Classification with electromagnetic waves

Abstract

The integration of neural networks and machine learning techniques has ushered in a revolution in various fields, including electromagnetic inversion, geophysical exploration, and microwave imaging. While these techniques have significantly improved image reconstruction and the resolution of complex inverse scattering problems, this paper explores a different question: Can near‐field electromagnetic waves be harnessed for object classification? To answer this question, we first create a dataset based on the MNIST dataset, where we transform the grayscale pixel values into relative electrical permittivity values to form scatterers and calculate the electromagnetic waves scattered from these objects using a 2D electromagnetic finite‐difference frequency‐domain solver. Then, we train various machine learning models with this dataset to classify the objects. When we compare the classification accuracy and efficiency of these models, we observe that the neural networks outperform others, achieving a 90% classification accuracy solely from the data without a need for projecting the input data into a latent space. The impacts of the training dataset size, the number of antennas, and the location of antennas on the accuracy and time spent during training are also investigated. These results demonstrate the potential for classifying objects with near‐field electromagnetic waves in a simple setup and lay the groundwork for further research in this exciting direction.

Full text

Received: 30 March 2024
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Revised: 16 September 2024
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Accepted: 27 September 2024
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IET Microwaves, Antennas & Propagation
DOI: 10.1049/mia2.12522
ORIGINAL RESEARCH
Classication with electromagnetic waves
Ergun Simsek
|Harish Reddy Manyam
Department of Computer Science and Electrical
Engineering, University of Maryland Baltimore
County, Baltimore, Maryland, USA
Correspondence
Ergun Simsek.
Email: simsek@umbc.edu
Funding information
UMBC, Grant/Award Number: 7040330
Abstract
The integration of neural networks and machine learning techniques has ushered in a
revolution in various elds, including electromagnetic inversion, geophysical exploration,
and microwave imaging. While these techniques have signicantly improved image
reconstruction and the resolution of complex inverse scattering problems, this paper
explores a different question: Can near‐field electromagnetic waves be harnessed for
object classification? To answer this question, we rst create a dataset based on the
MNIST dataset, where we transform the grayscale pixel values into relative electrical
permittivity values to form scatterers and calculate the electromagnetic waves scattered
from these objects using a 2D electromagnetic nite‐difference frequency‐domain solver.
Then, we train various machine learning models with this dataset to classify the objects.
When we compare the classication accuracy and efciency of these models, we observe
that the neural networks outperform others, achieving a 90% classication accuracy
solely from the data without a need for projecting the input data into a latent space.
The impacts of the training dataset size, the number of antennas, and the location of
antennas on the accuracy and time spent during training are also investigated. These
results demonstrate the potential for classifying objects with near‐eld electromagnetic
waves in a simple setup and lay the groundwork for further research in this exciting
direction.
KEYWORDS
electromagnetic wave scattering, learning (articial intelligence), neural nets
1
|
INTRODUCTION
In the elds of electromagnetic inversion, geophysical explo-
ration, and microwave imaging, the primary objective is to
extract valuable information about the internal structure of
objects or scenes by analysing their interactions with electro-
magnetic waves [1–12]. Traditional methods in these areas
often encounter challenges related to nonlinearity, ill‐
posedness, and high computational costs [1–12]. In recent
years, many novel machine learning‐based approaches have
been proposed to address these issues in applications related to
electromagnetics [13–25], geophysics [14, 26–30], and imaging
[17, 31, 32]. For instance, in ref. [13], a cascade of multilayer
complex‐valued residual convolutional neural network (NN)
modules is used to learn a general model for approximating the
underlying electromagnetic inverse scattering system and then
utilise this general model for solving highly nonlinear inverse
scattering problems accurately. In another study [17], a novel
NN architecture, termed the contrast source network, is
introduced to address the issue of traditional techniques getting
trapped in false local minima when recovering high permittivity
objects. In ref. [23], the authors provide a very broad review of
the recently developed deep learning‐based approaches for
solving electromagnetic inversion problems and recommend a
learning‐assisted objective‐function approach to achieve ac-
curacy with a desired level of condence.
Abbreviations: BIM, Born Iterative Method; CSI, Contrast Source Inversion; DBIM, Distorted Born Iterative Method; GBG, Gaussian Naive Bayes; kNN, k‐nearestneighbour;
MNIST, Modied National Institute of Standards and Technology; NN, neural network; PCA, principal components analysis; RF, random forest; SVM, support vector machine; t‐SNE,
t‐distributed stochastic neighbour embedding; XGB, gradient boosting.
This is an open access article under the terms of the Creative Commons Attribution‐NonCommercial‐NoDerivs License, which permits use and distribution in any medium, provided the
original work is properly cited, the use is non‐commercial and no modications or adaptations are made.
