaviors and reducing it for mis-labelled benign
behaviors. Effectively, this process adjusts the classifier’s hyperplane, as
shown in Figure 2.b, correcting false positives arising from the mis-labelled
benign segments.

Figure 3. Illustrates the Training and Inference steps of the Interaction-
based Statistical Classifier Algorithm 1 Training and Inference Approach

0: $X$: Multivariate time-series with $C$ channels $B$: Number of histogram
bins $W$: Window size $AF$: Anchor function

0: $\theta$: Template distributions for training $P_{M}$: Malware probability
for inference

1: Training Phase:

2: for $c_{1}=1$ to $C-1$ do

3: for $c_{2}=c_{1}+1$ to $C$ do

4: Select channel $c_{1}$ as distribution-channel

5: Select channel $c_{2}$ as anchor-channel

6: for non-overlapping windows $w\in W$ do

7: $h_{w}\leftarrow$ Histogram$(X_{c_{1},w},B)$ {Create histogram}

8: $a_{w}\leftarrow AF(X_{c_{2},w})$ {Determine anchor value}

9: $\theta_{c_{1},c_{2}}\leftarrow\theta_{c_{1},c_{2}}\cup{(h_{w},a_{w})}$
{Store template}

10: end for

11: end for

12: end for

13: Inference Phase:

14: for windows $w\in W$ do

15: $\hat{h}_{w},\hat{a}_{w}\leftarrow$ Histogram & Anchor$(X_{w})$ {Generate
for distr. and anchor-channels}

16: for $c_{1}=1$ to $C-1$ do

17: for $c_{2}=c_{1}+1$ to $C$ do

18: $\Phi_{w,B}^{c_{1},c_{2}}\leftarrow
KL(\hat{h}_{w},\theta_{c_{1},c_{2}}^{B})$ {Benign KL divergence}

19: $\Phi_{w,M}^{c_{1},c_{2}}\leftarrow
KL(\hat{h}_{w},\theta_{c_{1},c_{2}}^{M})$ {Malware KL divergence}

20:
$P^{c_{1},c_{2}}_{M,w}\leftarrow\text{softmax}({\Phi_{w,B}^{c_{1},c_{2}},\Phi_{w,M}^{c_{1},c_{2}}})$
{Malware probability}

21: end for

22: end for

23: for $(c_{1},c_{2})\in C\times C$ do

24: $\mathfrak{D}_{w}^{c_{1},c_{2}}\leftarrow
KL(\theta_{c_{1},c_{2}}^{B},\theta_{c_{1},c_{2}}^{M})$ {MDS}

25: end for

26:
$P_{M,w}\leftarrow\sum_{c_{1},c_{2}}P_{M,w}^{c_{1},c_{2}}\mathfrak{D}_{w}^{c_{1},c_{2}}/\sum_{c_{1},c_{2}}\mathfrak{D}_{w}^{c_{1},c_{2}}$

27:
$\mathfrak{D}_{w}\leftarrow\sum_{c_{1},c_{2}}\mathfrak{D}_{w}^{c_{1},c_{2}}$

28: end for

###  3.2. Training: Learning Template Distributions

The training approach, illustrated in Figure 3.a and summarized in Algorithm-1
Training Phase, focuses on creating template conditional distributions using
empirical histograms. This process involves moving a non-overlapping sliding
window across the multi-variate time-series. Within each window, a pair of
channels is selected: one as the distribution-channel and the other as the
anchor-channel. For the distribution-channel, a histogram based on the
observed DVFS states is constructed, and for the anchor-channel, a
representative anchor-value (a-value) is calculated using a predefined anchor
function. Combined with the labels that distinguish between benign and
malicious data sources, this forms a conditional distribution, expressed as:

(1) $\text{P}_{\text{template}}\left[\begin{subarray}{c}\text{distribution}\\\
\text{channel}\end{subarray}\bigg{|}\left(\begin{subarray}{c}\text{anchor}\\\
\text{channel}\end{subarray}=\text{a-value},\text{label}\right)\right]$

Generating the Template Conditional Distributions.  As the sliding window
traverses each segment of the time-series, it systematically captures key
parameters of the conditional distribution such as the distribution-channel,
anchor-channel, anchor-value, and label, which are used as unique keys to
retrieve and update the corresponding template histogram with new values
(using add operation). This method, applied across all multivariate time-
series in the training dataset creates a set of template conditional
distributions, through which we have learned the likelihood of observing
distributions in one channel, conditioned on a representative value in another
channel given the application class (malware or benign). The MDS is defined as
the Kullback-Leibler (KL) Divergence between template conditional
distributions sharing the same distribution-channel, anchor-channel, and
anchor-value, but differing in labels: one benign, one malicious. Intuitively,
MDS measures the uniqueness of interactions, with higher values signaling
exclusive malware behavior and lower ones indicating segment-behavior common
to both benign and malware time-series.

