\mu(A_{1})+\mu(A_{2})+\mu(A_{3})=0$.

######  Example 14.2.

Another solid-set function (hence, a topological measure) is obtained if in
the Example 14.1 we take $B$ to be any set of points of $X$, and $p\in
X\setminus B$.

######  Example 14.3.

Let $X$ be a sphere (or a square.) Fix points $p_{1},p_{2},p_{3}$ in $X$.
Define $\mu$ on solid sets as follows: $\mu(A)=1$ if $A$ contains the majority
of the three points, otherwise, $\mu(A)=0$. The resulting topological measure
is non-subadditive, since $\mu(X)=1$, and it is easy to represent $X$ as a
union of three overlapping solid sets each of which contains exactly one of
the points $x,y,z$ and, hence, has measure 0. Notice also that $\mu(A)=1$ for
any connected set $A$ that contains at least 2 points, since any component of
$X\setminus A$ (a solid set by Lemma 3.4) contains at most 1 point.

######  Example 14.4.

Let $X$ be a sphere and let $P=\\{p_{1},\ldots,p_{n}\\}$ be a set of $n$
distinct points in $X$, with $n$ an odd number. We define a solid-set function
$\mu$ on $X$ by letting $\mu(A)=1$ if $A\cap P$ contains a majority of points
of $P$; otherwise let $\mu(A)=0.$

######  Example 14.5.

Let $X$ be the unit sphere and $P=\\{p_{1},\ldots,p_{2n+1}\\}$ an odd-numbered
subset of $X$. If $A\in\mathscr{A}_{s}(X)$ let $\sharp A=$ the number of
points in $A\cap P.$ For $k=0,\ldots,n$ let $\mu(A)=k/n$ if $\sharp
A\in\\{2k,2k+1\\}.$ Thus defined, $\mu$ is a solid-set function in $X.$

######  Remark 14.6.

Example 14.1, Example 14.3, Example 14.5 were the first examples of
topological measures that are not (restrictions to
$\mathscr{O}(X)\cup\mathscr{C}(X)$ of) regular Borel measures. They were
presented by J. Aarnes in [3], [5] and [4]. For more examples of topological
measures on compact spaces see, for instance, [7] and [10].

##  15 Examples for a locally compact space

When $X$ is locally compact, the hardest condition in Definition 6.1 to verify
is the condition (s4) that deals with solid partitions. But, as we shall see
in this section, it turns out that this condition holds trivially for spaces
whose one-point compactification has genus $0$. We denote by $\hat{X}$ the
one-point compactification of $X$.

######  Lemma 15.1.

Let $X$ be locally compact noncompact and $\hat{X}$ be its one-point
compactification. If $A\in\mathscr{A}_{s}^{*}(X)$ then $A$ is solid in
$\hat{X}$.

###### Proof.

Since $A$ is connected in $X$, it is also is connected in $\hat{X}$. Let
$X\setminus A=\bigsqcup_{i=1}^{n}B_{i}$ be the decomposition into connected
components. Each $B_{i}$ is an unbounded subset of $X$. We can write
$\hat{X}\setminus A=\bigcup_{i=1}^{n}E_{i}$ where each
$E_{i}=B_{i}\cup\\{\infty\\}$. It is easy to see that each $E_{i}$ is
connected in $\hat{X}$. Thus, $\hat{X}\setminus A$ is connected, and so $A$ is
solid in $\hat{X}$. ∎

######  Lemma 15.2.

Let $X$ be a locally compact noncompact space whose one-point compactification
$\hat{X}$ has genus 0. If $A\in\mathscr{A}_{s}^{*}(X)$ then any solid
partition of $A$ is the set $A$ itself.

###### Proof.

Suppose first that $V\in\mathscr{O}_{s}^{*}(X)$ and its solid partition is
given by $V=\bigsqcup_{i=1}^{n}C_{i}\sqcup\bigsqcup_{j=1}^{m}U_{j}$, where
each $C_{i}\in\mathscr{K}_{s}(X)$ and each $U_{j}\in\mathscr{O}_{s}^{*}(X)$.
From Lemma 15.1 it follows that $\hat{X}\setminus V$ and each $C_{i}$ are
closed solid sets in $\hat{X}$. Since $\hat{X}$ has genus $0$, by Remark
11.11, $\hat{X}\setminus((\hat{X}\setminus
V)\sqcup\bigsqcup_{i=1}^{n}C_{i})=\bigsqcup_{j=1}^{m}U_{j}$ must be connected
in $\hat{X}$. It follows that $m=1$ and we may write
$V=\bigsqcup_{i=1}^{n}C_{i}\sqcup U_{1}.$ Then $\\{U_{1},\hat{X}\setminus
V,C_{1},\ldots,C_{n}\\}$ is a solid partition of $\hat{X}$, and it has only
one open set. By Remark 11.6 this solid partition also has only one closed set
in it, and it must be $\hat{X}\setminus V$. So each $C_{i}=\emptyset$, and the
solid partition of $V$ is $V=U_{1}$, i.e. the set itself.

