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# Heuristics for the Intelligent Prediction of Population Growth

Orukpe, Austin Oshoiribhor, Okorodudu Franklin Ovuolelolo, Omede Gracious C, Imianvan, Anthony Agboizebeta

► To cite this version:

Orukpe, Austin Oshoiribhor, Okorodudu Franklin Ovuolelolo, Omede Gracious C, Imianvan, Anthony Agboizebeta. Heuristics for the Intelligent Prediction of Population Growth. Asian Journal of Research in Computer Science, 2024, 17 (9), pp.27-38. 10.9734/ajrcos/2024/v17i9497. hal-04678283

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Submitted on 26 Aug 2024

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# Heuristics for the Intelligent Prediction of Population Growth

Orukpe, Austin Oshoiribhor<sup>a</sup>,
Okorodudu Franklin Ovuolelolo<sup>b*</sup>, Omede Gracious C<sup>b</sup>
and Imianvan, Anthony Agboizebeta<sup>c</sup>

## Authors' contributions

This work was carried out in collaboration among all authors. All authors read and approved the final
manuscript.

## Article Information

DOI: https://doi.org/10.9734/ajrcos/2024/v17i9497

**Open Peer Review History:**

This journal follows the Advanced Open Peer Review policy. Identity of the Reviewers, Editor(s) and additional Reviewers, peer review comments, different versions of the manuscript, comments of the editors, etc are available here:

https://www.sdiarticle5.com/review-history/121740

Received: 21/06/2024

Accepted: 23/08/2024

Published: 26/08/2024

## Original Research Article

## ABSTRACT

Population growth is a phenomenon that is inevitable in a life course and the components of population growth are fertility, mortality and migration. Because of the impact population growth exact upon the socio-economic nature of a country, it will be wise to know the future size and distribution of it so that adequate measures can be made to forestall possible problems. There are different population models and algorithms implemented to project population growth, ranging from statistical to machine learning models; these model techniques were very suitable in their time, such as the Malthusian theory, which, first and foremost, gives deeper consideration to the exponential growth model, while many implemented classification and linear regression algorithm. Linear regression machine learning algorithms were considered the most effective algorithm for

<footnote><sup>a</sup> National Population Commission, Edo State, Nigeria.</footnote>

<footnote><sup>b</sup> Department of Computer Science, Delta State University, Abraka, Nigeria.</footnote>

<footnote><sup>c</sup> Department of Computer Science University of Benin, Benin City, Nigeria.</footnote>

<footnote>*Corresponding author: E-mail: okoroblackx4@yahoo.co.uk;</footnote>
population growth projection. This study tends to develop a machine learning model that is data-
driven mathematically, capable of implementing the data-independent prediction model equation
that was used to predict the impact of the Non-pharmaceuticals approach and pharmaceuticals
approach (NPA and PA) in mitigating the spread of the Covid-19 virus, and both models were re-
modified to project Nigeria population growth. The data-independent prediction model (DIPM)
utilized onset data from the NPA and PA interventions to predict the probability of mitigating the
spread of the virus for a specific period. The DIPM has the properties of arithmetic and exponential
methods. The fusion of these two properties with the aid of machine learning model has further
reveal the data-independent prediction model as a conceptualization technique to reflect how data
are processed in an algorithm setting in a concrete world, with the support of the Java array list
algorithm, what all the statistical models and supervised machines learning model used in the past
studies could not achieve, have been accomplished succinctly. The data independent prediction
model is a robust technique for both projection and forecasting future population growth as well as
proffer answers to historical issues in mathematical modeling of population expansion.

Keywords: Intelligent prediction; population growth; mathematical modeling; algorithms; machine learning models; Malthusian theory.