There are three key parameters used in generating the conditional
distributions: the number of histogram bins ($B$), the window size ($W$), and
the anchor function ($AF$). A grid search was performed over $B$ and $W$ to
identify the optimal configuration which maximizes the MDS recorded over all
the template distributions. The $AF$ is used to calculate the anchor-value
which is bucketized to the nearest bin to simplify the tracking of template
histograms. Number of tracked template histograms:  Given $N$ channels in a
multivariate time-series from an application sample, there are $N$ possible
distribution-channel values and $N-1$ anchor-channel values. Each anchor-value
can assume $B$ values, and distributions are tracked separately for benign and
malicious labels. Thus, the overall number of template distributions monitored
during training is $N*N-1*B*2$.

###  3.3. Inference Methodology

The inference approach is illustrated in Figure 3.b and summarized in the
Inference Phase of Algorithm 1. It mirrors the training phase by generating
inference conditional distribution for each pairwise channel. The recorded
distribution-channel, anchor-channel, anchor-value parameters are used to
fetch the corresponding benign and malware template distributions ($j^{th}$).
The objective is to determine if the inference distribution resembles malware
or benign behavior recorded by the template distributions learned during
training. This is determined using the following KL-divergence scores: (1) KL
divergence between the benign template distribution and the inference
distribution ($\Phi_{j,B}$), assessing similarity to the benign behavior; (2)
KL divergence between the malware template distribution and the inference
distribution ($\Phi_{j,M}$), evaluating similarity to the malware behavior. A
softmax operation, as shown in Equation 2, calculates the malware probability:

(2) $P_{j,M}=\frac{e^{-\Phi_{j,M}}}{e^{-\Phi_{j,M}}+e^{-\Phi_{j,B}}}$

This operation offers a probabilistic measure of an interaction being
malicious. For each pairwise interaction within the inference window ($N\times
N-1$ possible interactions), a softmax probability is calculated, reflecting
the interaction’s similarity to malware behavior. The final prediction
probability for the i-th window, $P_{M,W_{i}}$, is obtained by averaging
$P_{j,M}$ for all $j$ in $N\times(N-1)$. For a uniquely malicious segment,
$\Phi_{j,M}>\Phi_{j,B}$, so that $P_{j,M}>0.5$. However, if benign and malware
interactions are similar, due to ambiguous labeling (Ozsoy et al., 2015;
Khasawneh et al., 2020; Kuruvila et al., 2021; Cronin and Yang, 2018),
$\Phi_{j,B}\approx\Phi_{j,M}$ , resulting in $P_{j,M}$ and consequently
$P_{M,W_{i}}\approx 0.5$. This ambiguity indicates classifier confusion due to
conflicting labels, resulting in erroneous predictions.

MDS-weighted decisions. To address this, we use the MDS to refine our
prediction process. Rather than a simple average, $P_{M,W_{i}}$ is computed as
a weighted average using the MDS values ($\mathfrak{D}_{j}$) of the
corresponding template distributions, as shown in Equation 3. This
modification ensures that if benign and malware interactions are similar,
resulting in a lower $\mathfrak{D}_{j}$, the prediction probability is
attenuated so that $P_{j,M}<<0.5$. The total MDS for the i-th window
($\mathfrak{D}_{W_{i}}$) is the sum of MDS values for all participating
conditional distributions, quantifying the overall MDS within the window, as
shown in Equation 4.

(3) $P_{M,W_{i}}=\frac{\sum_{j=1}^{N\times(N-1)}\mathfrak{D}_{j}\times
P_{j,M}}{\sum_{j=1}^{N\times(N-1)}\mathfrak{D}_{j}}$ (4)
$\mathfrak{D}_{W_{i}}=\sum_{i=1}^{N\times(N-1)}\mathfrak{D}_{j}$

This approach allows $P_{M,W_{i}}$ to factor in the similarity of benign and
malware interactions, thus refining the quality of the final prediction for
each window.

Figure 4. (a) Boxplot showing MDS of the template distributions for two
modalities of information: interaction (conditional distributions) and
channels of time-series treated independently (marginal distribution) for
different distribution-channels. Marginals do not capture the high MDS
behaviors between benign and malware; (b) Boxplot showing the frequency of
occurrence of segments (total segments: 101863, segment-length$\approx$1s)
stratified by MDS in the training dataset (y-axis is logarithmic). High MDS
interactions are less frequent; (c) Increase in AUC upon using MDS weighted
decision.