© 2024 The Author(s). IET Microwaves, Antennas & Propagation published by John Wiley & Sons Ltd on behalf of The Institution of Engineering and Technology.
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IET Microw. Antennas Propag. 2024;18:898–910. wileyonlinelibrary.com/journal/mia2

The integration of neural networks and machine learning
techniques has indeed signicantly improved the quality and
speed of image reconstruction, making it possible to tackle
problems that were previously deemed impractical when using
conventional methods. However, the central research question
of this work, which differs from what has previously been
considered, is, Can we achieve the task of classification using
electromagnetic data? So instead of determining, for example,
the electrical permittivity and conductivity distribution over a
certain domain, we are primarily interested in determining the
kinds (classes) of the objects that we have in that domain of
interest.
In the eld of computer vision, researchers— [33] and ref-
erences therein—have developed computer systems that can
automatically recognise and classify handwritten digits in images,
nding applications in postal mail sorting, bank check process-
ing, and form processing. The electromagnetic counterpart,
which involves recognising and classifying objects using elec-
tromagnetic waves, has potential applications in robotics for
enabling robots to perceive their environment and interact with
objects. The use of electromagnetic waves for object recognition
can offer advantages over conventional imaging systems, espe-
cially in scenarios where optical methods (e.g., cameras) are
insufcient. For example, electromagnetic waves can penetrate
certain materials that are opaque to visible light, enabling the
detection of hidden or occluded objects. Furthermore, cameras
rely on lighting conditions and may struggle to detect objects in
low‐visibility environments (such as fog, darkness, or smoke),
whereas electromagnetic waves, particularly in specic frequency
ranges like microwave or millimetre‐wave, can provide more
robust detection capabilities in these challenging environments.
In this work, we aim to determine whether it is possible to
assign labels or categories to objects based on the electro-
magnetic waves scattered from these objects in a simple setup.
We stress the emphasis on a simple setup, as some researchers
have proposed sophisticated approaches to achieve classica-
tion using light in reservoir computing applications. For
instance, in ref. [34], a new method for extreme deep learning
using electromagnetic waves is proposed, utilising specially
designed materials to create a nonlinear interaction between
light waves of different frequencies. This interaction is then
employed to perform complex learning tasks, such as fore-
casting chaotic time series or classifying various types of data.
This describes a signicant development in the eld of wave‐
based computing and has the potential to lead to new types of
optical computers that are much faster and more energy‐
efcient than traditional electronic computers. Nevertheless,
the primary aim of our study is more straightforward: to
classify individual objects based on electromagnetic data
collected by antennas situated in close proximity to the objects
scattering the waves. Successfully demonstrating this concept
might open up the possibility of exploring the practical ap-
plications of electromagnetic wave‐based classication in
various real‐world scenarios, particularly in the domains of
robotics and object recognition. The key potential advantages
of electromagnetic wave‐based object classication over
image‐based recognition can be summarised as follows.
�One of the primary advantages of using electromagnetic
waves, particularly at certain frequencies, is their ability to
penetrate materials that are opaque to visible light. This
means that our approach can detect and classify objects that
are hidden behind obstructions, covered by certain mate-
rials, or located in environments where optical methods fail
(e.g., smoke, fog, or darkness). Conventional image‐based
recognition systems, which rely on visible or near‐visible
light, would be severely limited or ineffective in such
scenarios.
�Image‐based pattern recognition systems rely on visual
features (shape, colour, texture, etc.) to classify objects.
However, they cannot directly discern the material proper-
ties of the objects they are identifying. In contrast, our
method is sensitive to the dielectric properties of objects,
which allows us to distinguish between materials that may
appear visually similar but have different electromagnetic
properties. This could be particularly useful in applications
where material composition is a key factor, such as detecting
hazardous materials, distinguishing between different types
of plastics, or even identifying materials based on their
electromagnetic response.
�Optical systems can be affected by environmental condi-
tions such as lighting, shadows, or reections, which can
introduce noise or distortions in image recognition tasks.
Electromagnetic wave‐based systems, on the other hand, are
less sensitive to such factors. They can operate effectively
across various environments without the need for specic
lighting conditions, making them more robust for real‐world
applications, especially in challenging or uncontrolled
environments.
�Unlike conventional image recognition, which only captures
surface information, electromagnetic wave scattering tech-
niques have the potential for sub‐surface imaging, allowing
for classication of objects that are buried or embedded
within other materials. This could be particularly useful in
non‐destructive testing, medical imaging, or geophysical
exploration, where it is crucial to identify the objects
beneath the surface.