# 1. INTRODUCTION

Projection is the idea of trying to know the future
condition of an entity. The use of machine
learning has facilitated this curiosity[1]. "Machine
learning" refers to a assemblage of methods that
let computers learn selflessly from the data; the
systems learn on their own rather than following
a precise programming pattern, which enables
them to function intelligently. As it advances
further, it can do better by learning effortlessly
and, after that, being able to execute knowledge-
related activities. Its learning method is carefully
spelt out in that it has a considerable size of data
that the computer will overrun in a brute force
procedure to reduce the deviation of its
prediction from the expected result. The principal
motive for applying machine learning is to
achieve efficiency and effectiveness in planning.
On the basis of this notion, machine learning
 extends from artificial network procedures and
can be regarded as a subset of artificial
intelligence (AI). It enables prediction; for this
purpose, its basic building blocks are algorithms.
It generates data-driven predictions by
developing models that discover patterns in
historical data and utilize those patterns to
generate predictions. Its data acquisition and
storage capacities in various fields of scientific
research introduce the issue of the tremendous
information age. It made available a novel
method of reasoning and techniques to analyze
and handle problems. Which systematically leads
to significant methods of research.[2,3]. The main
idea behind learning is the tradeoff between bias,
variance, and model complexity[4]. Among the
many branches of AI, machine learning can
integrate data with statistical tools for projection
and analytical power to predict results accurately

in an intelligent form and intelligently find hidden
insights using the supplied data in an automated
way[2,5,6,7,8]. It provides a new way of thinking
and approaches to analyzing and solving
problems, gradually becoming a significant
research method. Training of data at every stage
with good visualization gives good analysis of
data to project and prepare for the unknown to
avoid had I know when population growth takes
unaware, this ideology gives an insight to the
future in preparedness to equip every amenities
and the health sector to avoid the loss of
lives[9,10,11].

There are primarily three subfields within
machine learning: Supervised, Unsupervised,
and re-enforcement. One conspicuous difference
between the supervised and unsupervised is the
appearance of the target variable. In supervised
learning, we have a clear direction of what we
predict from the stated model. Thus, every record
feature or column has its specific label to be
predicted. Invariably, unsupervised learning does
not have a target variable; each record feature or
column is independent and has no specific or
fixed pathways to lead them. Supervised
machine learning is trained with the data and
with pre-labeled features or variables for the
model to learn the relationship in the data set.
Supervised learning requires more human
preparation at the initial process due to the need
for adequate labeling; the labeling serves as the
ruder to determine whether the pattern
recognition is a correct [12] Prediction models.

1.1 Unsupervised Machine Learning

The technique refers to algorithms that identify
patterns in a dataset containing data points that
are neither classified nor labeled. The algorithms
are permitted to classify, label and group the
data points within the data. Unsupervised
machine learning tasks infer a function (the
existing relationship) to describe hidden structure
from unlabeled data [13,14,15]. It is used to
deduce patterns in unlabeled datasets.

1.2 Reinforced Learning

The reinforced learning merged supervised and
unsupervised methods by applying a dynamic
machine learning composition. Yutaka et al. [16]
can perceive its environment for interpretation,
swing into actions and get educated through the
guess method [17,18].

1.3 Population Growth Projection

Population growth projection discloses the future
figures of fertility, mortality, and migration of
people in a country. Machine learning concepts
are currently expanding and favored for
predicting future values. In conjunction with the
data-independent prediction model, we
implemented the Nigeria population growth rate
projection, an unsupervised machine learning
concept to build the map between base year and
population growth.

2. LITERATURE REVIEW

Brintha et al.[19] investigated the population
growth of Indian population data using time
series forecasting machine learning techniques
and analyzed different machine learning
algorithms. Mohammad [20] deploys machine
learning to predict the population growth rate in a
country without historical data. Faith [21] applies
various machine learning algorithms to forecast
the population growth rate in Turkey. Ahmed [22]
predicted the future population of Bangladesh
with machine learning to estimate Rofingya
refugees. An investigation carried out by Gotelli
[23] gave attention to two main tools of projection
techniques geometric and exponential methods,
and equally thought of including the mortality and
fertility as unique components of change.
Thomas Malthus, a demographer of British
extraction, gave significant attention to the
exponential growth model; he studied a large
number of demographic data and came to a
conclusion that, in the operation of natural
population growth, the proportional increase is a
constant; the proportional increase is the
proportion of the population increase on per unit
of time to the total population at that time. Let the

