2023 International Conference on Intelligent Systems for Communication, IoT and Security (ICISCoIS) | 979-8-3503-3583-5/23/$31.00 ©2023 IEEE | DOI: 10.1109/ICISCOIS56541.2023.10100379

Data Anomaly Detection in Wireless Sensor
Networks using β-Variational Autoencoder
Arul Jothi S
Assistant Professor,PSG College Of
Technology Coimbatore,India
(Affliated to Anna University,Chennai)
saj.cse@psgtech.ac.in

Harini S
Student,PSG College Of Technology
Coimbatore,India
(Affliated to Anna University,Chennai)
19z317@psgtech.ac.in

Nivedha K
Student,PSG College Of Technology
Coimbatore,India
(Affliated to Anna University,Chennai)
19z336@psgtech.ac.in

Selva Keerthana B G
Student, PSG College Of Technology
Coimbatore,India
(Affliated to Anna University,Chennai)
19z346@psgtech.ac.in

Gokul R
Student,PSG College Of Technology
Coimbatore,India
(Affliated to Anna University,Chennai)
19z314@psgtech.ac.in

Jayasree B S
Student,PSG College Of Technology
Coimbatore,India
(Affliated to Anna University,Chennai)
19z322@psgtech.ac.in

Abstract— Anomaly detection is the process of identifying data
instances that drastically deviate from the majority of data
instances. Anomaly detection is a key challenge to ensure the
security in Wireless Sensor Networks. The detection of such
anomalous data is required to reduce false alarms. The data that
is generated from wireless sensor networks have several
imbalances. The term imbalance refers to uneven distribution of
data into classes that severely affects the performance of
traditional classifiers. Data imbalance is the major challenge in
machine learning models that is resolved in the proposed model
using deep learning technique. Deep learning technique
proposed is beta variational autoencoders in which a parameter
β is included to the KL divergence term of the Variational
Autoencoder (VAE)'s loss function. The introduction of the
parameter beta provides disentangled representation of data.
The proposed VAE model uses multivariate normal distribution
instead of normal distribution.
Keywords—Anomaly Detection, Data imbalance, VAE.

I. INTRODUCTION
Anomaly detection is a key consideration in the development
and deployment of machine learning and deep learning
algorithms. Data instances or observations that differ from the
majority of data instances are considered anomalies. Finding
those data points or instances is the process known as anomaly
detection. Anomaly detection(AD) is also known as outlier or
novelty detection. Because outliers have the potential to badly
skew the overall result of an analysis and because their
behavior may be precisely what is desired, it is crucial to
recognize and deal with them while evaluating data.
AD becomes a major challenge in Wireless Sensor networks
in order to reduce false alarms[12]. Sensors generate sensory
data and continuously monitor physical factors including
temperature, vibration, and motion. A sensor node may act as
a data router and data originator simultaneously. On the other
hand, a sink acts as the center of processing and gathers data
from sensors. To share data, the base station of a Wireless
Sensor Networks(WSN) system makes a connection to the
Internet.
Variational Autoencoder(VAE) is an autoencoder extension.
It, like an autoencoder, consists of an encoder and decoder
network component. A VAE learns to rebuild the original data
by sampling from a distribution based on a mapping from an
input. Normal data samples have a minimal reconstruction
error, while abnormal data samples have a substantial