It should also be noted that there are some other recent
studies that have shown the integration of machine learning
and electromagnetic wave analysis for material identication
and classication. For example, Harrison et al., proposed a
novel methodology for material identication using a micro-
wave sensor array [35]. Unlike traditional systems that use a
single resonating sensor, this method employs an array reso-
nating at different frequencies to improve identication accu-
racy. Machine learning algorithms were applied to the collected
data, and the approach was validated on various materials such
as wood, cardboard, and plastics. In another work, Cova-
rrubias‐Martínez et al., introduced a method for classifying
plastic materials using a microwave resonant sensor [36]. They
evaluated several machine learning classiers in material clas-
sication, accounting for uncertainties such as air gaps and
pellet positions. Their approach presents a fast, non‐
destructive method for identifying plastic raw materials with
SIMSEK and MANYAM
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industrial potential. Both in refs. [35, 36], the resonances in the
collected data play a crucial role because the primary intention
is the material identication. In a very recent study, Ting et al.,
proposed a material classication system utilising an embedded
random forest (RF) antenna array, which measures changes in
the received signal strength indicator values [37]. The study
combined a Kalman lter with a support vector machine
(SVM) classier, achieving over 96% accuracy in material
classication within a 2‐m range. Their system, designed for
mobile robotic applications such as warehouse automation,
focuses on real‐time, proximal remote sensing of materials.
Our work might be considered a numerical version of their
experimental study.
The structure of this paper is as follows. First, we provide a
brief overview of electromagnetic inversion and explain its main
difference from electromagnetic classication. Then, we
describe how we create our dataset. Note that the sample codes
to produce the results presented in this work and the dataset can
be found at ref. [38]. This dataset can be used for both electro-
magnetic classication and inversion problems. Third, we
compare the classication accuracy and efciency of several
machine learning models trained to classify 10 labels from the
electromagnetic data recorded by antennas placed around one‐
half of the domain of interest. Subsequently, we investigate
how accuracy and training time change with the training dataset
size, the number of antennas, and the location of antennas.
Following some discussions, we present our conclusions.
2
|
ELECTROMAGNETIC INVERSION
VS. ELECTROMAGNETIC
CLASSIFICATION
Consider a black box, as depicted in Figure 1a, surrounded by
an array of transmitter and receiver antennas. Inside this black
box, assume the presence of a concealed object characterised
by relative electrical permittivity 3.5, as illustrated in Figure 1b.
The surrounding medium is assumed to be air. In the context
of this simplied electromagnetic inversion problem, wherein
all materials involved are treated as lossless and non‐magnetic
dielectrics, the objective is to infer the permittivity distribution
across the domain of interest based on the electromagnetic
data acquired by the receiver antennas. One can solve this
electromagnetic inversion problem numerically and iteratively
[1–11, 23, 39] as follows.
Consider a scenario where there exist MTilluminating
sources for exciting the medium and MRreceivers for collecting
the scattered eld. Consequently, the overall number of ac-
quired data points is denoted as M¼MT�MR. Let the
reconstruction domain Dbe discretised into Nsmall cells, with
constant eld quantities and contrast function within each cell.
The total electric eld at position rwithin the dielectric object,
induced by an exciting source situated at rT, can be expressed
as a sum of the incident and scattered elds. This summation is
governed by the superposition principle and can be repre-
sented as follows:
E r;rT
ð Þ ¼ Einc r;rT
ð Þ þ k2þ∇ ∇ ⋅
� �
ZDGAJ r;r0
ð Þ ⋅χr0
ð ÞE r0;rT
ð Þdr0;r2Dð1Þ
where GAJ r;r0
ð Þ is an auxiliary dyadic Green's function rep-
resenting the magnetic vector potential, the wavenumber is
given by k2¼ω2μ~
eand χðrÞis the contrast, that is,
χðrÞ ¼ ~
eðrÞ−eð Þ=~
e. Equation (1) is called the object equation,
which is a Fredholm integral equation of the second kind for
the unknown eld inside the object. Once the total electric
eld is obtained, then the scattered eld recorded at any of the
receiver antennas, let's say located on path ℓcan be calculated
with the data equation which denes the scattered eld at the
observation point, that is,
FIGURE 1 (a) Domain of interest is surrounded by a group of transmitter and receiver antennas, (b) an object embedded in the domain of interest, and a
typical output of (c) an electromagnetic inversion and (d) electromagnetic classication.
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Esca
mr;rT
ð Þ ¼ jω~
eZDGEJ r;r0
ð Þ ⋅χr0
ð ÞE r0;rT
ð Þdr0;r2ℓð2Þ
where GEJ r;r0
ð Þ is the electric dyadic Green's function at the
observation point rrelated to a unit current source at the
point r0.