total population be P(t) at time t, and let the
population growth rate (birth rate subtracted from
death rate) be r. According to Malthus's theory, in
the activity of natural population growth, r is the
increase in the population per unit of time and is
directly proportional to the total population. For
the fact that population growth constantly
increases, it can be regarded as a differentiable
constant function. He opined that population
increase, if is not commensurate with the food
increase, that will spark trouble, more especially
if increases in food supply is following arithmetic
method while the population increases is
following an exponential order, so this
lopsidedness could spell doom for the inhabitants
of a society and the government, and it is
obvious that development will be hindered
subsequently.

The National Population Commission (NPC)[24]
deploys the Cohort component method, it is a
method that is often used to forecast the various
demographic variables including gender. It is
used too as a plan of action that forecast the
population by mimicking the way the population
changes with the dictates of population
components of change, on the ground of
previous information supposition are put
together, regarding the trends in the time to
come in areas of fertility, mortality and net-
migration. Thereafter, the estimated rates are
put in an application in the age and gender
composition of the population of reference, then
replicating it with the thought that people are
susceptible to death, that the female gives birth
and some persons can change their address.
Typical of this method is known as component
method. The component approach of forecast of
population stick to unit of all the group of persons
according to their ages throughout their lifespan
with the application of the component of change
individually. From the initial population with age
and gender, per person has the chance to exit by
death as intended by the forecast according to
the age and gender. Immediately the mortality is
approximated they are deleted from the existing
population and living ones continue to aged. Birth
rates are estimated among the women
procreative population regarding the birth
occurrence on yearly basis. Every unit of children
giving birth to is also expected to be susceptible
to death. Especially, the component method
examines both the in-migrants and out-migrant
by adding them to the population of reference.
Migrants are included, or removed from the
population of reference in every vestige of the
particular age and gender. This method is
replicated on yearly basis of the forecast, which
yields the forecasted population by sex and
gender, likewise the mortality, fertility and crude
death and natural increase and growth rate
patterns for every year. Demographers use the
component method often times because of its
holistic nature of treating variable of population
simultaneously. NPC [24]., Simon [25] and Guy
J.et al [26] considers Bayesian techniques as a
tool for predicting future populations. The primary
rationale is the need for incorporating uncertainty
in population forecasts, advocated by many
authors since the 1980s [27,28,29]. Some
techniques have also been developed to bring
together aspects of all of these methods, for
instance, the parameters from time series
models have been constrained according to
expert opinions [30,31] or to target levels and
age distributions of fertility and mortality. We
believe Bayesian methods offer a more natural
framework than traditional frequents methods to
forecast future population with uncertainty. First,
the Bayesian approach offers an explicit, a
unified and open process for incorporating data
and parameter uncertainty of the model and the
model itself, by using probability distributions.
Second, it allows the inclusion of expert
judgments, including uncertainty, into the model
framework. Third, the predictive distributions
follow directly from the probabilistic model
applied. As a result, probabilistic population
forecasts, with more reliable and coherent
estimates of predictive distributions, can be
successfully acquired. When used together, they
may make it easier to quantify prediction
uncertainty, which would enhance our capacity to
prepare for and comprehend population change.

Vikas et al [32] study future population
forecasting in India using the geometrical model
to census population data. In this model, the
average increase in future population forecasting
every ten years is computed using historical
census data. To determine the population in the
next ten years, this increment is added to the
current population. Thus, it is assumed that the
population is increasing at constant rate. Next
was the use of Graphical model representation In
this process, the populations of last few decades
are correctly plotted to suitable scale on graph.
The population curve is easily expanded to
accommodate future population growth. This
expansion calls for meticulous execution as well
as the right knowledge and discernment. The
most effective method of using this process is to
extend the curve by comparing with population
curve of some other population having the