c
979-8-3503-3583-5/23/$31.00 2023
IEEE

reconstruction error. The reconstruction probability, as in [2]
is employed as an anomaly score. The VAE model is trained
by minimizing the difference between the model's estimated
distribution and the data's true distribution. This difference is
assessed using the Kullback-Leibler divergence, which
measures the distance between two distributions by calculating
how much information is lost when one distribution is used to
represent the other.
β-VAEs learn a disentangled representation of a data
distribution; that is, a single unit in the latent code is only
responsive to a single generating element. The benefit of using
a disentangled representation is that the model is
straightforward to generalize and interpret. For the loss
function, beta divergence is employed instead of KL
divergence as in [1]. The purpose for adding this hyper
parameter is to optimize the likelihood of generating a true
dataset while decreasing the likelihood of real to estimated
data being minimal, under epsilon.
II. LITERATURE SURVEY
The authors in [4] proposed an anomaly detection
methodology in wireless sensor networks using ensemble
random forest. Decision tree, naïve bayes and kNN were the
base learners of the ensemble. The test results show that better
performance can be got using multiple learners in the
ensemble.
Incremental Principal Component Analysis and Support
Vector Machine (OCSVM) was published in [6], This study
focuses on building a lightweight anomaly detection system
that uses one-class learning schemes and dimension reduction
concepts to produce data gathering that is trustworthy while
consuming less energy. Due to its strengths in categorizing
unlabeled data, the one-class support vector machine
(OCSVM) is utilised as an anomaly detection technique,
whereas the hyper-ellipsoid variance may detect multivariate
data.
Author in [7] focuses on attack detection and proposes a model
for intrusion detection that is compatible with WSN features.
This approach is based on the online Passive aggressive
classifier and information gain ratio. A dataset from a wireless
sensor network detection system (WSN-DS) was used for the
investigation. The suggested model ID-GOPA achieves a 96%

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detection rate when deciding if the network is operating
normally or is vulnerable to attacks of any kind.
A model based on Inverse Weight Clustering(IWC) and a C5.
0 decision tree was proposed by the author in [8]. IWC and
C5.0 decision tree algorithms is employed in this study to
create a model that can distinguish between abnormal and
typical activity in a wireless sensor network. IWC is used to
classify groups and assign label to groups, and then use a C5.0
classifier to train and test the model. The University of North
Carolina at Greensboro (UNCG), the Intel Berkeley Research
Lab (IBRL), and the Bharatpur Airport dataset were used in
the experiment. The findings demonstrate that the technique
with the highest accuracy rate for detecting anomalies on IBRL
is IWC+C5. 0.
[9] investigated the use of autoencoders to improve forecast
performance for imbalanced binary classification problems.
Authors consider breast cancer detection as an application
domain; this is an unbalanced classification issue. The
investigation of deep autoencoders' capacity to recognise
patterns in classes of benign and malignant instances is one of
the objectives of this paper. Second, they suggest and contrast
two classification models for the detection of breast cancer
based on autoencoders.
On the basis of an autoencoder architecture, a neural model for
the detection of abnormal behaviour is developed in [10] . A
variational autoencoder will be compared to this solution to
examine the improvements that can be made. To validate the
proposal, the well-known dataset known as UK-DALE will be
employed.
The author in [11] compared three distinct pre-processing
techniques for imbalanced categorization data. Three
imbalanced classification data sets with various class
imbalances are subjected to the use of Variational
Autoencoder, Random Under-Sampling Boosting, and a
mixture of the two. While the hybrid technique performs
poorly for moderate class imbalanced data and best for
extremely imbalanced data, when total classification
performance is examined, both VAE and RUSBoost display
better classification results.
In [13] Online Locally Weighted Projection Regression is used
where only a subset of data is used which is non-parametric
and local functions that only use the subset of data make the
present forecasts. Because of this, the processing complexity
will be minimal. OLWPR achieves an 86 percent detection rate
and a remarkably low 16% error rate.
The author in [16] presented a high-dimensional, very
unbalanced set of data is well-suited for the variance weighted
multi-headed auto-encoder classification model . In addition
to using weighting or sampling techniques to deal with the
extremely unbalanced data, , the model predicts many outputs
at the same time by combining output multi-task weighting
and supervised representation learning.
The paper [18] proposes a data detection approach based on
time series which addresses the issue that the sampling values
of sensors change significantly in hard conditions and the
detection results of events are erroneous with the growth of
fault nodes in WSN.