##  4\. Evaluation results

###  4.1. Analyzing Segment Behavior

Distinguishability of Interactions. We examine distinguishability of multi-
variate interactions within a time segment, assessed via the MDS of the
template distributions. Figure 4.a shows the MDS obtained from template
conditional distributions. We observe a wide variance in MDS values indicating
that the template distributions are learning both unique and common behaviors
between the malware and benign time-series segments. Channels with limited
DVFS states, such as channel-5, yield lower MDS due to insufficient
information for capturing interactions. The marginal template distributions
which treats the channels independently as shown in Equation 5, are depicted
with markers and consistently show lower MDS values. This underlines the
necessity of leveraging conditional distributions to extract a richer set of
discriminative features, highlighting the importance of inter-channel
interactions over single channel analysis in a multi-variate time-series.

(5) $\text{P}_{\text{template}}\left[\begin{subarray}{c}\text{distribution}\\\
\text{channel}\end{subarray}\bigg{|}\text{label}\right]$

Frequency of High MDS Segments in time-series. Next, we aim to quantify the
occurrence of high MDS segments, which are indicative of distinct malware
interactions, against the backdrop of our hypothesis that a malware time-
series comprises both benign and malicious segments. Figure 4.b shows the
number of segments (in the training dataset) that contribute to template
distributions across various MDS intervals. The y-axis, on a logarithmic
scale, represents the count of segments, while the x-axis shows MDS intervals.
The plot reveals a predominance of lower MDS segments, suggesting that common
interactions arising from malware-labelled benign segments are frequently
encountered, which substantiates our hypothesis. Conversely, segments with
high MDS that reflect unique behaviors specific to malware, are rarer. This
observation confirms our intuition that labeling segments solely based on the
time-series they belong to—as current methods do—results in mislabeling, given
the frequent commonality between segments observed in benign and malware
labeled time-series.

###  4.2. Impact on Classification Performance

Table 2. Precision and Recall for different anchor functions

Anchor Function | Precision | Recall
---|---|---
| w/o MDS | with MDS | w/o MDS | with MDS
max | 0.86 | 0.89 | 0.89 | 0.89
mean | 0.80 | 0.85 | 0.85 | 0.89
median | 0.84 | 0.88 | 0.88 | 0.90
min | 0.83 | 0.87 | 0.89 | 0.89
mode | 0.85 | 0.90 | 0.89 | 0.89

Classifier Performance with MDS Weighting. Our evaluation investigates how MDS
weighting influences classifier metrics, such as precision and recall,
compared to baseline methods that average predictions without weighting. Due
to the absence of ground truth for individual segments, we assess performance
based on the entire time-series. The overall time-series prediction with MDS
weighting is computed as:

(6) $P_{M}=\frac{\sum_{i=1}^{S}\mathfrak{D}_{W_{i}}\times
P_{M,W_{i}}}{\sum_{i=1}^{S}\mathfrak{D}_{W_{i}}}$

We compare the MDS-weighted decision to a baseline that aggregates predictions
without MDS weighting, reflecting current practices where benign segments in
malware time-series are inaccurately labeled (Ozsoy et al., 2015; Khasawneh et
al., 2020; Kuruvila et al., 2021; Cronin and Yang, 2018). We report our
findings in Figure 4.c and Table 2. The ROC curve in Figure 4.c, with the mode
as the anchor function, shows an improvement in AUC score when incorporating
MDS weighted decision. Notably, for a given True Positive Rate (TPR), the MDS-
weighted classifier demonstrates a reduced False Positive Rate (FPR),
signifying a refined specificity. Table 2 further reveals that across
different anchor functions, MDS weighting consistently enhances precision
without compromising—and occasionally improving—recall. This performance
improvement aligns with our hypothesis that MDS weighting mitigates the impact
of incorrectly labelled benign segments, thereby improving precision. It’s
important to note that while Kumar et al.’s dataset is balanced, in real-world
scenarios—where benign instances vastly outnumber malicious ones—the observed
precision improvement serves as a conservative estimate, as precision is
particularly sensitive to the prevalence of benign samples which have a higher
base rate in malware detection (Arp et al., 2022).

Figure 5. An MDS-based saliency heatmap highlighting localized malicious
behavior within the hardware telemetry (multivariate time-series). Each
channel of the time-series corresponds to the channels outlined in Table 1.