Now suppose that $C\in\mathscr{K}_{s}(X)$ and its solid partition is given by
$C=\bigsqcup_{i=1}^{n}C_{i}\sqcup\bigsqcup_{j=1}^{m}U_{j}$, where each
$C_{i}\in\mathscr{K}_{s}(X)$ and each $U_{j}\in\mathscr{O}_{s}^{*}(X)$. Then
$\\{\hat{X}\setminus C,U_{1},\ldots,U_{m},C_{1},\ldots,C_{n}\\}$ is a solid
partition of $\hat{X}$. Again by Remark 11.11,
$\hat{X}\setminus\bigsqcup_{i=1}^{n}C_{i}=(\hat{X}\setminus C)\sqcup
U_{1}\ldots\sqcup U_{m}$ must be connected in $\hat{X}$. It follows that
$U_{j}=\emptyset$ for $j=1,\ldots,m$. Then by connectedness of $C$ we see that
the solid partition of $C$ must be the set itself. ∎

######  Remark 15.3.

From Lemma 15.2 it follows that for any locally compact noncompact space whose
one-point compactification has genus 0 the last condition of Definition 6.1
holds trivially. This is true, for example, for $X=\mathbb{R}^{n}$, half-plane
in $\mathbb{R}^{n}$ with $n\geq 2$, or for a punctured ball in
$\mathbb{R}^{n}$ with the relative topology.

######  Example 15.4.

Lemma 15.2 may not be true for spaces whose one-point compactification has
genus greater than $0$. For example, let $X$ be an infinite strip
$\mathbb{R}\times[0,1]$ without the ball of radius $1/4$ centered at
$(-1/2,1/2)$, so $\hat{X}$ has genus greater than $0$. It is easy to give an
example of a solid partition of a bounded solid set (say, rectangle
$[0,n]\times[0,1]$ or $(0,n)\times[0,1]$) which consists of $n$ solid sets
(rectangles of the type $(i,i+1)\times[0,1]$ or $[i,i+1]\times[0,1]$) for any
given odd $n\in\mathbb{N},\,n>1$.

We are ready to give examples of topological measures on locally compact
spaces.

######  Example 15.5.

Let $X$ be a locally compact space whose one-point compactification has genus
0. Let $\lambda$ be a real-valued topological measure on $X$ (or, more
generally, a real-valued deficient topological measure on $X$; for definition
and properties of deficient topological measures on locally compact spaces see
[11]). Let $P$ be a set of two distinct points. For each
$A\in\mathscr{A}_{s}^{*}(X)$ let $\nu(A)=0$ if $\sharp A=0$,
$\nu(A)=\lambda(A)$ if $\sharp A=1$, and $\nu(A)=2\lambda(X)$ if $\sharp A=2$,
where $\sharp A$ is the number of points in $A\cap P$. We claim that $\nu$ is
a solid-set function. By Remark 15.3 we only need to check the first three
conditions of Definition 6.1. The first one is easy to see. Using Lemma 3.10
it is easy to verify conditions (s2) and (s3) of Definition 6.1. The solid-set
function $\nu$ extends to a unique compact-finite topological measure on $X$.
Suppose, for example, that $\lambda$ is the Lebesgue measure on
$X=\mathbb{R}^{2}$, the set $P$ consists of two points $p_{1}=(0,0)$ and
$p_{2}=(2,0)$. Let $K_{i}$ be the closed ball of radius $1$ centered at
$p_{i}$ for $i=1,2$. Then $K_{1},K_{2}$ and $C=K_{1}\cup K_{2}$ are compact
solid sets, $\nu(K_{1})=\nu(K_{2})=\pi,\,\nu(C)=4\pi$. Since $\nu$ is not
subadditive, $\nu$ is a topological measure that is not a measure. Note that
$\nu(X)=\infty$.

