A Sparse Representation Classification for Noise Robust
Wrist-based Fall Detection
Farah Othmen
1,3,4 a
, Andr
´
e Eugenio Lazzaretti
2 b
, Mouna Baklouti
3
,
Marwa Jmal
4
and Mohamed Abid
3
1
Ecole Polytechnique de Tunisie, Universit
´
e de Carthage, La Marsa, Tunisia
2
CPGEI, Universidade Tecnol
´
ogica Federal do Paran
´
a, Curitiba, Brazil
3
CES Lab, National School of Engineers of Sfax, University of Sfax, Tunisia
4
Telnet Innovation Labs, Telnet Holding, Ariana, Tunisia
Keywords:
Additive White Gaussian Noise, Machine Learning, Supervised Dictionary Learning, Wearable Fall detection.
Abstract:
Elderly falls are becoming a more crucial and major health problem relatively with the significant growth of the
involved population over the years. Wrist-based fall detection solution gained much interest for its comfortable
and indoor-outdoor use, yet, a very moving and unstable location to the Inertial measurement unit. Indeed,
acquired data might be exposed to random noises challenging the classifier’s reliability to spot falls among
other daily activities. In this paper, we address the limits faced by Machine Learning models regarding noisy
and overlapped data by proposing a study of the Supervised Dictionary Learning (SDL) technique for on-
wrist fall detection. Following the same prior work experimental protocol, the five most popular SDL models
were evaluated and compared in performance with two benchmark Machine learning models. The evaluation
setup follows two main experiments; processing clean data and casting different additive white Gaussian
noise (AWGN). A distinguishable achievement was obtained by the SDL algorithms, of which the Sparse
Representation-based Classifier (SRC) algorithm surpass other models especially using noisy data. The latter
maintained almost 98% for 0db AWGN versus 96.4% for KNN.
1 INTRODUCTION
The rate of the elderly population has seen an impos-
ing growth over the last decades and is projected to
be still increasing throughout the upcoming years to
outpass children under-five population. This notable
phenomenon has been aroused by both proportions:
a steady increase in life expectancy and the decline
in fertility rate (World Health Organization and US
National Institute of Aging,2011). Indeed, this dra-
matic increase of such a fragile population will even-
tually affect the global world’s health and well being
as the dependency rate will respectively boost. One of
the most crucial health risks faced by the older pop-
ulation is falling. It has been classified as a disease
in the eleventh version of the International Classifica-
tion of Diseases (World Health Organization, 2019).
Therefore, statistics from (World Health Organiza-
tion, 2008) show that 30% of people older than age
a
https://orcid.org/0000-0003-1699-7653
b
https://orcid.org/0000-0003-1861-3369
65 and 50% of people older than age 85 will face a
fall risk at least once per year. Accordingly, one-third
of those who fall, seek for medical care, believing it
may lead to losing their independence.
Wearable fall detection systems have attracted
much research interest with the emergence of smart
wearable devices and sensors over the recent years,
stimulated by their anywhere-anytime accessibility
and comfortable use. Two main wearable fall de-
tection approaches have been proposed in the re-
lated literature, namely, threshold-based and machine
learning-based, as the latter has received more interest
lately (Xu et al., 2018), (Ramachandran and Karup-
piah, 2020). To enhance system’s reliability, an opti-
mal combination of feature extractors and classifiers
has been extensively researched in most related works
as (Vallabh et al., 2016), (Casilari-P
´
erez and Garc
´
ıa-
Lagos, 2019), (Zhang et al., 2019), (de Quadros et al.,
2018). However, classification performance can de-
grade substantially, since hand-crafted features may
be very specific to a given acquisition device, its
on-body placement and the trained dataset (Casilari-
Othmen, F., Lazzaretti, A., Baklouti, M., Jmal, M. and Abid, M.
A Sparse Representation Classification for Noise Robust Wrist-based Fall Detection.
DOI: 10.5220/0010238804090416
In Proceedings of the 14th International Joint Conference on Biomedical Engineering Systems and Technologies (BIOSTEC 2021) - Volume 5: HEALTHINF, pages 409-416
ISBN: 978-989-758-490-9
Copyright
c
 2021 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
409

P
´
erez et al., 2017), (Aziz et al., 2016).