The data equation, establishing the connection between the
measured data and the unknown contrast of the material, can
be expressed in a discretised form as follows:
f riR;riT
ð Þ ¼ ω~
eqX
N
k¼1
GEJ riR;r0
k
 �⋅E r0
k;riT
 �χr0
k
 �ΔSð3Þ
where fis a 2M‐dimensional data column vector whose ele-
ments are given measured scattered electric eld data, ΔSis the
surface element, iR¼1;…;MRand iT¼1;…;MTdenote
indices for the receiver and transmitter, respectively. Note that
if this was a three‐dimensional problem, then fwould be a 3M‐
dimensional data and instead of surface element ðΔSÞ, we
would be using volume elements ðΔVÞ. For Mmeasurements
and Ndiscretised cells, Equation (3) can be written compactly
as follows:
f¼Mx;ð4Þ
where xis a N‐dimensional column vector of the contrast
function χ, and Mis a 2M�Nmatrix whose elements are
given using the following equation:
Mik ¼jω~
eqGEJ
mq riR;r0
k
 �⋅E r0
k;riT
 �ΔSð5Þ
where i¼iRþiT−1ð ÞMR, and k¼1;…;N.
Since the total electric eld Ewithin the objects is an un-
known function of the material contrast χ, Equation (4) becomes
a nonlinear equation. Furthermore, the limited amount of
available information renders the problem non‐unique. This
equation can be solved iteratively using either the Contrast
Source Inversion (CSI) method [8, 9, 12], or the Born Iterative
Method (BIM) [2, 7, 39], or the Distorted Born Iterative Method
(DBIM) [10, 11, 39]. The CSI method constructs a sequence of
contrast sources and contrasts iteratively without relying on a
forward solver. While it is a stable method, it requires a large
number of iterations to achieve the desired accuracy. Born
Iterative Method and DBIM are commonly employed iterative
methods for solving nonlinear inverse scattering problems, as
they typically demand fewer iterations. The primary distinction
between BIM and DBIM is that the latter utilises an updated
background Green's function for each iteration, a necessity when
addressing electromagnetic inversion problems involving inho-
mogeneous backgrounds, such as multi‐layered media. Due to
this difference, DBIM is computationally more expensive than
BIM, but it boasts second‐order convergence, whereas BIM only
achieves rst‐order convergence. This computational cost/
convergence order trade‐off can be managed through a two‐step
algorithm, as elucidated in ref. [7].
Over the past two decades, both computational electro-
magnetics and geophysics societies have witnessed a growing
interest in enhancing the efciency of existing methodologies
through the incorporation of machine learning techniques,
with a particular emphasis on the application of deep learning.
This convergence marks a signicant paradigm shift in the
pursuit of optimising electromagnetic and geophysical simu-
lations for diverse applications. One major avenue of explo-
ration involves training neural networks to directly reconstruct
the contrast of scatterers based on the measured scattered
elds [13–16, 28, 40, 41]. This approach capitalises on the
inherent capacity of deep learning models to discern complex
patterns and relationships within datasets. By leveraging these
capabilities, researchers aim to enhance the accuracy and speed
of contrast reconstruction, enabling a more precise represen-
tation of the underlying electromagnetic or geophysical prop-
erties. In parallel, another compelling avenue unfolds where
neural networks are harnessed to learn dynamically throughout
the iterative solution process [17, 18, 20–22, 24, 25, 30, 31].
This innovative approach stands in contrast to traditional
methods by enabling the network to adapt and rene its un-
derstanding of the problem space as the solution evolves.
Through this adaptive learning process, neural networks can
capture intricate features and nuances in the data, thereby
contributing to more robust and efcient solutions.
However, the focus here is not on determining the
permittivity distribution across the domain of interest. Instead,
the objective is to identify the object within the black box,
exemplied in Figure 1d. One possible approach to tackle this
classication task involves training neural networks, with the
input data being the electromagnetic data recorded by the
receiver antennas and the outputs corresponding to the object
types (classes). Given the absence of an extensive dataset
conducive to such a study, the subsequent section outlines our
efforts to generate one from a well‐established dataset, as
detailed below.
3
|
THE DATASET
The Modied National Institute of Standards and Technology
(MNIST) dataset [42] is a collection of handwritten digits and
widely used in the eld of machine learning and computer
vision for training and testing various machine learning algo-
rithms, particularly for tasks like image classication and
character recognition. It consists of 28 �28‐pixel square
grayscale images of handwritten digits, ranging from 0 to 9.
Each image is associated with a corresponding label that
species which digit the handwritten image represents.