growth condition. Another technique was the
Comparative Graphical model. In this process
the census populations of India already
developed under similar conditions are plotted.
The curve of past population of the India under
consideration is plotted on the same graph. The
curve is extended carefully by comparing with the
population curve having the similar condition of
growth. The advantage of this process is that the
future population can be predicted from the
present population even in the absence of some
of the past census report—these various
geometrical methods as suitable for the growth
pattern. The fourth method was the Master Plan
Model. The big and metropolitan cities are
generally not developed haphazardly, but are
planned and regulated by local bodies according
to master plan. The master plan is prepared for
the city's next 25 to 30 years. According to the
master plan, the city is divided into various
zones: residence, commerce and industry. The
population densities are fixed for various zones
in the master plan. From this population density,
the total water demand and wastewater
generation for that zone can be worked out. With
this method, it is straightforward to access the
design population precisely. Lastly was the
Logistic curve Model. This process is used when
the growth rate population as a result of births,
deaths, and migrations takes place under
everyday situations and it is not subjected to any
extraordinary changes like epidemics, war,
earthquakes or any natural disasters, etc. The
population follows the growth curve
characteristics of living things within limited
space and economic opportunity. If the
population of India is plotted concerning time, the
curve so obtained under normal conditions looks
like an S-shaped curve and is known as a logistic
curve.

Jabrayilova [33] developed an intelligent
demographic forecasting system using fuzzy time
series model. The author analyzed things that
affect economic changes and how they are
interconnected with demographic processes.
According to the author, the study's main aim is
to develop an intelligent demographic forecasting
system that supports demographic situation
management decisions based on predictions. To
achieve this aim, the author modeled and
develops a demographic prediction technique.
The author adopted a fuzzy time series for
estimating model parameters. The analysis of
this series involves constructing a mathematical
model of time series of observation of real
processes.
Folorunso, et al, [34] used controlled Artificial Neural Network technique to predict the population of Nigeria. Their prediction was done using training, validation, and test dataset in their research, Population Prediction Using Artificial Neural Network. Their study employed the artificial neural network for population prediction (ANNPP), which handles the inconsistent and incomplete nature of data, often experienced in mathematical and demographical models while carrying out population prediction. Three major dynamics of population changes (fertility, mortality, and migration) were considered in the input dataset. Vikas et al, [32], Applied Mathematical Modeling to project the population growth of India. While, Nusrat Rahima et al, [35], uses mathematical growth model to explore and determine an effective and plausible mathematical growth model to predict the future population growth of India. Poogodai [36] uses regression models to study the accuracy of population forecasts. It also looks at how population size and growth rate affect projection mistakes. Caleb Robinson, et al, [37] used the deep learning model to create high resolution population estimations from satellite imagery in the USA, to answer the question where do people live and how many people live there. Fasagba Irewole et al, [38] deploy Statistical package for social sciences (SPSS) Multiple linear regression to obtain the equation to model the population projection in Nigeria.

### 3. RESEARCH METHODOLOGY_AND_SYSTEM DESIGN

The study adopted the design of machine learning model. Which intend to apply data independent prediction model, based on onset data using the 2006 conducted census data as the input data presented to the machine learning algorithm to project the Nigeria population growth.

Conventionally, the projection model requires exploiting the data set to infer more information regarding the variable of interest. The data independent prediction model (DIPM), is the projection technique we are using in this study, in conjunction with the machine learning model conceptualization, for the reason that the prediction model by convention can exploit the dataset to deduce more information regarding the variable of interest, such as the growth rate, and time index of the census data, its algorithm can detect uncertainties on demographic composition and social-economic characteristics

of the data and analyze the historical data, the model was re-modified from the covid-19 model equation to population prediction model.