Dictionary learning approaches (DLA) have
gained a lot of interest in image processing includ-
ing sparse representation based classification algo-
rithm for face recognition (Xu et al., 2017), as it
has shown robustness especially for a narrow num-
ber of channels and samples. Recently, DLA has
emerged to cover classification and pattern recogni-
tion tasks in many fields in order to reduce the need to
select the best feature and classifier combination for
the application. Thus, some related works have been
proposed based on Supervised Dictionary Learning
Technique (SDL) for biomedical signal processing
field, mainly for Electroencephalogram (EEG) (Mo
et al., 2017), (Sheykhivand et al., 2020) and Elec-
trocardiogram (ECG), (Ceylan, 2018), (Andrysiak,
2018) for anomaly detection.
To the extent of our knowledge, such a dictionary-
based approach is still uncharted in the wearable-
based fall detection systems. We have first started
by proposing the SDL as main contribution for on-
wrist based fall detection as an autonomous feature
extractor and classification combiner from acquired
raw data in a previous work (Othmen et al., 2020).
This paper aims to conduct an advanced exploration
of the SDL technique to demonstrate its efficiency and
robustness in fall detection systems and to compare its
performances with previous machine learning-based
study (de Quadros et al., 2018). Therefore, the imple-
mented machine learning model may face challenges
caused by the unstable on-wrist location that affects
the inertial measurement unit (IMU), as the acquired
data may face random distortion resulting in noisy
and overlapped data. Assuming that IMU measure-
ment noise can be accurately modeled using the white
noise model (Barrett et al., 2012), we will be adapt-
ing the same experimental protocol of the previous
study along side with Additive White Gaussian noise
(AWGN) to assess the robustness, reliability of vari-
ous SDL, and sparse representation algorithms, com-
pared to ML methods.
The paper is organized as follows: Section II pro-
vides an overview of the proposed method and briefly
describes the SDL techniques, where the most used
algorithms are also presented. Section III illustrates
the obtained results and compares them with prior
work. Conclusion and future related works are pro-
vided in Section IV.
2 METHOD AND BACKGROUND
Considering that wrist-worn devices are the most
comfortable body location for the patient (Ozdemir,
2016), they are yet very unstable for the IMU. Since
arms are usually very moving parts of the body, many
hand movements, i.e., clapping, rising and releasing
hands, may present similar motion patterns compared
with fall movements. These movement features sim-
ilarities may present a bottleneck in the MLM, es-
pecially when it comes to noisy acquired data. One
of the most faced challenges for MLM is the overfit-
ting problem that is mainly caused by learning noisy
and overlapped data. Although we can manage to
filter some external influence, low cost MEMS IMU
has random internal noise sources associated with it
that manipulates the classification algorithm structure
(Barrett et al., 2012), (Kj et al., 2016).
To overcome this issue while bearing in mind
the system reliability, we propose SDL technique as
it has previously proven its effectiveness to man-
age raw and noisy data processing and maintain-
ing a considerable efficiency (Othmen et al., 2020).
To compare prediction performances, we adapt the
same implemented experimental protocols employed
in (de Quadros et al., 2018) using clean and differ-
ent Signal-to-Noise Ratios (SNR). Therefore, differ-
ent SDL algorithms will be evaluated and compared
through their prediction performances with Machine
Learning classifiers.
The pipeline of the designed architecture is illus-
trated in Fig 1 and it is detailed in the following sub-
sections.
2.1 Data Collection and Preprocessing
The data set has been gathered all through the
(de Quadros et al., 2018) study. In fact, the sig-
nal acquisition was done by the employment of three
main tri-axial IMU sensors, namely, accelerometer,
gyroscope, and magnetometer which are embedded
within the GY-80 IMU model device. To amass and
register data signals from the latter sensors, an Ar-
duino Uno was integrated with the IMU device into
a wrist-worn band paced at the non-dominant hand.
The raw sensors data were obtained in a 100 Hz sam-
pling rate and therefor the accelerometer, gyroscope,
and magnetometer sensors were configured as 4g, 500
degrees/sec and 0.88 Ga respectively.