In this work, the 60,000 digital images of the MNIST
dataset are used to create a scatterer database as follows. In the
MNIST dataset, the value of each pixel in an image represents
the grayscale intensity of that pixel. The pixel values, du;vfor
u;v¼1;2;…;28, are typically scaled to fall within a range of
0–255, with 0 indicating white (no ink) and 255 indicating black
(maximum ink saturation). Values between 0 and 255 represent
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various shades of grey. These values can be converted into
relative electrical permittivity values ranging from emin
rto emax
r
using the following equation:
erðu;vÞ ¼ emin
rþemax
r−emin
r
 �du;v
255 ð6Þ
where uand vare the row and column numbers. We set
emin
r¼1 and emax
r¼4 for the reasons that are discussed below.
To create the electromagnetic scattering dataset, we utilise a
freely available 2D electromagnetic nite difference frequency
domain simulation tool called Ceviche [43]. The computation
domain, shown in Figure 2a, has dimensions of 2λ�2λand is
uniformly meshed along the xand ydirections, with
Δx¼Δy¼λ=150, where λrepresents the wavelength of the
electromagnetic waves generated by a transmitter antenna with
a length of λ. The thickness of the perfectly matched layers
along all directions is λ=7:5. Initially, the permittivity of each
cell is assumed to be 1.
Since the original les in the MNIST dataset (28 �28
pixels) are too small compared to our computation domain
(300 �300 pixels), we use a 2D cubic interpolation to update
the permittivity of the 140‐pixel by 140‐pixel region at the
centre of the computation domain with the permittivity values
obtained using Equation (6), as illustrated in Figure 2a.
Figure 2b displays the permittivity distribution across the
computation domain for one of the examples studied in this
work. In this setup, we consider two groups of receiver an-
tennas. The rst group comprises Nr=2 receiver antennas
uniformly placed between x¼0:4λand x¼1:57λat y¼1:6λ,
while the second group consists of Nr=2 receiver antennas
uniformly placed between y¼0:4λand y¼1:57λat x¼1:6λ,
where Nris an even integer that represents the total number of
receiver antennas. Note that these antennas are not intended to
physically capture the permittivity values of each pixel but
rather capture the scattered electromagnetic elds resulting
from the permittivity distributions created with Equation (6)
from the pixelated MNIST images. The connection lies in how
the pixel values of the MNIST images affect the permittivity
distribution, which in turn inuences the electromagnetic elds
that the antennas record. Additionally, there are two trans-
mitter antennas: transmitter antenna‐1 is positioned at
x¼0:2λbetween y¼0:5λand y¼1:5λ, while transmitter
antenna‐2 is situated at y¼0:2λbetween x¼0:5λand
x¼1:5λ. Since we treat the problem as a 2D problem, we only
deal with three eld components: the zcomponent of the
electric eld Ez
ð Þ and the xand ycomponents of the magnetic
eld (Hxand Hy). We begin by assuming that transmitter
antenna‐1 is active and proceed to calculate Ez,Hx, and Hyat
Nrreceiver antennas. We then repeat this process, assuming
that only transmitter antenna‐2 is active. The real and imagi-
nary parts of the calculated electric and magnetic elds are
stored in separate columns of the dataset. Consequently, the
input section of the dataset consists of 60,000 rows and 624
columns. These 624 columns represent the maximum number
of receiver antennas, Nmax
r¼52, two transmitter antennas,
three elds, and two components (real and imaginary parts).
The output section of the dataset consists of the labels (digits),
resulting in a 60;000 �1 vector. Note that in the rst part of
the numerical studies, we only 10 receiver antennas. The reason
we record the electric eld intensities at 52 different locations
is that in the second part of the numerical studies, we aim to
FIGURE 2 (a) The computation domain covers a 2λby 2λregion that is uniformly meshed along the xand yaxes at a mesh sampling density of λ=150.
Grey‐shaded areas represent the perfectly matched layers. (b) Permittivity distribution for one of the example geometries studied. The purple regions have a relative
permittivity of 1. The regions with higher relative permittivity values are represented by lighter colours. The locations of transmitter antennas are indicated by yellow
dashed lines, while white circles depict the positions of the 52 receiver antennas.
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determine the affect of antenna locations and inter‐antenna
spacing on the classication accuracy.
For the sake of brevity, we do not provide a gure that
depicts the electric eld intensities jEzjð Þ recorded by the
receiver antennas for each label, but we would like to briey
emphasise that there is no clear pattern recognisable by
humans for identifying the labels from the eld proles. Also,
to investigate the complexity of our data, we project 5000
samples from our dataset to two latent spaces using principal
components analysis (PCA) [44, 45] and t‐distributed sto-
chastic neighbour embedding (t‐SNE) [45, 46]. The visual-
isations are provided in Figure 3. Unlike for the original
MNIST dataset [45], here we do not have a clear interpretation
even after projections.