Enhanced Interpretability through MDS. Our model introduces a refined layer of
interpretability by utilizing the product of $\mathfrak{D}_{W_{i}}$ and
$P_{M,W_{i}}$ as attention weights, as depicted in Figure 5. Unlike
traditional interpretability mechanisms that generate saliency maps without
explaining the underlying rationale, the MDS-based saliency map assigns a
definitive meaning to these weights, suggesting that the classifier detects
behavior with a high discriminative capability. The saliency map in Figure 5
illustrates the classifier’s capability to localize malicious segments,
supporting our hypothesis that not all segments of a malware time-series
demonstrate distinctively malicious behavior.

##  5\. Conclusion and Future Work

In conclusion, our research addresses a critical gap in HMDs by introducing a
MIL framework that captures the episodic nature of malware within segmented
time-series data, mitigating the label misrepresentation and subsequent false
positives. Leveraging the MDS, we enhance HMD performance by distinguishing
between benign and malicious segment behaviors, enhancing the precision and
interpretability of threat detection. Our empirical results, demonstrated
using a novel statistical classifier, confirm the efficacy of the MIL
formulation in the development of robust real-time malware detection
solutions. While this study concentrates on statistical classification methods
applied to DVFS-based time-series, future works aim to extend MDS computation
to ML algorithms and examine its viability in Hardware Performance Counter
contexts, broadening the scope and applicability of the proposed solution.

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$\approx$0.4 Solar, while mid-K to mid-M dwarfs have values of 0.2 Solar or
lower. At the age of Praesepe and Hyades, these two sets of stars coincide
with the difference between slow and fast rotators, or high and low
$R_{\mathrm{o}}$ numbers, thus suggesting that coronal abundance is directly
linked to $P_{\mathrm{rot}}$ and, thus, to magnetic activity level.

We find that in both clusters $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ increases
from F through early G types, then flattens between early G and early M types,
and then increases again beyond early M types. Binary stars show a larger
spread than the single counterparts in this
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ trend. In particular, late K dwarf binary
Hyads are almost one order of magnitude more luminous in $L_{\mathrm{X}}$ than
their single counterparts, partially supporting previous findings in the
literature. Single stars with RUWE $>$ 1.4—a threshold we adopt to indicate
unresolved binaries—have the similar $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
levels as stars with RUWE $\leq$ 1.4, suggesting that X-ray emission in the
former is not significantly inflated by binary interactions compared to single
stars.

In the $R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ plane of both
clusters, we find a saturated regime, in which
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ $\approx$10-3 and independent from stellar
rotation for stars with $R_{\mathrm{o}}$ $\buildrel<\over{\sim}$ 0.1 or 0.2,
and an unsaturated regime, in which $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$
depends on $R_{\mathrm{o}}$ following a power law with slope $\beta$ between
$-3.93$ and $-3.24$ for single stars, and $-2.82$ and $-2.22$ for binaries. As
$L_{\mathrm{X}}$, $L_{\mathrm{bol}}$, and $R_{\mathrm{o}}$ measurements of
unresolved binary systems are ambiguous and problematic, we reiterate that the
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ relation in stars with
secular angular momentum evolution must be studied in samples that exclude
unresolved binaries.

We find tentative evidence for supersaturation for single stars in both
clusters with 0.002 $<$ $R_{\mathrm{o}}$ $\buildrel<\over{\sim}$ 0.01. In this
$R_{\mathrm{o}}$ regime, stars follow a power-law with slope between 0.24 and
0.76. However, both the slope and the $R_{\mathrm{o}}$ threshold between
supersaturation and saturation are not as well constrained as the parameters
in the saturated and unsaturated regimes.

Lastly, in our large coeval sample of single known rotators with unsaturated
X-ray emission, a change of 0.5 orders of magnitude in $R_{\mathrm{o}}$
translates into a change in up to two orders of magnitude in
$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$. This steep relationship highlights the
sensitivity of coronal activity to the rotation of a star. On the other hand,
fully convective stars have small $R_{\mathrm{o}}$ values spanning two orders
of magnitude, and $L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ values, roughly one
order of magnitude. The latter phenomenon may be driven by the fact that fully
convective stars at the age of Praesepe and Hyades are fully within the
saturated regime and, thus, restricted in their activity levels by whatever
mechanisms drive saturation.

A.N. acknowledges support provided by the NSF through grant 2138089. M.A.A.
acknowledges support provided by NASA through grant NNX17AD71G. J.J.D. was
supported by NASA contract NAS8-39073 to the Chandra X-ray Center and thanks
the Director, P. Slane, for continuing advice and support.

We estimated the spectral types used in our analysis and several figures using
a ($G-K$)-spectral type relation based on the Stellar Color and Effective
Temperature Sequence of E. Mamajek, available at
http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt (v.
2021.03.02).