In order to create a more generalized and accurate
dataset, twenty-two volunteers with different ages,
heights, and weights were engaged during this exper-
imentation. Each one performs two main event cate-
gories, i.e, fall incidents and activities of daily living
(ADL). The registered falls enclose forward to fall,
backward fall, right-side fall, left-side fall, fall after
rotating the waist clockwise, and fall after rotating the
waist counterclockwise. The ADL’s performed activi-
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410

Figure 1: Pipeline of the proposed achitecture.
ties cover walking, clapping hands, moving an object,
tying shoes, and sitting on a chair. The average dura-
tion of the recorded activities is 9.2 seconds, assuming
that every one starts with a resting arm (resting state)
followed by a few steps before the activity’s perfor-
mance.
For the sake of removing any external influence
that affects the accelerometer (Vallabh et al., 2016),
the accelerometer data was preprocessed with a mov-
ing average filter with a window size of 40 and a sub-
traction of a fixed value equal to 1G to eliminate the
gravity-related information.
2.2 Feature Extraction
This work implements SDL classification approaches
in a wrist-based fall detection system while benefiting
from its capacity to generate more discriminative fea-
tures using sparse representation. For this purpose,
we maintained the same feature engineering proto-
col adopted in the previous work (de Quadros et al.,
2018), since the selected features will play an impera-
tive role in system efficiency and its comparison with
other proposed approaches.
The feature extraction depends on two main sig-
nal categories, i.e., movement-based and orientation-
based. Concerning the movement, the most used pop-
ular extracted movement pattern is the Total acceler-
ation (TA) (Vallabh and Malekian, 2017), (Pannurat
et al., 2014), described by the following equation (1):
TA =
q
x(t)
2
+ y(t)
2
+ z(t)
2
, (1)
where x(t), y(t), z(t) represents respectively the reg-
istered x, y and z axis of the accelerometer. For a
clearer movement decomposition, five other signals
have been obtained, which are described as: (a) VA
is The Vertical Acceleration considering only the ver-
tical component of TA; (b) TV is the Total Velocity
obtained through time window integration of TA; (c)
Vertical Velocity VV is the time window integration
of VA; (d) TD is the Total Displacement considering
the time window integration of TV; (e) Vertical Dis-
placement VD obtained from the time window inte-
gration of VV.
The orientation-based decomposition is acquired
through an orientation filter. In fact, the Madgwick’s
orientation decomposition method defined in (Madg-
wick, 2010) has been employed. Indeed, it uses data
provided from IMU sensors to describe the estimated
nature of orientations in three-dimensions through a
quaternion representation. These angle representation
of the quaternion are called Euler angles and defined
by the Yaw, Pich, and Roll angles.
Taking into account the feature extraction, the se-
lected features were the maximum and mean of each
window interval of the obtained vertical component,
VA, VV, and VD respectively. On the other hand, only
the mean values of the sine and cosine corresponding
to the Euler angels (Yaw, Pich, and Roll) were con-
sidered. Afterward, the twelve selected features were
normalized in the range of [-1, 1].
2.3 Supervised Dictionary Learning
Technique
In general, the main idea of dictionary learning is to
find a sparse representation of a signal or an image us-
ing a dictionary from a predefined training set. DLA
is fitted to many problem domain as it has proven
state-of-the-art achievements mainly in computer vi-
A Sparse Representation Classification for Noise Robust Wrist-based Fall Detection
411

sion, both in supervised and unsupervised tasks, i.e.,
in information retrieval, image reconstruction, and
pattern recognition (Gangeh et al., 2015). Taking
into account the classification task, several Super-
vised dictionary-based learning methods are recently
presented in the literature to enhance it’s efficiency.
As discussed in (Xu et al., 2017), SDL methods can
be divided into shared, class-specific, commonality
and particularity, auxiliary, and domain adaptive dic-
tionary learning.
As being a branch of Machine Learning, the clas-
sification based on SDL involves two main phases,
namely the training and the testing phases. In the
training phase, the goal of the SDL algorithm is to
map the low dimensional training data X to a high
and sparse dimensional representation denoted A over
an optimised and learned dictionary D, to make more
discriminative pattern and easier to be distinguished.