The development of machine learning model, and the simulation methodology to validate the performance of the model, using the data independent prediction model which combines the exponential and Arithmetic properties, is designated as hybrid. These combination distinguished the implemented method and depute it as high-level model because, the marrying of the two techniques makes the model very robust and superior to the existing model, the results will be more reliable and accurate as the deployed model is poised to balance the excesses of each other, and come up with dependable and verifiable results. The data-independent prediction model, which comprises of both the Non-Pharmaceuticals concept approach and pharmaceutical approach is presented in equation (1.) and (2)

$$K(\theta) = Pe^{pt} \quad \dots\dots \quad .. (1)$$

The NPA model in equation 1 is known as data independent prediction model (DIPM), is clearly a non-pharmaceutical concept applied to predict the probability of safety from Covid-19 infection using the social distancing values. While the equation (2),

$$pi = [\alpha e - \delta(t)] \quad \dots\dots \quad .. (2)$$

The Pharmaceutical approach model (PA) came into inception when the vaccines for the Covid-19 infection started arriving. Data from both models were utilized to combat the Covid-19 infection to a standstill. The data from both models were geared towards projection.

Okwonu, et al, [39] and Santosh, [40]. This study reformulate the data-independent prediction model to suit the population projection model because the model has the properties of arithmetic and exponential method, which is dependent on onset data or base data, and extends from such value using the embellished parameters with the automation of Java programming language, using machine learning model format to describe the functionalities of the system and thereafter simulate the model with secondary data from the 2006 conducted census. And compare the output value with the existing value to ascertain the model minimal error. Hence, equation (3)
The modified model in (3), reads the population projection model which is the crux of the study.

$$ \beta [\lambda e^{-\Phi(t)}] \qquad (3) $$

The equation 3 model possesses the characteristics of arithmetic and exponential properties, and the fitting parameters are:

β = starting population

λ = denotes tuning parameter for prediction control and

e = is the exponential constant (2.7818). Then, the following are defined

(i) φ = growth rate

(ii) t = represent the distant future of choice

### Keys

IL: Integration Layer

PL: Processing Layer

SL: Storage Layer

AL: Analytical Layer

VL: Visualization Layer

AV: Actual Value

## 3.1 User Interface

The user interface provides a platform for users of the system to enter the required features for population projection.

## 3.2 Dataset component

The dataset component consists of dataset from the National Population Commission and is formatted into four columns, base figure, multiplier, growth rate, and time index represented by the mathematical equation of the model.

## 3.3 Java Array List Algorithm:

The Java Array list component optimized the population growth rate by performing feature extraction and selection and utilizes the value encoding techniques where each value is considered according to their role in the layer Jbutton, Jlabel, Jlayer etc. in the JArray list. The Java Array list module contains the initialization phase, the assigner, separator, generator, concluder and preprocessor phases.

## 3.4 Initialize Phase

In this phase, the data set is entered into the frontend. Is a method that NetBeans swing

designer utilize to initialize components (set as defaults values) as a method it can be called within anytime you wants to use it, it is called inside the constructor to control the parameters you passed through your Graphical User Interface editor of NetBeans. It is a connector between the GUI Editor and Java. Removing it will disable the link between the functionality that NetBeans supplied to work with the components

## 3.5 Assigner Phase

The assigner allocates task value to each respected data point, helping to find an avenue to attain ease optimality. There is different assigner method in existence, we have adopted and implemented the pattern by Mohammed et al, 2012, though used in the health data regarding tumor dataset, we reformed it and use it in the population data projection.

$$ Assigner = \delta^* Error + \pi \frac{|n|-|j|}{|n|} \qquad (4) $$

Where

|n| is the entire features

|j| is the selected number of features

$\delta^*$ are outside features

$$ error rate = Av - pg/n $$

Where

Av: the actual number in the dataset

pg: the projected number set aside in dataset

n: the surplus number or difference between the actual value and projected in dataset

We adopt the Mohammed et al, [41] though was applied in the health dataset we find it useful in this data projection problem at hand.

Where

Av: the actual number in the dataset

pg: the projected number set aside in dataset

n: the surplus number or difference between the actual value and projected in dataset

We adopt the Mohammed et al, (2012) though was applied in the health dataset we find it useful for insight purposes in this data for projection problem at hand.