632

One-class principle component classifier was suggested in
study [19]. In this work, a cluster-based distributed anomaly
detection method for WSNs was developed. The model makes
use of the spatial correlation of sensing data in a small area to
increase the efficiency and efficacy of detection (i.e., cluster).
The proposed approach aims to overcome the limitations of
existing detection algorithms by making efficient use of the
limited resources of sensors.
Author in [20] put out a model that uses correlations between
several physiological data variables and hybrid Convolutional
Long Short-Term Memory (ConvLSTM) approaches to
identify both straightforward point anomalies and contextual
anomalies in the massive amount of WBAN data.
Experimental analyses showed that the suggested model
reported better results than that achieved by both CNN and
LSTM independently.
III. DATASETS
A. IBRL(Intel Berkeley Research Laboratory) Dataset
The dataset carries information concerning data
gathered from fifty-four sensors utilized in the Intel Berkeley
research laboratory between February twenty eighth and April
5th, 2004. each thirty-one seconds, Mica2Dot sensors
equipped with clapboards gathered time-stamped topological
data alongside measurements of the humidity, temperature,
light, and voltage. The data was gathered using the TinyOSbased TinyDB in-network query processing technology.

Fig 1.Deployment of Sensors in IBRL

Schema:

Fig 2. IBRL Dataset Schema

x Epoch- The data was compiled with an epoch period of
around 30, resulting in the collection of 65,000 epochs and
approximately 2.3 million readings.
x Moteid- At the same moment, two readings from the same
epoch number were produced from different motes. As
mote Ids, sensors are numbered from 1 to 54.
x Temperature-Temperature is collected in degrees Celsius.
x Humidity- Humidity is measured as temperature corrected
relative humidity on a scale of 0 to 100.
x Light -Light is measured in Lux.
x Voltage- Voltage is measured in volts and ranges from 2 to
3; it has stayed relatively steady throughout their lives.
Temperature and voltage variations are highly interrelated.

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B. ISSNIP (The Intelligent Sensors, Sensor Networks &
Information Processing) Dataset:

"probabilistic encoder," which characterises the distribution of
the encoded variable given the decoded one, which naturally
defines the word "probabilistic decoder," which explains the
distribution of the decoded variable given the encoded one.
The Bayes theorem connects the posterior p(z|x), likelihood
p(x|z), and prior p(z) as represented in (1).

The Intelligent Sensors, Sensor Networks, and
Information Processing (ISSNIP) collection contains realworld humidity-temperature sensor data acquired using
TelosB motes in single-hop WSNs. This dataset has controlled
anomalies, and they are all present. There are four sensor
nodes in total: two indoor and two outdoor sensor nodes. The
data comprises of temperature and humidity readings taken
every 5 seconds for 6 hours. To generate anomalies, a hotwater kettle is utilized..

‫݌‬ሺ‫ݖ‬ሻ ൌ ߋሺͲǡ ‫ܫ‬ሻ

(2)

Schema:

‫݌‬ሺ‫ݔ‬ȁ‫ݖ‬ሻ ൌ ܰሺ݂ሺ‫ݖ‬ሻǡ ܿ‫ܫ‬ሻ݂߳‫ ܿܨ‬൐ Ͳே

(3)

‫݌‬ሺ‫ݖ‬ȁ‫ݔ‬ሻ ൌ

௣ሺ‫ ݔ‬ȁ‫ ݖ‬ሻ௣ሺ௭ሻ
௣ሺ௫ሻ

ൌ

௣ሺ‫ ݔ‬ȁ‫ ݖ‬ሻ௣ሺ௭ሻ

(1)

