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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Analysis of Different Loss Function for Designing Custom CNN for Traffic Sign Recognition</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Virendra Patel</string-name>
          <email>virendra23aitr@gmail.com</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Sanyam Shukla</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Manasi Gyanchandani</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Loss function</institution>
          ,
          <addr-line>Image recognition, GTSRB, TSR, Regularized CNN</addr-line>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Maulana Azad National Institute of Technology</institution>
          ,
          <addr-line>Bhopal</addr-line>
          ,
          <country country="IN">India</country>
        </aff>
      </contrib-group>
      <fpage>31</fpage>
      <lpage>38</lpage>
      <abstract>
        <p>Traffic sign recognition has got important due to emerging AI based vehicles, one of the tasks required by these vehicles is automatic traffic sign recognition. CNN is a popular at tool which is deployed for image classification tasks. Several CNN based solutions have been proposed for traffic sign recognition, this work also develop a custom CNN for traffic sign recognition. The choice of loss function is a part of designing custom neural network. This work analyses different loss function for traffic sign recognition. The GTSRB dataset (German Traffic Sign Recognition Benchmark) is used in this study to conduct the trials. The outcomes of our experiments suggest that our prediction is right. For TSR, the suggested classifier beats previous techniques. This study attempts to address such an element by training the network to react in linewith a rich database consisting 39,209 color photographs spanning 43 distinct kinds of signalized intersections, as well as system testing with 12,630 samples and reaching 99.81% accuracy.</p>
      </abstract>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Traffic sign recognition is an area of interest for researches due to emerging advanced small
vehicles. These vehicles have feature like voice command, Driver assistance system, Autopilot, fuel
measurement and alert. The automatic feature like autopilot, driver assistance requires the vehicle to
identify the traffic sign [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Traffic sign recognition has following based steps:
1. Traffic sign detection
2. Traffic sign recognition
Several approaches have been proving for traffic sign recognition problems.
      </p>
      <p>Shallow neural networks for traffic sign recognition:</p>
      <p>
        Color is an important part of the data supplied to a user in needed to guarantee that the goals of the
speed limit signs are realized. As a consequence, in important to stand out, road signs and its color are
selected to clash with the natural setting or surroundings. The recognition of these indicators in
exterior images taken from a passing car will aid the operator in deciding the best feasible in the
shortest amount of time, leading to fewer fatalities, lower emissions, and improved security [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
      </p>
      <p>Deep neural networks for traffic sign recognition:</p>
      <p>2022 Copyright for this paper by its authors.</p>
      <p>
        The 'deep' in a 'Deep CNN' refers to the network's layers. In a standard CNN, 5–10 or even more
feature learning layers are usual. Networks of more than 50–100 layers are common in modern
topologies utilized in cutting-edge applications [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ].
      </p>
      <p>1. Classification of traffic sign recognition using feature extraction method:
•
•
•
•
•</p>
      <p>
        Wavelet transform: A wave sequence is a set of basic functions created by a wavefront
that represents the value of a rectangular shape. A ripple is a pulse fluctuation that pulsates
from zero-to-zero current and from zero to low resistance at a frequency that pulsates from
zero to low resistance [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ].
      </p>
      <p>
        Fast Fourier Transform (FFT): A signal is then converted from the duration region to
the spectral domain and return using the Fourier Transform. It converts
capacitydependent units into values that are based on geographic frequency. If the organised pairs
defining the input data value are scattered evenly in their response variable, Fast Fourier
Transform is considered Discrete Fourier Change [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ].
      </p>
      <p>
        Curvelet transform: Wavelet coefficients generalise the Transformation function by
employing a foundation that incorporates both location and geometric characteristics. The
use of kernels that are also localised in position when directing harmonic transformations
for three-dimensional inputs goes even further [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ].
      </p>
      <p>
        Gabor filter: The Gabor filter is a texture analysis linear filter that searches an image for
certain frequency components in specific directions within a constrained region around
the research point or region [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ].