## 3.6 Separator Phase

Separator functions used in Roulette Wheel, (RWS), implemented in the health sector, Razamin et al.,[42] in determining dataset allocation is adapted, it is like an Array,
ArrayList is a java class been a mother of all functionalities in Java. It does all the required procedure in Java programming, such as add, delete, concatenate, divide, store data, decides, allocate data etc. it has numerous features. Where data points are required to be utilized, like initializing, allocations, and probability cases, it is like a vector in C++, etc. The separator get the allocated data points to be projected in a complete number, and extends it with the aid of a function such as multiplication using the exponential and the provided variables such as growth rate and time interval to be projected, it is sensitive to the data trends. Once the data is provided with the accompanied variable of the projection, it takes it up from there. Every other internal function within the constructor is called within to achieve the required output as outlined in the equation 3.

$$ \beta [\lambda^e - \phi(t)] \quad (5) $$

The equation 3.model possesses the characteristics of arithmetic and exponential properties, and the fitting parameters are:

β = starting population

λ = denotes tuning parameter for prediction control and

e = is the exponential constant (2.7818). Then, the following are defined

(i) φ = growth rate

(ii) t = represent the distant future of choice

i. PROCEDURE::doseparator

ii. START_OF do separator: PROCEDURE

iii. //initialize a real number precision variable that holds the entire number of all PG_Dataset

iv. PG Assignersum:=0.00 // Assignersum of all PG datapoint

v. for loop_counter:=0 to row-1

vi. START for loop_counter

vii. Assignersum:= Assignersum+PG Assigner[loop_counter]

viii. Loop_counter:=loop_counter +1

ix. END for loop_counter //round the Assignersum to 2d.p

x. Assignersum:= ROUND(Assignersum, "2dp" // time interval of PG datapoint

xi. For loop_counter:= 0 to row-1

xii. START for loop_counter

xiii. PG_timeinterval:=PG Assigner[loop_counter]/Assignersum

xiv. Loop_counter:=loop_counter +1

xv. END for loop_counter//cumulative projection value for

xvi. PG_dataset with initialized variable value to zero

xvii. For loop_counter:= 0 to row-1

xviii. START for loop_counter

xix. PG cumdatapoint[loop_counter]:=

xx. 0+PG cum projection[loop_counter]

xxi. Loop_counter:=loop_counter+1

xxii. END for loop_counter

xxiii. //separatorPG-datasetfor concatenating with cumulative

xxiv. projection loop counter set to 0

xxv. n:=0 //cumulative projection_counter

xxvi. //initialize an array to hold popul. with all PG cumulative dataset

xxvii. Population []:=0 to row -1

xxviii. //initialize arrays to hold both PG_dataset from PG_Population

xxix. PG_dataset1:=R[row] // firstPg_dataset

xxx. PG-Dataset2:=S[row] //secondPg_dataset

xxxii. PEPEAT UNTIL n>number_rows

xxxii. START REPEAT UNTIL BLOCK

xxxiii. //PopulatePG-datasetarrays with Random_Population_dataset

xxxiv. R[n]:=RANDOM_POPULATION_DAT ASET()

xxxv. R[n]:=RANDOM_POPULATION_DAT ASET()

xxxvi. for loop_counter:= 0 to (number_rows

xxxvii. STARTPG_dataset1for loop_counter

xxxviii. IF(R[n] >= cumprojection[loop_counter] AND

xxxix. R[n] < cum projection[loop_counter+1])

xl. START IF BLOCK

xli. PG_dataset1[loop_counter]:= loop_counter

xlii. END IF BLOCK

xliii. Loop_counter:=loop_counter+1

xliiv. ENDPG_dataset1for loop_counter

xlv. For loop_counter:= 0 to number_rows/2) -1

xlvii. STARTPG_dataset2 for loop_counter

xlvii. IF(S[n] >= cum projection[loop_counter] AND S[n] < cum projection[loop_counter +1])

xlviii. START IF BLOCK

xlix. PG_DATASET2[loop_counter]:=loop_counter

l. END IF BLOCK
li. loop_counter:=loop_counter +1

lii. ENDPG _ dataset 2 for loop_counter
//increment loop counter, two
SeparatedPG_dataset

liii. n:=n+2;