The next two examples are adapted from [6, Example 2.2] and are related to
Example 14.1.

######  Example 15.6.

Let $X$ be the unit disk on the plane with removed origin. $X$ is a locally
compact Hausdorff space with respect to the relative topology. Any subset of
$X$ whose closure in $\mathbb{R}^{2}$ contains the origin is unbounded in $X$.
For $A\in\mathscr{A}_{s}^{*}(X)$ (since $A$ is also a solid subset of the unit
disk by Lemma 15.1) we define $\mu^{\prime}(A)=\mu(A)$ where $\mu$ is the
solid-set function on the unit disk from Example 14.1. From Remark 15.3, Lemma
3.10, and the fact that $\mu$ is a solid-set function on $\hat{X}$ we see that
$\mu^{\prime}$ is a solid-set function on $X$. By Theorem 10.7 $\mu^{\prime}$
extends uniquely to a topological measure on $X$, which we also call
$\mu^{\prime}$. Note that $\mu^{\prime}$ is simple. We claim that
$\mu^{\prime}$ is not a measure. Let $U_{1}=\\{z\in X:\ Im\ z>0\\},\
U_{2}=\\{z\in X:\ Im\ z<0\\}$ and $F=\\{z\in X:\ Im\ z=0\\}$. Then
$U_{1},U_{2}$ are open (unbounded) in $X$ and $F$ is a closed (unbounded) set
in $X$ consisting of two disjoint segments. Note that $X=F\cup U_{1}\cup
U_{2}$. Using Remark 10.8 we calculate
$\mu^{\prime}(F)=\mu^{\prime}(U_{1})=\mu^{\prime}(U_{2})=0$. The boundary of
the disk, $C$, is a compact connected set, $X\setminus C$ is unbounded in $X$,
so $C\in\mathscr{K}_{s}(X)$. Since $\mu^{\prime}(C)=1$, we have
$\mu^{\prime}(X)=1$. Thus, $\mu^{\prime}$ is not subadditive, so it is not a
measure.

This example also shows that on the unit disk without the origin (a locally
compact space) finite additivity of topological measures holds on
$\mathscr{K}(X)\cup\mathscr{O}(X)$ by Definition 5.1, but fails on
$\mathscr{C}(X)\cup\mathscr{O}(X)$. This is in contrast to topological
measures on the unit disk (and on all compact spaces), where finite additivity
holds on $\mathscr{C}(X)\cup\mathscr{O}(X)$.

######  Example 15.7.

Let $X=\mathbb{R}^{2},\ l$ be a straight line and $p$ a point of $X$ not on
the line $l$. For $A\in\mathscr{A}_{s}^{*}(X)$ define $\mu(A)=1$ if $A\cap
l\neq\emptyset$ and $p\in A$; otherwise, let $\mu(A)=0$. Using Lemma 3.10 it
is easy to verify the first three conditions of Definition 6.1. From Remark
15.3 it follows that $\mu$ is a solid-set function on $X$. By Theorem 10.7
$\mu$ extends uniquely to a topological measure on $X$, which we also call
$\mu$. Note that $\mu$ is simple. We claim that $\mu$ is not a measure. Let
$F$ be the closed half-plane determined by $l$ which does not contain $p$.
Then using Remark 10.8 we calculate $\mu(F)=\mu(X\setminus F)=0$, and
$\mu(X)=1$. Failure of subadditivity shows that $\mu$ is not a measure.

The sets $F$ and $X\setminus F$ are both unbounded. Now take a bounded open
disk $V$ around $p$ that does not intersect $l$. Then $X=V\sqcup(X\setminus
V),$ where $V\in\mathscr{O}^{*}(X),\ \mu(V)=\mu(X\setminus V)=0$, while
$\mu(X)=1$.

This example also shows that on a locally compact space finite additivity of
topological measures holds on $\mathscr{K}(X)\cup\mathscr{O}(X)$ by Definition
5.1, but fails on $\mathscr{C}(X)\cup\mathscr{O}(X)$. It fails even in the
situation $X=V\sqcup F$, where $V$ is a bounded open set, and $F$ is a closed
set.

The last two examples suggest the following result.