‫ ׬‬௣ሺ‫ ݔ‬ȁ‫ ݑ‬ሻ௣ሺ௨ሻௗ௨

Variational inference formulation:
Fig 3. ISSNIP Dataset Schema

x MoteID- At the same moment, two readings from the same
epoch number were generated from various motes.
x Humidity-Humidity is temperature corrected relative
humidity
x Temperature-Temperature is in degrees Celsius.
x Label-Anomalies are labeled as 1 and the normal data is
labeled as 0.
IV. VARIATIONAL AUTOENCODER
VAE causes the encoder to produce a probability distribution
rather than a single output value in the bottleneck layer. The
samples in the dataset can be statistically represented in latent
space using variational autoencoders as opposed to
autoencoders. The phrase "variational autoencoder" refers to
an autoencoder with controlled training to avoid overfitting
and guarantee that the latent space has desired characteristics
that allow regenerative processes.
The use of normal encoding distributions enables the encoder
to be trained to return the Gaussian mean and covariance
matrix. The encoder's generated distributions must also be
close to a typical normal distribution. The proposed model
uses multivariate normal distribution since the anomalies are
detected in multivariate time series datasets.
The "reconstruction term" (on the final layer) aims to make
the encoding-decoding strategy as performant as possible,
whereas the "regularization term" (on the latent layer) tends to
normalize the organization of the latent space by bringing the
encoder's distributions close to a standard normal distribution.
As a result, when training a VAE, the loss function that is
reduced is made up of these two terms. That regularization
term is given as the Kulback-Leibler divergence between the
returned distribution and a typical Gaussian.
Mathematics behind VAE:
For each data point, the following two steps generative process
is assumed:
1. From the prior distribution p, a latent representation z
is sampled (z).
2. x is drawn from the conditional likelihood
distribution p(x|z).
In contrast to p(x|z), p(z|x) defines the phrase

Variational inference (VI) is a statistical method for
approximating complex distributions. Here, q_x(z) is a
Gaussian distribution that approximates p(z|x), and g and h are
two functions of the parameter x that define its mean and
covariance as expressed in (4).
‫ݍ‬௫ ሺ‫ݖ‬ሻ ‫ߋ ؠ‬ሺ݃ሺ‫ݔ‬ሻǡ ݄ሺ‫ݔ‬ሻሻ݃߳‫ܪ݄߳ܩ‬

(4)

The optimum approximation is discovered by minimizing the
Kullback-Leibler divergence between the approximation and
the target p(z|x) by optimizing the functions g and h (really,
their parameters).
(g*,h*)

= ƒ”‰  ‹  ‫ܮܭ‬ԛ൫‫ݍ‬௫ ሺ‫ݖ‬ሻǡ ‫݌‬ሺ‫ݖ‬ȁ‫ݔ‬ሻ൯
ሺ௚ǡ௛ሻఢԛீൈு

= ƒ”‰  ‹ ቀ‫ܧ‬௭ି௤ೣ െ
ሺ௚ǡ௛ሻఢீൈு

ԛหȁ௫ି௙ሺ௫ሻ ȁหమ
ଶ௖

ቁ ԛ െ ‫ܮܭ‬൫‫ݍ‬௫ ሺ‫ݖ‬ሻǡ ‫݌‬ሺ‫ݖ‬ሻ൯

(5)

The function f is selected so that, when z is sampled from q*
_x, the predicted log-likelihood of x given z is maximized (z)
as shown in (6).
݂ ‫ כ‬ൌ ܽ‫ܧ šƒ ݃ݎ‬௭̱௤ೣ‫ כ‬ሺŽ‘‰ ‫݌‬ሺ‫ݔ‬ȁ‫ݖ‬ሻሻ
௙ఢி

݂ ‫ כ‬ൌ ܽ‫ܧ šƒ ݃ݎ‬௭̱௤ೣ‫ כ‬ቀെ
௙ఢி

ԛหȁ௫ି௙ሺ௫ሻ ȁหమ
ଶ௖

ቁ

(6)

Gathering all the pieces together, we are looking for optimal
f*, g* and h* as shown in (7) such that
ሺ݂ ‫ כ‬ǡ ݃‫ כ‬ǡ ݄‫ כ‬ሻ ൌ ƒ”‰  ƒš ቆ‫ܧ‬௭̱௤ೣ ቀെ
ሺ௙ǡ௚ǡ௛ሻఢிൈீൈு