The objective here is to define D and the sparse rep-
resentation X while respecting extra constraints f
A
(.)
and f
D
(.) through an optimization problem generally
defined by the following equation (2):
min
D,A
{
N
∑
i=1
(
1
2
||x
i
− Da
i
||
2
2
+ λ
1
||a
i
||
q
)
+λ
2
f
A
(A) + λ
3
f
D
(D)},
(2)
Based on (Suo et al., 2014), the function f
A
(.) could
be a logistic function, a linear classifier, a label con-
sistency term, a low-rank constraint or Fisher discrim-
ination criterion. As for f
D
(.) is to force the incoher-
ence of the dictionary for different classes. Hence, it
is possible to jointly learn the dictionary and classifi-
cation model, which attempt to optimize the learned
dictionary for classification tasks (Jiang et al., 2011).
The testing phase follows two fundamental processes:
First, the used algorithm generates the sparse co-
efficient a
test
of the test sample x
test
directly through
the learned Dictionary D satisfying the previous equa-
tion (2).
Second, the label of each test sample is assigned
while maintaining the class with the minimum recon-
struction error rate according to:
Label(x
test
) = min
i
r
i
(x
test
), (3)
where, r
i
= ||x
test
−Dσ
i
(a
test
)||
2
2
designs the error rate
equation, σ
i
is the selective function of the coefficient
vector associated to the class i. and used as a feature
descriptor of the data. Thus, the test samples are rep-
resented as a linear combination of just the training
samples corresponding to the same class.
Assuming that supervised dictionary learning
methods and sparse representation differ in the way
they exploit class labels, we focused on the most pop-
ular and utilized ones in the experimentation. For this
purpose, five different SDL algorithms for classifica-
tion were evaluated and compared in term of perfor-
mance, namely, sparse representation-based classifier
(SRC) (Wright et al., 2009), Label consistent K-SVD
(LC-KSVD) (Jiang et al., 2013), Dictionary Learn-
ing with Structured Incoherence (DLSI) (Ramirez
et al., 2010), Fisher Discrimination Dictionary Learn-
ing (FDDL) (Yang et al., 2011), and two versions of
Low-Rank Shared Dictionary (LRSDL and D2L2R2)
(Vu and Monga, 2016), (Vu and Monga, 2016).
3 EXPERIMENTAL VALIDATION
In this section, we present a set of results to illus-
trate the performance of our proposed approach based
on the most popular SDL for classification and those
of the Machine Learning algorithms experienced in
(de Quadros et al., 2018). Hence, we consider three
benchmark Machine Learning Models in fall detec-
tion (Aziz et al., 2016) which are: Support Vector
Machine (SVM), K-Nearest Neighbour (KNN) and
Linear Discriminant Analysis (DLA). Additionally,
five SDL-based techniques which were briefly intro-
duced in section II, namely SRC, FDDL, DLSI, and
both versions of LRSDL, are presented. The evalua-
tion is implemented based on an open-source Matlab
Dictionary Learning Toolbox ”DICTOL” available on
Github
1
, as used in (Vu and Monga, 2016) and (Vu
and Monga, 2016).
In this section, we will initiate our experimental
validation with a preliminary study in which we will
extract the best fitted amount of data needed to train
the SDL algorithms and the best configuration. After-
wards, we will follow two main experiments. In the
first experiment (A), we evaluate SDL and ML algo-
rithms based on clean data. As for the second exper-
iment (B), we will assess both techniques robustness
for different generated AWGN.
3.1 Evaluation Metrics
This study is evaluated based on two common met-
rics, namely, Accuracy (AC) and Sensitivity (SE). In
this sense, AC represents the overall true detection
and SE represents the ability to detect authentic falls
among all detected falls.
1
https://github.com/tiepvupsu/DICTOL
HEALTHINF 2021 - 14th International Conference on Health Informatics
412

3.2 Preliminary Experiment and
Configuration
For a preliminary SDL analysis, we consider two ran-
dom data splitting scenarios in order to extract the
best fitted amount of data needed to train the SDL al-
gorithms as follows:
1. 50% for training and 50% for testing;
2. 75% for training and 25% for testing.