      </p>
      <p>
        CNN as a feature extraction: CNN is a multilayer perceptron that collects input feature
representations and classifies them to use another neural net. The extracting features
network uses the input image. The neural network uses the feature extraction signals to
classify the data [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>
        This work develops a custom CNN based solution for traffic sign recognition, one of the important
factors for designing custom CNN is choice of loss function. This work studies following loss function
for the design of custom CNN:
1. KL-Divergence loss function
2. Poisson loss function
3. Categorical cross entropy loss function
4. Categorical hinge loss function
5. Binary cross entropy loss function
2. Related Work
1. TsingNet CNN Model: The TsingNet Convolution Layer can be used to train magnitude and
situational features in order to recognize and categories undersized and limited highway
signage in real time. TSingNet creates a worldwide active learning interest bidirectional
multi-layer perception neural structure that combines underneath and leading network nodesto
flow low-, mid-, and higher ambient interpretations [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ].
      </p>
      <p>
        DeepThin CNN Model: Because each convolution operation in this technique involves
around 43 variables, we may create our CNN architecture without requiring a GPU.Using the
massive GTSRB sample, we begin assessing the suggested architect's productivity. The
suggested architecture outperformed current traffic sign approaches, which had at least 5
times less characteristics in each end-to-end learning link [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ].
      </p>
      <p>
        ResNet50: In a ResNet variation, ResNet50 has 48 Convolution operations, 1 MaxPool layer,
and 1 Average Pooling layer. There are 3.8 x 109 bobbing processes in it. We spent a lot of
time looking at the ResNet50 architecture because it's a prevalent ResNet architecture.
ResNet-50 is, in fact, a 50-layer neural network. We can import a from Imagenet, which has
been learned from over a thousand photos and was before iteration of the structure. The
algorithm, which previously recognised 1000 different item kinds in pictures, has been
improved [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
4. VGG-16: The number 16 in the VGG-16 designation refers to the assumption that there are a
total of 16 layers, each with a different weight. With almost 138 million parameters, this is a
massive network. The major issue was that it was a rather large network in terms of the
number of variables to be learned [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ].
      </p>
    </sec>
    <sec id="sec-2">
      <title>3. Proposed Work</title>
      <p>The GTSRB dataset is a freely available sample that is being utilised in a research investigation.
The dataset is pre-processed before being split into training and testing sets in this study. Batch
Normalization and Dropout regularised techniques, as well as the Adam optimizer, were used. To
analyse the progress of the training and validation sessions, a graph for accuracy and loss function is
generated. The GTSRB training set consists of 39,209 image characteristics separated into 43 classes,
whereas the testing set consists of 12,630 samples.</p>
      <p>Five different loss functions KL-Divergence loss function, Poisson loss function, Categorical cross
entropy loss function, Categorical hinge loss function and Binary cross entropy loss function uses for
analysis of custom CNN model.</p>
      <p>We employed four convolution layers, two MaxPooling layers, one Flatten layer, one Dense layer,
twoDropout layers, and three Batch Normalization Regularization techniques in our customised CNN
model. Convolutional layers are used to add filters to the original image or even a different set of inputs
within a deep network. The majority of subscriber variables are stored within the system.</p>
      <p>The most important qualities are the frequency and size of kernels. MaxPooling is a method of
filteringthat selects the largest component from the feature space covered by the filtering. Like a result,
the max-pooling layer's output is an excellent approach to identify the dataset's more notable traits.</p>
      <p>The technique of consolidating data in one place collection for it at a high level is known as
flattening. We compress the convolution theory's output to generate a unique long influence the
structure. It's also linked to the final categorization approach, also known as the completely layering
framework. In a CNNdesign, a dense layer is one that is tightly related to the one before it, meaning
that the layer's cells are linked to every cell in the layer before it. This is by far the most commonly
used layer in convolutionalneural network systems.</p>
      <p>The relu and softmax activation functions were used in our customised CNN model. The activation
function of a deep neural network can be defined and added to aid in the acquisition of complex data
patterns. The activation function, in contrast to the nerve cell image we see in our heads, is in a better
position to decide what should be given to another brain at the end of the process. The usage of ReLU
prevents the amount of computing power required to run the neural network from rising exponentially.</p>
      <p>As the size of the CNN grows, the computational complexity of integrating more ReLU velocity
grows. The ReLU has been the most extensively used bias vector in the planet right now. It has been
used in practically all deeper neural network models analytical approaches ever since. To determine a
regression analysis conditional probability, the softmax function is employed as the perceptron in the
hidden layers of normal neural analysis. Softmax is used as the activation function for interclassification
challenges needing classifiers on more than two words. To avoid overfitting our CNN model, we used
Adam optimizer.</p>
      <p>Adam is a deep learning training method that uses a different algorithm than gradient descent to
create deep learning models. By integrating the best aspects of the AdaGrad and RMSProp approaches,
Adam develops an optimization strategy for noisy situations with dense gradients.