4
|
MACHINE LEARNING MODELS
We employ various machine‐learning models, namely k‐nearest
neighbour (kNN), RF, Gaussian Naive Bayes (GNB), SVM,
gradient boosting (XGB), and a NN, to assess whether they
exhibit similar levels of learning from the data or not. For the
rst four models (kNN, RF, GNB, and SVM), we utilise scikit‐
learn [47], which is a free software machine learning library for
the Python programming language. For the XGB imple-
mentation, we use another freely available library [48], which is
developed based on XGBoost [49]. Hyperparameter tuning is
done using the Grid Search Cross‐Validation (GridSearchCV)
module [50] that is available in the scikit‐learn [47] library.
For the NN implementations, we employ Keras' [51]
functional application programme interface running on top of
TensorFlow [52]. The model starts with an input layer of Nc
dimensions, where Nc¼12 �Nris the number of columns
of our input data, followed by a dense layer with 500 units,
utilising the HeNormal weight initialisation [53] and
employing the rectied linear unit activation function [54].
Subsequently, another dense layer with 250 units continues
the ow, maintaining the same initialisation and activation
choices. To enhance the model's robustness, a dropout layer
with a dropout rate of 0.2 is introduced to mitigate over-
tting. The architecture then proceeds with a dense layer of
100 units, followed by a smaller layer with 30 units, both
sharing the same initialisation and activation congurations.
To further optimise the network, a batch normalisation layer
is integrated, contributing to the stability and efciency of the
learning process. The nal touch is a dense layer with 10
units and a softmax activation function [55], tailored for a
classication task with 10 output classes. The model's learning
process is guided by the Adam optimiser [56], with a learning
rate set at 0.001. The categorical cross‐entropy loss [57] is
chosen as the optimisation objective, and categorical accuracy
is monitored as a metric to gauge performance. During
training, adaptive strategies are implemented. Specically,
a learning rate reduction is triggered by the Reduc‐
eLROnPlateau callback, which responds to changes in vali-
dation categorical accuracy. Additionally, the EarlyStopping
callback monitors the same metric, terminating training early
if improvements plateau for an extended period. To ensure
the preservation of the best‐performing model, the Mod‐
elCheckpoint callback is employed. It saves the model
whenever a new high in validation categorical accuracy is
achieved, promoting the retention of optimal weights. The
architecture as a whole embodies a holistic approach,
combining architectural choices and training strategies for an
effective and adaptive NN. All the code is executed on
Google Colaboratory using T4 GPU accelerators.
5
|
NUMERICAL RESULTS
In this section, we rst evaluate the accuracy of two machine
learning models and then investigate how different factors,
such as dataset size and the number and location of antennas,
inuence the results.
FIGURE 3 Visualisations of the labels in two latent spaces obtained with (a) principal components analysis (PCA) and (b) t‐SNE.
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5.1
|
Accuracy of different ML methods
For the initial set of calculations, we use 10 receiver antennas
and allocate 50% of the dataset for training and the other 50%
for testing. Table 1presents the time spent during training for
each model, as well as their accuracy, precision, recall, and F1
scores. We observe that SVM, XGB, and NN implementations
achieve higher accuracy (>80%), precision, recall, and F1
scores compared to the kNN, RF, and GNB implementations.
Although the NN's training time is longer than the SVM and
XGB, it delivers the highest classication accuracy (90.17%).
This result is promising but not surprising, given the NN's
ability to identify extremely complex patterns when trained on
sufciently large datasets. It is worth noting that the classi-
cation accuracy obtained with the NN is higher than the pre-
viously reported value [34] of 85.3%.
Figure 4displays the confusion matrix of the NN imple-
mentation, revealing that the most accurately classied label is
1, while eight is the least accurately classied. Notably, 5.7%
and 3.8% of objects labelled as 8 are in fact 3 and 5s.
One of the signicant advantages of working with neural
networks is the ease with which you can quantify and visualise
the learning process's efciency. Figure 5a,b illustrate how
accuracy and loss change with respect to the epoch number for
both training (solid curves) and validation (dashed curves). The
little misalignment of these curves informs us that the number
of neurons in the NN architecture is slightly higher than the
optimal but the overtting is not serious. The convergent
behaviour observed in both gures indicates that the number
of epochs used during the training is sufcient. In the same
gure, we also observe that the training is ended at the 68th
TABLE 1The time spent during training, accuracy, precision, recall,
and F1‐score of the k‐nearest neighbour (kNN), random forest (RF),
Gaussian Naive Bayes (GNB), support vector machine (SVM), gradient
boosting (XGB), and neural network (NN) implementations using the 50%
of the dataset for training and the remaining 50% for testing.
Method Time (s) Accuracy Precision Recall F1 score
kNN 0.1 0.66 0.67 0.66 0.65
RF 495 0.76 0.75 0.75 0.75
GNB 0.52 0.61 0.61 0.60 0.60
SVM 296 0.85 0.85 0.85 0.85
XGB 183.7 0.84 0.84 0.84 0.84
NN 434 0.90 0.90 0.90 0.90
FIGURE 4 Confusion matrix of the neural network (NN) implementation. Since none of the 7s is predicted as a 6, the corresponding cell is blank.