For each experiment scenario, we have fixed the
number of the atoms in Dictionary equal to the num-
ber of samples in the training data, i.e., 300 and 594,
respectively.
(a) Scenario 1
(b) Scenario 2
Figure 2: Performance of Dictionary learning algorithms
based on fixed Dictionary size.(a) Scenario 1: 50% of the
data for training; (b) Scenario 2: 75% of the data for train-
ing.
Figure 2 demonstrates the performance of every
SDL algorithm tested on both mentioned scenarios
based on a Dictionary size equal to the number of
training samples. Results show that increasing the
training data has an impact on increasing the fall de-
tection performance for most SDL algorithms. In
both tests, the SRC outperforms other algorithms with
an accuracy of 96.2% and 99% for scenario 1 and
scenario 2 respectively. However, the DLSI algo-
rithm showed a decrease from 92.2% to 90% in per-
formance as the training set increased from 50% to
75% of the data.
From our exploratory experiment, the SDL algo-
rithms’ hyper-parameters are founded on the best-
achieved performances for our dataset using random
training features. Thus, collected data set is subdi-
vided such as scenario 2, namely 75% of the data is
for the training phase and 25% for the test phase. Ac-
cordingly, every used SDL algorithm is configured as
follows: SRC: λ =0.01; LC-KSVD:α=0.01, β=0.1;
DLSI: λ
2
=0.1, η=0.001; FDDL: λ
1
= λ
2
=0.001;
LRSDL and D2L2R2: λ
1
=0.001, λ
2
=0.01, η=0.02.
3.3 Experiment (A): Clean Data
Evaluation
In order to observe the performance behavior of the
each of the assessed SDL models in consonance with
the variance of the dictionary size, we have com-
pared different SDL algorithms based on the num-
ber of dictionary atoms per class that ranges between
50 and 300. The result is shown in Fig. 3. Ac-
cordingly, the best overall result was accomplished
by the D2L2R2 algorithm that is the extended ver-
sion of LRSDL which showed, in contrast, the low-
est overall performances. In this sense, the best algo-
rithm achieved an accuracy rate of 99% for a dictio-
nary size of 200 atoms per class, very close to 98.96%
of SRC and DLSI algorithms based on a Dictionary
size equals to 300 and 150 respectively.
Intending to prove the efficiency of our proposed
method, we additionally compared the best perfor-
mance of each classification SDL algorithm with the
result reported in previous work (de Quadros et al.,
2018) based on the machine learning approach. As
summarized in Table 1, the accuracy rate obtained by
SRC and D2L2R2, for D equals respectively 300 and
200 atoms/class, are very analogous with the one ob-
tained by KNN algorithms in the previous work.
3.4 Experiment (B): Noisy Data
Evaluation
In this experiment, we have managed to randomly ad-
just different SNR decibel values, i.e., 0dB, 0.5dB,
5dB, 10dB, 20dB, and 100dB to generate multiple
Additive white Gaussian noise. Fig.4 illustrates an
example of VA signal and the extracted features men-
tioned in section II for fall and ADL events. As one
A Sparse Representation Classification for Noise Robust Wrist-based Fall Detection
413

Figure 3: Comparison between classification-based SDL algorithms in accordance with Dictionary size.
Table 1: Comparison of DL-based approach and previous
ML-based approach.
Approach Algorithm Best performance
Accuracy D size
SRC 98.9 300
LC-KSVD 98.5 300
SDL
DLSI 98.9 150
FDDL 96.9 200
LRSDL 93.8 150
D2L2R2 99.0 200
KNN 99.0
MLM
SVM 97.4
DLA 96.4
can observe, features 6 to 12, i.e the selected features
corresponding to Euler Angles, are the most affected
by the insertion of noise.