ԛหȁ௫ି௙ሺ௫ሻ ȁหమ
ଶ௖

ቁെ

‫ܮܭ‬൫‫ݍ‬௫ ሺ‫ݖ‬ሻǡ ‫݌‬ሺ‫ݖ‬ሻ൯ቇ

(7)

The gradient descent is facilitated amidst the random
sampling that occurs halfway through the architecture by a
simple trick known as the reparameterization trick, which
takes advantage of the fact that if z is a random variable with
a Gaussian distribution with mean g(x) and covariance H(x)=h,
then (x).
β-Variational Autoencoder:
β-VAEs learn a disentangled representation of a data
distribution; that is, a single unit in the latent code is only
responsive to a single generating element. If each variable is

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sensitive to only one feature/property of the dataset while
being largely invariant to another, the dataset is said to be
disentangled. The benefit of using a disentangled
representation is that the model is straightforward to generalize
and interpret[14]. ߚ-VAE use beta percentage of KL
divergence for the loss function [5].
‫ ݏݏ݋ܮ‬ൌ ‫ܮ‬ሺ‫ݔ‬ǡ ‫ݔ‬ොሻ ൅ ߚ σ௝ ‫ܮܭ‬ሺ‫ݍ‬௝ ሺ‫ݖ‬ȁ‫ݔ‬ሻȁȁ‫݌‬ሺ‫ݖ‬ሻ

(8)

V. PROPOSED SOLUTION

STEPS:
1.Data Preprocessing:
A pandas dataframe is initially loaded with the data. Date,
time, moteid, reading number, and label columns are deleted
from the dataframe. The duplicate rows are then deleted. The
last step is to eliminate the rows with NaN values.
Training and testing sets of the data have been separated. A
certain percentage of outliers are introduced into the testing
dataset and scaled. The training and testing numpy arrays are
transformed into tensors using Data Builder. To iterate through
the data and manage batches, a data loader is employed.
2.VAE model specification:
TABLE I.

ENCODER AND DECODER NETWORK

Encoder

Decoder

Hidden Layer

Number of
Hidden Layer
Number of
neurons
neurons
1
50
1
12
2
12
2
50
Latent space dimension = 2
Activation Function = Relu
Loss function = Reconstruction error+0.2*KL divergence
Distribution = Multivariate Normal

3.Training:

Fig 4. Steps in the model

The training dataset consists of 70% of the dataset and does
not involve anomalies in it[3]. The train function is defined
where for each batch in the training set, encoding,
reparameterization and decoding is performed. The latent
space distribution is chosen to be multi variate normal
distribution. The loss is calculated as in (8) and the average
loss of the batch is appended to a list. The loss is
backpropagated during each epoch. The threshold for anomaly
classification is set as the maximum of the average losses of
each batch and the threshold is returned. The threshold at the
end of all epochs is passed to the test phase.

A. Algorithm

4.Testing:

1.Preprocess the data.
2.Split the data into training and testing set.
3.Define the Variational Auto encoder class
4.Training
For each batch
Run the model to get the reconstructed values, mean,
variance
Calculate the loss for the batch and update the
parameters(weight and bias)
Set threshold to the max (average(batchsize))
5.Repeat Step 4 for 50 epochs
6.Testing(threshold)
Run the model to get the reconstructed values, mean,
variance
Calculate the loss for each sample
If the loss > threshold,
increment the outlier count.