######  Theorem 15.8.

Let $X$ be a noncompact locally compact, connected, locally connected space
whose one-point compactification $\hat{X}$ has genus 0. Suppose $\nu$ is a
solid-set function on $\hat{X}$. For $A\in\mathscr{A}_{s}^{*}(X)$ define
$\mu(A)=\nu(A)$. Then $\mu$ is a solid-set function on $X$ and, thus, extends
uniquely to a topological measure on $X$.

###### Proof.

Let $A\in\mathscr{A}_{s}^{*}(X)$. By Lemma 15.1, $A$ is a solid set in
$\hat{X}$. Using Lemma 3.10, the fact that $\nu$ is a solid-set function on
$\hat{X}$, and that a bounded solid set does not contain $\infty$ it is easy
to verify the first three conditions of Definition 6.1. By Remark 15.3 $\mu$
is a solid-set function on $X$. ∎

Theorem 15.8 allows us to obtain a large variety of topological measures on a
locally compact space from examples of topological measures on compact spaces.

######  Example 15.9.

Let $X$ be a locally compact space whose one-point compactification has genus
0. Let $n$ be a natural number. Let $P$ be the set of distinct $2n+1$ points.
For each $A\in\mathscr{A}_{s}^{*}(X)$ let $\nu(A)=i/n$ if $\sharp A=2i$ or
$2i+1$, where $\sharp A$ is the number of points in $A\cap P$. By Example 14.5
and Theorem 15.8 $\nu$ is a solid-set function on $X$; it extends to a unique
topological measure on $X$ that assumes values $0,1/n,\ldots,1$.

We conclude with an example of another infinite topological measure.

######  Example 15.10.

Let $X=\mathbb{R}^{n}$ for any $n\geq 2$, and $\lambda$ be the Lebesque
measure on $X$. For $U\in\mathscr{O}_{s}^{*}(X)$ define $\mu(U)=0$ if
$0\leq\lambda(U)\leq 1$ and $\mu(U)=\lambda(U)$ if $\lambda(U)>1$. For
$C\in\mathscr{K}_{s}(X)$ define $\mu(C)=0$ if $0\leq\lambda(C)<1$ and
$\mu(C)=\lambda(C)$ if $\lambda(C)\geq 1$. It is not hard to check the first
three conditions of Definition 6.1. From Remark 15.3 it follows that $\mu$ is
a solid-set function on $X$. By Theorem 10.7 $\mu$ extends uniquely to a
topological measure on $X$, which we also call $\mu$. Note that
$\mu(X)=\infty$. $\mu$ is not subadditive, for we may cover a compact ball
with Lebesque measure greater than 1 by finitely many balls of Lebesque
measure less than 1. Hence, $\mu$ is not a measure.

The vast majority of papers dealing with quasi-linear functionals and
topological measures (including papers in symplectic geometry) consider a
compact underlying space, finite topological measures and bounded quasi-linear
functionals. In symplectic geometry one often sees quasi-linear functionals
corresponding to simple topological measures. This section shows how to obtain
a variety of finite and infinite topological measures on locally compact
spaces.

Acknowledgments: This work was conducted at the Department of Mathematics at
the University of California Santa Barbara. The author would like to thank the
department for its hospitality and supportive environment.

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# A Method for Waste Segregation using Convolutional Neural Networks

Jash Shah  Department of Information Technology
K J Somaiya College of Engineering
Mumbai, India,
<EMAIL_ADDRESS>Sagar Kamat  Department of Information Technology
K J Somaiya College of Engineering
Mumbai, India,
<EMAIL_ADDRESS>
###### Abstract

Segregation of garbage is a primary concern in many nations across the world.
Even though we are in the modern era, many people still do not know how to
distinguish between organic and recyclable waste. It is because of this that
the world is facing a major crisis of waste disposal. In this paper, we try to
use deep learning algorithms to help solve this problem of waste
classification. The waste is classified into two categories like organic and
recyclable. Our proposed model achieves an accuracy of 94.9%. Although the
other two models also show promising results, the Proposed Model stands out
with the greatest accuracy. With the help of deep learning, one of the
greatest obstacles to efficient waste management can finally be removed.

###### Keywords:

Waste classification, convolutional neural networks, deep learning, machine
learning

##  I Introduction

The garbage and recycling businesses are being overwhelmed by the ever-
increasing volume of global garbage. As a result, the demand for smart
solutions for environmental monitoring and recycling process improvement is
stronger than ever [1]. Human life and the environment are both affected by
waste disposal, whether directly or indirectly. The negative consequences of
waste materials can be mitigated with the use of a competent waste management
system [2]. Currently, there are two types of waste classification and
separation: manual waste classification and automated waste classification
using multiple techniques. The first may be accomplished with human
intelligence and power, while the second entails the automatic search for
appropriate waste classification techniques [3].