This work has made use of data from the European Space Agency (ESA) mission
Gaia (https://www.cosmos.esa.int/gaia), processed by the Gaia Data Processing
and Analysis Consortium (DPAC,
https://www.cosmos.esa.int/web/gaia/dpac/consortium). Funding for the DPAC has
been provided by national institutions, in particular the institutions
participating in the Gaia Multilateral Agreement.

This research has made use of the NASA/IPAC Infrared Science Archive, which is
operated by the Jet Propulsion Laboratory, California Institute of Technology,
under contract with the National Aeronautics and Space Administration. The Two
Micron All-Sky Survey was a joint project of the University of Massachusetts
and IPAC.

Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P.
Sloan Foundation, the U.S. Department of Energy Office of Science, and the
Participating Institutions. SDSS acknowledges support and resources from the
Center for High-Performance Computing at the University of Utah. The SDSS
website is www.sdss.org.

This research has made use of data obtained from the 4XMM XMM-Newton
Serendipitous Source Catalog compiled by the 10 institutes of the XMM-Newton
Survey Science Centre selected by ESA, and of data obtained from the Chandra
Source Catalog, provided by the Chandra X-ray Center as part of the Chandra
Data Archive.

This work made use of data supplied by the UK Swift Science Data Centre at the
University of Leicester.

This research has made use of NASA’s Astrophysics Data System Bibliographic
Services, the SIMBAD database, operated at CDS, Strasbourg, France, the VizieR
database of astronomical catalogs (Ochsenbein et al., 2000), and the “Aladin
Sky Atlas”, developed at CDS, Strasbourg Observatory, France.

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##  Appendix A Marginalized Posterior Probability Distributions for the MCMC
Analysis of Our $R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ Model

We present the marginalized posterior probability distributions from the MCMC
analysis we performed on six different subsamples of Praesepe and Hyades
stars: single members of each cluster, binary members for each cluster, single
members of both clusters combined, and binary members of both clusters
combined (see Section 5.3 and Table 8). The binary samples include candidate
and confirmed binaries, including single stars with RUWE $>$ 1.4. Figure 14
shows an example of the marginalized posterior probability distributions for
the subsample of single members from both clusters.

Fig. Set14. Marginalized posterior probability distributions from the MCMC
analysis of Our $R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ Model

Figure 14: Marginalized posterior probability distributions from the MCMC
analysis of our $R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ model
using emcee for single members in both Praesepe and Hyades. The parameter
values of the a posteriori model are the peaks of the one-dimensional
distributions; the vertical dashed lines approximate the median and 16th,
50th, and 84th percentiles. The two-dimensional distributions illustrate
covariances between parameters; the contour lines approximate the 1$\sigma$
and 2$\sigma$ levels of the distributions. The complete figure set, which
includes an image for each of the six subsamples in Table 8, is available in
the online journal.

##  Appendix B MCMC Results for Our Modified
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ Model with
Supersaturation

We present the results and marginalized posterior probability distributions
from the MCMC analysis we performed on six different subsamples of Praesepe
and Hyades stars: single members of each cluster, binary members for each
cluster, single members of both clusters combined, and binary members of both
clusters combined, using a modified
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ model that includes a
secondary power-law at small $R_{\mathrm{o}}$ to represent the supersaturated
regime (see Section 5.3.2). Figure 15 shows the modified
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ model on the six
subsamples, using the same format as in Figure 12. Figure 16 shows an example
of the marginalized posterior probability distributions for the subsample of
single members from both clusters.

Figure 15: Same as Figure 12, but for a modified
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ model that includes a
secondary power-law with index $\beta_{\mathrm{sup}}$ for $R_{\mathrm{o}}$ $<$
$R_{\mathrm{o}}$,sup, where $R_{\mathrm{o}}$,sup is the threshold
$R_{\mathrm{o}}$ value between supersaturation and saturation. We find only
tentative evidence for supersaturation in single stars with $R_{\mathrm{o}}$
$\buildrel<\over{\sim}$ 0.01, for which the power law index
$\beta_{\mathrm{sup}}$ is distinct enough from zero.

Fig. Set16. Marginalized posterior probability distributions from the MCMC
analysis of Our Modified Model with Supersaturation

Figure 16: Same as Figure 14, but from the MCMC analysis of our modified
$R_{\mathrm{o}}$–$L_{\mathrm{X}}$/$L_{\mathrm{bol}}$ model with
supersaturation (see Section 5.3.2). The complete figure set, which includes
an image for each of the six subsamples in Table 8, is available in the online
journal.