904
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SIMSEK and MANYAM

epoch even the number of epochs is set to 100 thanks to the
EarlyStopping callback monitor. Also, the learning rate is
dropped from 10−3to 4:398 �10−5in 14 steps triggered by
the ReduceLROnPlateau callback.
Machine learning‐based computer vision algorithms can
achieve a classication accuracy of over 97% for handwritten
digits [33]. However, these studies typically use all pixels to
achieve such high accuracy, while we use only electromagnetic
data recorded by antennas placed on two one‐dimensional lines
near the objects. Therefore, we consider a 90% classication
accuracy using electromagnetic waves to be a successful
approach.
5.2
|
Inuence of dataset size and number
and location of antennas on the accuracy
For the results presented in Table 1and Figures 4and 5, we use
50% of the data for training, with the remaining 50% used for
testing. In other words, we use 30,000 samples for training and
other 30,000 samples that have not been seen by the NN
before for testing. To examine the impact of the training
dataset size Ntrain
ð Þ on accuracy and training time, we conduct
an additional two sets of calculations. For the rst set, we use
10% of the data for training Ntrain ¼6000ð Þ and the remaining
90% for testing. For the second set, we use 1% of the data for
training Ntrain ¼600ð Þ and the remaining 99% for testing. The
accuracy of each method is listed in Table 2. As expected, the
accuracies drop for all methods. However, we would like to
emphasise one important detail: NN is the most accurate when
the dataset is large enough (Ntrain is 6000 or higher in this case),
however, their accuracy drops signicantly for small datasets
and other methods–such as XGB in this case–can perform
better. We might conclude that if we are going to implement a
NN for object classication, then we should have a large
enough dataset to achieve high accuracy.
Next, we investigate the inuence of the number of antennas
over the accuracy as follows. For the three cases above, where the
training dataset size is changed from 50% to 10% rst and then
to 1%, we decrease the number of receiver antennas from 10 to 8,
4, and 2, and monitor the accuracy and training times. The results
are plotted in Figure 6. Note that the number of transmitter
antennas is still 2, which means that the number of data points is
2�Nr. As we examine Figure 6a–c, we rst observe that both
the accuracy and training times decrease with decreasing dataset
size but the accuracy remains almost constant when the receiver
antenna number is reduced from 10 to 4. Hence, we might claim
that having an inter‐antenna spacing of λ=4 is adequate for ac-
curate classication as long as we have a large training dataset. In
terms of training time, we observe a slight decrease in training
times with a decreasing number of antennas, but this decrease is
not linear and the main factor that determines the training time is
the dataset size.
Next, we investigate the inuence of antenna locations
over the accuracy as follows. Since the accuracy signicantly
drops when we have two receiver antennas only, we rst start
FIGURE 5 (a) Accuracy and (b) loss versus epoch number of the neural network (NN) implementation, which uses 50% of the dataset for training and the
remaining 50% for testing.
TABLE 2Accuracy (in percentile) of the k‐nearest neighbour (kNN),
random forest (RF), Gaussian Naive Bayes (GNB), support vector machine
(SVM), XGB, and neural network (NN) implementations using 50%, 10%,
and 1% of the dataset for training and the remaining data for testing.
Training/Testing ratio kNN RF GNB SVM XGB NN
50%/50% 66 76 61 85 84 90
10%/90% 56 67 55.5 76 79 81
1%/99% 29 48 37 49 57 54
SIMSEK and MANYAM
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investigating this scenario by creating pairs of antennas by
selecting one antenna from the top antenna group and one
antenna from the side antenna group at a time. As mentioned
before, our dataset includes eld intensities recorded at 52
different locations. Here, for the pair‐i, we select antennas Ri
and Riþ26 for i¼1;2;…;13 as shown in Figure 7a for the rst
two pairs, and we monitor the accuracy. The blue curve in
Figure 7c shows how the accuracy changes with the pair
number. Even though the results change slightly (�0:6%), we
can understand the trend (peaking near the middle), by
considering the following two facts: (i) the scatterers are placed
parallel to the x‐axis, so the antennas from the top group are
likely to carry more information about the scatterer than the
side antennas, and (ii) when we increase i, we get closer to
the scatterer centre but at the same time, the distance between
the left transmitter antenna and ith receiver antenna increases
while the distance between the bottom transmitter antenna and
iþ26th receiver antenna decreases.