Taking into account result obtained in experiment
(A), we have fixed the best obtained D size corre-
spondingly to the most efficient models: SRC, DLSI,
and D2L2R2 for SDL; KNN and SVM for ML. Ta-
ble 2 and 3 exhibit the efficiency behavior of SDL
and ML models respectively to different AWGN sig-
nals. Based on table 3, SDL algorithm showed a re-
markable stability throughout the decreasing on the
SNR value. Despite the fact that D2L2R2 reached
the best performance in regard of clean data, SRC
showed the best overall performances for almost all
the tested SNR. Giving the example of AWGN equals
to 0dB, SRC has reached approximately 98% of ac-
curacy and an appreciable capacity to detect true falls
of 100% compared to the notable performance de-
Table 2: Robustness of Supervised Dictionary learning
models to Additive White Gaussian Noise.
SRC DLSI D2L2R2
SNR AC SE AC SE AC SE
0dB 97.9 100 96.9 100 95.3 100
0.5dB 97.9 97.9 96.4 96.9 95.3 95.8
5dB 98.4 99.0 98.4 99.0 97.9 97.9
10dB 98.4 100 98.9 100 97.9 100
20dB 98.9 100 98.9 98.9 98.4 97.9
100dB 98.4 100 98.9 98.9 99.0 100
Table 3: Robustness of Machine learning learning models
to Additive White Gaussian Noise.
KNN SVM
SNR AC SE AC SE
0dB 92.7 100 91.7 84.4
0.5dB 92.7 96.9 90.6 82.3
5dB 94.3 97.9 2.19 84.8
10dB 94.3 97.9 92.71 85.4
20dB 95.5 99.0 92.71 90.1
100dB 96.4 99.0 91.7 98.9
crease of DLSI and D2L2R2. Regarding Table 3,
both algorithms showed a massive decrease in per-
formances reaching 92.7% and 91.7% for 0dB SNR.
Even though, KNN algorithm has maintained a good
Specificity for falls compared to SVM. In general,
SRC outperformed other SDL and ML models by
maintaining its robustness regarding overlapped data,
thus, confirms the main objective of Dictionary learn-
ing based approach.
HEALTHINF 2021 - 14th International Conference on Health Informatics
414

Figure 4: Illustration of Vertical acceleration (VA) signal and the 12 respective extracted features of clean and 0dB AWGN
data (a) Fall event, (b) ADL event.
4 CONCLUSION
In this work, we introduced a novel classification
method, Supervised Dictionary Learning, for a Ro-
bust wrist-based fall detection system. Being a very
moving part of the body, fall detection systems placed
on wrist are highly susceptible to acquire noisy yet
overlapped data that can affect their efficiency and re-
liability. For this propose, our contribution mainly
lies in exploring and applying the effectiveness of
Dictionary Learning-based classifiers into a wearable
fall detection system located on wrist. The study ex-
plores Supervised dictionary learning models for clas-
sification and compares their performances to those
reported in previous work while preserving the same
standard protocol, i.e., data collection and preprocess-
ing. Indeed, two main experimental evaluations were
conducted. The first explores six of the most com-
mon SDL-based classifiers namely, SRC, LC-KSVD,
DLSI, FDDL, LRSDL, and D2L2R2 with different
scenario for clean data-set. In the second, we gen-
erated Additive white Gaussian noise using multiple
Signal-to-noise ratios in order to bring out the effec-
tiveness of the proposed method. The conducted re-
sults showed that the SDL algorithm presents a very
robust model regarding original and noisy data. In-
deed, SRC has proved its efficiency reaching almost
99% of accuracy, similar to the achieved one by the
machine learning classifier KNN, still maintained the
best achievement for noisy data reaching an accuracy
of almost 98% with 100% of sensitivity.
A thorough experimentation will be conducted in
future work, to take further advantage of the DLA
benefits. As being a popular representation based
paradigm, we plan next to test the performance of the
SDL on jointly learn a frame-like representation of
raw data vectors (over-complete dictionary and sparse
representation) and classification parameters in order
to enhance system’s reliability.
In our future related work, we expect additional
improvement of results even further by incorporating
the feature extraction phase and the learning phase us-
ing the DLA technique in order to automatically learn
relevant feature of the acquired raw signals.
ACKNOWLEDGEMENTS
This research and innovation work is supported by
MOBIDOC grants from the EU and National Agency
for the Promotion of Scientific Research under the
AMORI project and in collaboration with Telnet In-
novation Labs.
A Sparse Representation Classification for Noise Robust Wrist-based Fall Detection
415

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