3.1.</p>
    </sec>
    <sec id="sec-3">
      <title>Architecture of Proposed CNN Model</title>
    </sec>
    <sec id="sec-4">
      <title>3.1.1. Choice of loss function for above CNN model</title>
      <p>This work determines the optional choice of loss function for the above CNN by experimentation
the loss function consider for the design of custom CNN’s are:
1.</p>
      <p>
        KL-Divergence loss function: Kullback-Leibler divergence is a score that determines how far
one probability distribution differs from another. Jensen-Shannon divergence is an extension
of KL divergence that determines a symmetric scoring and proximity measurement between
two probabilistic. The KL divergence is the minus summation of every show's probability in P
multiplied by the log of the show's probability in Q over the probability of the event in P [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ].
2. Poisson loss function: When modelling count data, the poisson loss function is utilised for
regression. The poisson distribution is used for data. For example, next week's consumer churn.
      </p>
      <p>
        The loss manifests itself as:
4. Categorical hinge loss function: The hinges loss is an error term used it to training
classifications in computer vision. For "maximum-margin" classification, the hinge loss is
utilised, most notably for support vector machines (SVMs). The hinge loss of the prediction y
is defined as for an expected output t = ±1 and a classifier score y [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ].
5. Binary cross entropy loss function: The current class result, which might be either 0 or 1, is
checked to every one of the predicted chances. The rating would then be computed, with
chances being penalised based on how far they deviate from of the projected value. This
indicates whether near however far a number is to the true value [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ].
 ( ) =
      </p>
      <p>( ,  −  .  )
Where ŷ is the predicted expected value.</p>
      <p>
        Minimizing the Poisson loss is the same as maximising the data's likelihood under the assumption that
the target is drawn from a Poisson distribution that is conditioned on the input [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ].
3. Categorical cross entropy loss function: Categorical cross entropy is a loss function in
multiclass text categorization. All of those are issues where an instance can only fit into one of
several classes, and the system have to choose one. Its basic goal is to compare two probability
distribution function and identify the difference [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ].
      </p>
    </sec>
    <sec id="sec-5">
      <title>4. Dataset</title>
      <p>This dataset was obtained from Kaggle Library by GTSRB (German Traffic Sign Recognition
Benchmark), and it is freely available. A total of 51839 images are used, with 39209 and 12630 images
accounting for around 70% and 30% of the training and testing sets, respectively. The photos are
512*512 pixels in size and 32*32 pixels in size, respectively.</p>
      <p />
      <p>(1)
(2)
(3)
(4)
(5)</p>
      <sec id="sec-5-1">
        <title>Loss function</title>
      </sec>
      <sec id="sec-5-2">
        <title>KL-Divergence</title>
      </sec>
      <sec id="sec-5-3">
        <title>Poisson</title>
      </sec>
      <sec id="sec-5-4">
        <title>Categorical Cross entropy</title>
      </sec>
      <sec id="sec-5-5">
        <title>Categorical hinge</title>
      </sec>
      <sec id="sec-5-6">
        <title>Binary Cross entropy</title>
      </sec>
      <sec id="sec-5-7">
        <title>CNN Model</title>
      </sec>
      <sec id="sec-5-8">
        <title>SCN model [1]</title>
      </sec>
      <sec id="sec-5-9">
        <title>MLADA Model [5]</title>
      </sec>
      <sec id="sec-5-10">
        <title>BBAS model [3]</title>
      </sec>
      <sec id="sec-5-11">
        <title>CoDefend model [4]</title>
        <p>Proposed CNN model</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>5. Experimental Result and Analysis</title>
    </sec>
    <sec id="sec-7">
      <title>6. Conclusion</title>
      <p>This paper introduces a new traffic sign identification system based on a customized neural network.
This paper investigates the use of different loss functions such as KL-Divergence loss function, Poisson
loss function, Categorical cross entropy loss function, Categorical hinge loss function and Binary cross
entropy loss function to improve TSR performance. In noisy photos and when the weather is not clear,
our proposed CNN model outperforms the existing approach. Future study will include a thorough
examination of CNN design and learning algorithms in order to improve performance even more. Future
study will also include the development of image annotation techniques to improve the amount of
framing data available, resulting in a higher TSR.</p>
    </sec>
    <sec id="sec-8">
      <title>7. References</title>
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