liv. END REPEAT UNTILL BLOCK

lv. END_OF doSeparator:PROCEDURE

**Algorithm 1. The Separator Algorithm for**
**population growth projection**

3.7 Generators Phase

Generator institute produces and takes out
optimal features from the projection growth rate
dataset; Generator takes some random data and
attempts to imitate the training data and generate
false images; it aims to undercut the
discriminator by attempting to generate images
that exactly replicate the training dataset. You
require a single ArrayList to store the result. At
each point, you randomly choose an element
from one of the two input ArrayLists with 0.5
probability. You can use a random number
generator to choose between 0 and 1, say
(Random::nextInt (0,2)). You store the resulting
element in the result array List. You don't have to
make new array lists if you don't need
background data after crossover. Generate
synthetic data.

3.8 Concluder/Acceptance Phase

The concluder recognizes a practicable
benchmark in terminating the projection of
population growth optimization process. Using
generation as a concluder standard for projection
of population growth dataset was dependent on
its adaptive nature.

The adaptability provides:

1. Malleability as terminating criterion for any given dataset.

2. Terminating at any given iteration.

3.9 Preprocessor Phase

The pre-processor secures the optimized
population growth projection crumbly dataset and
transforms it into frizzy appearance in a
coordinated form and thereafter stored the
dataset in the knowledgebase. Applying the norm
of fuzzy pre-processor is dependent on its ability
to modify the optimized crumbly values into frizzy
coordinated values as against to more
approaches. The equation 5 is the standard pre-
processor implemented, for crisp values

transformation into fuzzy set. The fuzzy value of
y' for the population growth projection decision
variables D in the ith row is calculated as:

$$
\text{Preprocessor} \quad y = \frac{y - \min(D)}{\text{Max}(D) - \min(D)} \quad (6)
$$

Where:

ý = optimized population growth fuzzy sample
decision variable D in the ith data point

y = optimized population growth number of
sample decision variable D in the ith data
point

min (D) = minimum population projection figure
of sample decision variable D in dataset

max (D) = maximum population growth figure of
sample decision variable D in dataset

The knowledge domain (KD) obeys repository
rule for the operational data which is been
processed. This encompasses possessing
structured and unstructured knowledge about the
problem realm. The database constituents of the
KD and sample decision variable values. These
constituents or units perform the operational
input for the data independent prediction model,
as the trainer and using the Java programming
language as the main classifier. The data
independent prediction model and training block
as portrayed in Fig. 1. Layer 1, Layer 2, Layer3,
Layer 4, Layer 5 and Layer 6.

3.10 Training Input

The training input acquires operational
data held within the knowledge domain and
transfers it directly to the consecutive layers.
Layer 1 shows four sample decision variables.
The indicated variables serve as the input for
the data independent prediction model training
block.

4. DISCUSSION

The designed machine learning model have
applied the data independent prediction model
equation based on onset data to predict the
Nigeria population growth, as a standard, the
prediction model utilize the data set to conjecture
more information regarding the variable of
interest. Several population models have been
used such as statistical bleeding tools, various
machine learning algorithms relying
predominantly on the historical input data. But
our designed machine learning model
serves better in accuracy, consistency and
unbiased.
<figure><img src="image_3.png" /><figcaption>Fig. 1. A detailed design of the Machine learning model for projecting Nigeria Population Growth (MLM-PG)</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>Fig. 2. Flow chart showing the logic that the machine is used to learn the logic to carry out the sequential method of the projection of 2006 conducted population census</figcaption></figure>
## 5. CONCLUSION

The data independent prediction model is a robust technique for both projection and forecasting future population growth as well as proffer answers to historical issues in mathematical modeling of population expansion. In this study, we have designed a machine learning model conceptualization on how the data independent prediction model an unsupervised machine learning model characteristics, can project the Nigeria population growth to archive accuracy and consistency.

## DISCLAIMER (ARTIFICIAL INTELLIGENCE)

Author(s) hereby declare that NO generative AI technologies such as Large Language Models (ChatGPT, COPILOT, etc) and text-to-image generators have been used during writing or editing of manuscripts.

## COMPETING INTERESTS

Authors have declared that no competing interests exist.

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