Recycling is rapidly becoming an essential component of a sustainable society.
However, the entire recycling process has a high hidden cost. This is caused
by the recycling materials’ selection, categorization, and processing. Even
while many customers nowadays are able to perform their own garbage sorting,
they may be puzzled about how to select the correct waste category when
disposing of a wide range of items. Finding an automated approach to recycling
is currently extremely valuable in today’s industrial and information-based
world since it offers both environmental and economic benefits [4].

Dumping organic wastes in landfills is a big concern, not because of the
resources lost in the process, but because the organic waste undergoes
anaerobic decomposition in the landfill, resulting in methane production.
Methane has a greater greenhouse gas effect than carbon dioxide when
discharged into the atmosphere. Organic waste, on the other hand, has its own
set of issues, since it may be a source of greenhouse gases, methane, and
pollution. If organic waste is not properly cleaned or controlled, it can
infiltrate water sources and feed bacteria, resulting in the formation of
fungus, which can be hazardous to society.

The majority of municipal trash is not segregated at the source of origin and
ends up in sanitary landfills. That is why we require a more effective system
for distinguishing recyclable materials, and this is where we can help. We can
identify, remove, and sort those items on a moving conveyor using computer
vision and artificial intelligence (AI). CNN (convolutional neural networks)
characteristics are used by the majority of today’s top-performing object
detection networks. A more automated approach allows us to ship fewer
recyclables to landfills. In this paper, we built three models, namely
ResNet-34, VGG16 and a proposed deep neural network for image classification,
segmentation, and detection and compared the results that we obtained. The
categorization of recyclable and organic materials is a difficult topic that
necessitates the use of advanced approaches. A worldwide strategy for
industrial applications is required, in addition to dataset gathering. We
offer a more accurate and optimum waste categorization approach in this study.

##  II Literature Survey

In paper [5], the OpenCV computer vision library is used in this study to
conduct data improvement, and picture preparation on the waste images
gathered. A VGG16 convolutional neural network is created using TensorFlow as
the model training backdrop, with the RELU activation function and the
addition of a BN layer to enhance the rate of convergence of model and
recognition accuracy rate. The correct rate of the scheme described in this
paper is 75.6 per cent after testing on the test set. The scheme described in
this paper can effectively classify domestic garbage into toxic garbage,
kitchen waste, other garbage, and recyclable waste, meeting the needs of
practical applications.

In paper [6], a comparison is made between a proposed model that is WasteNet
and various other models like VGG, AlexNet, ResNet, DenseNet and SqueezeNet on
four different metrics. The waste is categorised into six different
categories. It was found that the proposed model performed better on all four
metrics and had an accuracy of 97%. Hence, it was then used to make a smart
dustbin that classifies the waste that comes into the dustbin.

The paper [7] proposes a neural network for waste classification into three
categories: recyclable, non-recyclable and organic waste, with an accuracy of
81.22%. The paper also compares other models like VGG16, Inception-Net, Dense-
Net and Mobile-Net. Out of all these transfer learning models, Mobile-Net
showed the highest accuracy of 92.65%.

Paper [8] suggests using a Convolutional Neural Network and a Support Vector
Machine algorithm for better waste classification. They have used ResNet-50 as
the transfer learning model as the dataset was small. They segregate waste
into four categories: glass, paper, plastic and paper. By this approach, they
have achieved an accuracy of 87% on epoch number 12.

Trashnet datasets were utilized to conduct this [9] study. The performance of
the SVM classification using the SIFT feature is compared to the performance
of the same technique using the SIFT-PCA combined feature. The results of the
experiments indicate that categorization using SIFT feature extraction
achieves a 62 per cent accuracy.

The authors of [10] look at a variety of approaches and give a thorough
assessment. Support vector machines using HOG features, basic convolutional
neural networks (CNN), and CNN with residual blocks were among the models we
used. The authors concluded that basic CNN networks with or without residual
blocks perform well, based on the results of the study.