Then we repeat the same procedure for groups of 4 an-
tennas at a time. In this case, the group‐iis formed by select
antennas Riand Riþ13 from the top group and antennas Riþ26
and Riþ39 from the side group as shown in Figure 7b for the
rst two groups. How accuracy changes with the group
number is depicted with the red curve in Figure 7c. In this
case, the accuracy decreases almost steadily. Again, we believe
that the increasing distance from the left transmitter antenna
with increasing iand hence the weakening scattering data is the
main cause of this decaying accuracy.
6
|
DISCUSSIONS
In this work, the main aim was to achieve high classication
accuracy without projecting the input data into a latent space.
If such projections, for example, PCA, are used, both neural
networks and gradient‐boosted decision trees achieve the same
accuracy. However, it should be noted that unlike the original
MNIST dataset, here we have to utilise more than 30 principal
components to achieve a 90% accuracy due to the complex
nature of electromagnetic scattering data. If 20 principal
components or fewer are used, the accuracy drops signicantly.
Figure 8shows the explained variance ratio of the rst 40
principal components on a logarithmic scale.
The accuracy of the classication depends on the permit-
tivity range of the scatterers. In this work, we choose the
maximum allowed relative permittivity to be 4 for two reasons.
First, such narrow permittivity ranges, where emax
r=emin
r<10
are already being reported, for example, in [58]. Second, larger
permittivity values would impede the propagation of electro-
magnetic waves through the objects. For instance, if the
maximum allowed electrical permittivity is set to 12, the ac-
curacy of the NN implementation drops to 79%, primarily due
FIGURE 6 (left) Accuracy and (right) training time as a function of the number of receiver antennas when (a) N
training ¼15000, (b) Ntraining ¼6000,
and (c) Ntraining ¼600.
906
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SIMSEK and MANYAM

to the strong reectance from the objects back to the trans-
mitter antennas.
Another important factor is the orientation of the scat-
terers. In this study, all the scatterers were parallel to the x‐axis.
When we rotate the scatterers, we observe that the accuracy of
classication decreases to 58%. To achieve higher accuracy for
objects with arbitrary alignments, it is necessary to place
receiver antennas all around the domain of interest.
FIGURE 7 (a) Pairing two antennas by selecting only one antenna from the top antenna group and one antenna from the side antenna group, (b) grouping
4 antennas by selecting two antennas from the top and side antenna groups while keeping the inter‐antenna distance xed, (c) accuracy versus pair or group
number.
SIMSEK and MANYAM
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907

7
|
CONCLUSION
In this paper, we have explored the application of machine
learning and NN techniques in the context of electromagnetic
wave‐based object classication. The objective of our work
was to determine whether it is feasible to classify objects based
on the electromagnetic waves scattered from them in a simple
experimental setup. We began by creating a dataset using the
MNIST data, where we transformed grayscale pixel values into
relative electrical permittivity values. A 2D electromagnetic
nite difference frequency domain simulation tool was
employed to calculate the electric and magnetic eld data
recorded by receiver antennas placed around the objects
partially. We evaluated the classication performance of
various machine learning models, including kNN, RF, GNB,
SVM, gradient boosting, and a NN. The NN architecture
demonstrated the highest accuracy, achieving an 90% classi-
cation accuracy. We also investigated the impact of the training
dataset size, number of antennas, and location of antennas on
accuracy and training time, highlighting the advantages of using
a NN, especially as the dataset size is increased. However, we
also observe that the number of samples of the dataset is more
important than the number of receiver antennas to achieve a
high accuracy to classify objects whose dimensions are close to
the wavelength of excitation and we use four or more receiver
antennas placed uniformly over one wavelength long region.
While computer vision algorithms can achieve higher accuracy
for handwritten digit recognition, our approach demonstrates
that classifying objects using electromagnetic waves is a
promising avenue. This research opens the door to exploring
the potential of electromagnetic wave‐based classication for
various applications, including robotics and object recognition.
AUTHOR CONTRIBUTIONS
Ergun Simsek: Conceptualisation; Data curation; Formal
analysis; Investigation; Methodology; Project administration;
Supervision; Validation; Visualisation; Writing ‐original draft;
Writing ‐review & editing. Harish Reddy Manyam: Inves-
tigation; Validation.
CONFLICT OF INTEREST STATEMENT
The authors declare no conicts of interest.
DATA AVAILABILITY STATEMENT
Sample codes to produce the results presented in this work and
the dataset can be found at https://github.com/simsekergun/
CwEMW. This dataset can be used for both electromagnetic
classication and inversion problems.
ORCID
Ergun Simsek
https://orcid.org/0000-0001-9075-7071
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How to cite this article: Simsek, E., Manyam, H.R.:
Classication with electromagnetic waves. IET Microw.
Antennas Propag. 18(12), 898–910 (2024). https://doi.
org/10.1049/mia2.12522
910
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