For the purpose of testing, testing dataset (30% of original
dataset) with different abnormality ranges were used. The test
function is defined where for each batch in the testing set,
encoding, reparameterization and decoding is performed. The
threshold for anomaly classification got from training is
passed as a parameter for testing. The loss is calculated for
each sample and the ones that are greater than the threshold is
classified as anomalous data.
VI. RESULT ANALYSIS
Train/Test Loss:
β- Variational Autoencoder's loss function is
composed of two terms:
Reconstruction Loss:
The difference between input representation and
output representation is known as reconstruction error or
reconstruction loss (error between input vector and output

634

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vector). With regards to the β-variational autoencoder model,
the reconstruction error is the mean squared loss.
Regularization Term:
That regularization term is expressed as the Kulback-Leibler
divergence between the returned distribution and a standard
Gaussian. Minimizing the KL divergence here means
optimizing the probability distribution parameters (μ and σ) to
closely resemble that of the target distribution. In β-VAE, only
βamount of KL divergence is considered in the train/test loss
which is expressed in (8).
Since the β-variational autoencoder is trained on normal data,
the loss of the β- variational autoencoder is larger when it
attempts to reconstruct anomalous data than when it attempts
to reconstruct normal data. This maximum of the loss function
in training phase is taken as a threshold for classification in the
testing phase.

Fig 6. Train Loss for IBRL

The Fig 8 and Fig 9 gives false positive analysis for ISSNIP
and IBRL datasets respectively.
False Positive Analysis

Number
of
outliers
introduced
into the testing
dataset
150
300
450
600

FALSE POSITIVE RATE FOR ISSNIP

Percentage of
anomalies
introduced in
the
testing
dataset
4.41%
8.82%
13.24%
17.65%

Percentage of
anomalies
predicted by
the model

False Positive
Rate

4.17%
8.85%
13.3%
15.89%

0.24
0.03
0.06
1.76

Percentage

TABLE II.

20

10
0
150

300

Actual anomalies

450

600

Predicted anomalies

Fig 7. False Positive Analysis for ISSNIP

Number
of
outliers
introduced
into the testing
dataset
25,000
50,000
75,000

FALSE POSITIVE RATE FOR IBRL

Percentage of
anomalies
introduced in
the
testing
dataset
5.28
10.03
15.04

Percentage of
anomalies
predicted by
the model

False Positive
Rate

6.05
11.84
15.63

0.77
1.81
0.59

False Positive Analysis
Percentage

TABLE III.

20
10
0
25,000

Actual anomalies

Table II and table III shows the percentage of anomalies
introduced into the testing dataset and the percentage of data
points predicted as anomalies by the model and the difference
between them for ISSNIP and IBRL datasets respectively.
The Training Loss for ISSNIP and IBRL dataset decreases as
the number of epochs increases.

50,000

75,000

Predicted anomalies

Fig 8. False Positive Analysis for IBRL

The Figure 10 and Figure 11 shows the difference between
actual and predicted anomalies for ISSNIP and IBRL datasets
respectively

False Positive rate

False Positive Rate
8
6
4
2
0
0

200

400

600

800

Number of anomalies
Fig 9. False Positive Rate for ISSNIP

Fig 5. Train Loss for ISSNIP

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False Positive Rate

[4]

False Positive Rate

[5]

8
6
4
2
0

[6]

0

20,000 40,000 60,000 80,000

[7]

Number of anomalies
[8]
Fig 10. False Positive Rate for IBRL
[9]

The results show that ઺-variational autoencoders that uses
multivariate normal distribution was able to detect anomalies
in imbalanced dataset[15][17].
CONCLUSION
We presented an anomaly detection approach in wireless
sensor networks using ઺-variational autoencoders. Normal
sensor values from IBRL and ISSNIP datasets are given as
input to the model for training where we set the threshold to be
the maximum of the average train losses. Testing is done with
by introducing outliers into the dataset and classifying the test
sample as anomaly if it's loss as in (8) falls above the threshold
value. Š‡ ’”‘’‘•‡† ઺-variational autoencoders uses only
20% of the KL divergence while calculating the loss function
and makes use of multivariate normal distribution, In the
future, if the threshold that we calculate from the training loss
is not that efficient, then we can check whether the threshold
can be fixed by taking the mean or standard deviation. Further,
the goal is to design a mechanism to see whether we can
replace the outlier with statistical measures.
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2023 International Conference on Intelligent Systems for Communication, IoT and Security (ICISCoIS)

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