The critical component of the system mentioned in [11] is a garbage container
that will automatically sort waste using the Internet of Things and Machine
Learning technologies. The bin is linked to the cloud, which aids in the waste
collection by recording and uploading numerous data points for each bin. This
study describes two versions of the system, the first of which achieves a 75
per cent accuracy in categorising garbage as wet or dry, and the second of
which achieves a 90 per cent accuracy in sorting waste into six unique
categories.

In paper [12], the performance of four CNN-based Waste Classifiers, namely
ResNet-50, VGG16, MobileNet V2 and DenseNet-121. The waste was categorized
into four categories like hazardous waste, general waste, recyclable waste and
compostable waste. The highest accuracy of 94.8 per cent was obtained for
ResNet-50.

Using a deep learning technique, the paper [13] examines a unique approach for
waste sorting for successful recycling and disposal. The YOLOv3 method was
used to train a self-made dataset in the Darknet framework. The network has
been taught to recognise six different categories of objects. The detection
test was also done using YOLOv3-tiny for comparative assessment to evaluate
the competency of the YOLOv3 algorithm.

The authors in paper [14] have classified the waste into four classes like
cardboard, paper, metal and plastic. They designed a Convolutional Neural
Network, which attained the highest testing accuracy of 76 per cent for 100
epochs for 50x50 size images.

##  III Dataset

Kaggle provided the dataset for the transfer learning model and the proposed
CNN model. It is waste classification data, which comprises approximately
25,077 waste images split into two categories: organic and recyclable. Table I
indicates the number of images in each class, whereas Fig. 1 depicts the same
in a pie chart. Fig. 2 shows some sample images in the input dataset.

TABLE I: Number of waste images in the dataset. | Organic | Recyclable
---|---|---
Training data | 12565 | 9999
Testing data | 1401 | 1112
Total | 13966 | 11111

Figure 1: Distribution of waste images in dataset. Figure 2: Types of waste
images in dataset.

##  IV Methodology

###  IV-A VGG16

In 2014, Zisserman and Simonyan suggested the VGG16 network structure as one
of the VGG NET networks [15]. It’s a more advanced version of the AlexNet
network. When recognising and categorising pictures, it can more correctly
convey the features of the data collection. Large-scale data sets and
complicated backdrop recognition tasks benefit from it. Thirteen convolutional
layers, three fully connected layers, and five pool layers make up the network
structure. The convolution kernel used in the 13 convolutional layers
contained in VGG16 is a medium-sized 3 x 3 matrix with a moving step of 1
compared to other networks. The number of convolution kernels steadily grew
from 64 in the first layer to 128 in the second, 256 in the third, and finally
512 in the final layer. The pooling layer’s convolutional kernel is 2 x 2 in
size, and the step size is 2. It performs better on the retrieved features
than other networks with a convolution kernel size of 5 x 5. VGG model offers
superior processing capabilities for training data sets with tiny amounts of
data, and it is easier to deploy and has higher recognition accuracy than
other deep convolutional neural networks [16].

The VGG16 network model, on the other hand, offers both advantages and
downsides in terms of precise identification. The number of model parameters
and the complexity of computations during training has risen as the network
structure has been deepened, resulting in a long training period and low
training efficiency. The following approaches are utilised to enhance the
VGG16 model in this work in order to maintain the key features of the model
extraction without lowering the accuracy of recognition while also improving
the pace of model training and minimising the time it takes to train the
model. The Relu function is used to activate the VGG 16 network in the VGG
network, and the formula is:

$f(x)=\begin{cases}x&\text{ if }x\geq 0\\\ 0&\text{ if }x<0\end{cases}$ (1)

Where: x is the input of the Relu function; f(x) is the function’s output. The
loss function is used to measure the difference between the predicted and
actual values throughout the model training process. In the VGG 16 network,
use the CrossEntropyLoss loss function, which has the following formula:

$E(t,y)=-\sum_{j}t_{j}\log y_{j}$ (2)

Among them: t and y represent the target label and output of the neural
network, respectively, and represents the softmax loss function:

$y_{j}=e^{z_{j}}/\sum_{k}e^{z_{k}}$ (3)

###  IV-B ResNet - 34 (FastAI)

ResNet-34 is a state-of-the-art image classification model with 34 layers of
convolutional neural networks. This is a model that has been pre-trained on
the ImageNet dataset, which has 100,000+ pictures divided into 200 categories
[17]. It differs from traditional neural networks in the sense that it uses
the residuals from each layer in the subsequent connected layers.

The infrastructure of the ResNet-34 network is the residual building
component, and it makes up the majority of the network. The residual building
block used a shortcut connection to skip the convolutional layers, effectively
alleviating the problem of gradient disappearance or explosion characterized
by increasing depth in neural networks and allowing us to build CNN structures
more freely and improve the rate of recognition [18].

ResNet has one convolution and pooling step, the four layers of identical
behaviour. Each layer follows a similar pattern. They execute 3x3 convolution
with a fixed feature map dimension (F) of [64, 128, 256, 512] and skip the
input after every two convolutions. Furthermore, the width (W) and height (H)
of the layer stay consistent throughout. [19]

###  IV-C Proposed Model

####  IV-C1 Convolutional Layer

The input image is first passed via a convolutional layer of the convolutional
neural network. The convolutional layers use convolution to extract high-level
characteristics from an input image. A convolution is a linear procedure in
which the input is multiplied by a set of filters. The convolutional neural
network, unlike previous algorithms, learns the filters from the training
dataset. The earlier convolutional layers generally capture the lower-level
features such as gradient orientation, edges, and so on. Increasing the number
of convolutional layers enhances the ability to encode higher-level features.
[20]

####  IV-C2 Pooling Layer

In the pooling layer, the output of the ReLU function is then dimension
reduced. To extract the salient characteristics important in the feature maps,
the pooling layer uses a max-pooling method. The maximum pooling layer’s
output is more rotational and translational invariant. Max pooling can also be
used to filter out noisy and minor activations, lowering the number of
computing resources required.

Figure 3: Architecture of proposed CNN model.

####  IV-C3 Fully Connected Layer

The features are flattened and sent into the fully connected layer after going
through the above stages. The fully connected layer receives the features from
the previous layers and uses the backpropagation technique to learn the non-
linear functions of the features. The last fully-connected layer uses a
softmax function to calculate each class’s probability. All of the classes’
probabilities will add up to one.

####  IV-C4 Activation Layer

Before passing to the next layer, the output from the convolution layer is
activated by a ReLU activation function. When compared to the commonly used
sigmoid and tanh functions, the ReLU function has the advantage of just
activating non-negative neurons, making it more computationally efficient.

In this work, the desired shape of input images is 224x224 with an RGB color
scheme. The CNN used in this work contains 6 Conv2D layers, 3 MaxPool2D layers
and three fully connected Dense layers. ReLU acts as the activation function
in the fully connected layers. The output layer contains only a single neuron
which will contain values as 0 or 1, where 0 stands for class (’Organic’) and
1 for class (’Recycled’).

##  V Results

In ResNet-34 architecture with seven epochs, an accuracy of 91.8% was
achieved. For the VGG16 model, an accuracy of 93.37% was obtained on training
the model for five epochs and a batch size of 32.

TABLE II: Classification report on test data.

| VGG16 | ResNet-34 | Proposed model
---|---|---|---
| Organic | Recyclable | Organic | Recyclable | Organic | Recyclable
Precision | 0.86 | 0.89 | 0.94 | 0.92 | 0.96 | 0.95
Recall | 0.92 | 0.81 | 0.93 | 0.91 | 0.94 | 0.96
f1-score | 0.89 | 0.85 | 0.94 | 0.93 | 0.95 | 0.94

Figure 4: Evaluation of loss function of ResNet-34 model.

Figure 5: Evaluation of loss function of VGG16 model.

In the proposed model, the batch size was set to 64, and the number of epochs
was kept at 10, but it was observed that the accuracy of the model was not
improving after epoch number 7. Hence, an early stopping method was applied,
and accuracy of 94.96% was attained.

Figure 6: Evaluation of accuracy for proposed CNN model.

Figure 7: Evaluation of loss function for proposed CNN model.

Figure 8: Bar chart representation of accuracies of various models.

## Conclusion

Segregation and management of waste have been a long-standing issue that has
impacted a vast percentage of the ecosystem. It is easier to manage waste
using today’s technology if they are applied properly.

As we can see from the findings of this study, the problem of waste image
categorization can be tackled with deep learning algorithms with a high degree
of accuracy. It can thus be seen from the comparison of accuracies of the
three deep learning models the proposed has the highest accuracy of 94.9%.
Though the accuracy of other models doesn’t come at par with the proposed
model, still these models can be considered for further improvement since the
accuracy of those architectures is above 90%.

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