An automated economics prediction model for world cities using adaptive deep capsule network with attention mechanism

Abstract

Globalization leads to expanding international trade and the integration of national economies into the global economy. Global cities also known as world cities, are increasingly recognized as powerful and economically competitive hubs in the global economy. These cities are characterized by their high levels of interconnectedness, both within their urban fabric and with other major cities around the globe. A global city’s economic strength is a key factor since it attracts foreign investors and citizens. Thus, examining the economics of global cities has gained popularity among specialists as a research topic. However, several economic methods have been utilized to forecast the world economy in recent decades. Yet, their prediction rates are quite low. Hence, analyzing the economics in the world cities has become a hot research topic among experts. Despite the implementation of various economic prediction techniques over the past decades, their performance in accurately forecasting economic outcomes remains low. Hence, in this research work, an automated economic analysis strategy is introduced for the world cities to tackle this problem. Firstly, data from various benchmark sources have been collected to gather data on world cities for predicting economic status. Further, the garnered data are involved with the data pre-processing, where the data are processed to produce better predictions without any false rate. Subsequently, deep features are extracted from the resultant pre-processed data to enhance network performance. Finally, the extracted deep features are subjected to the Adaptive Deep Capsule Network with Attention Mechanism (ADCapNet-AM) for the economic forecast of the world cities. Here, the Improved Humboldt Squid Optimization Algorithm (IHSOA) is employed for optimizing the network parameters in ADCapNet-AM. Finally, the predicted outcomes are analyzed and balanced with the existing prediction techniques to showcase the effectiveness of the designed model.

Keywords

World cities economics analysis economic status prediction Adaptive Deep Capsule Network with Attention Mechanism Improved Humboldt Squid Optimization Algorithm

1. Introduction

The growing economic interdependence of national economies worldwide due to a sharp rise in the international movement of capital, products, services, and technology is known as economic globalization [1]. It is the process of growing economic integration among nations, which results in the development of a global marketplace or single world market [2]. In contrast, business globalization is focused on the reduction of international trade regulations as well as taxation and some other barriers that reduce global trade. Globalization of production is the process of acquiring goods and services from a specific source that has been located throughout the world to take benefit of differences in cost and quality [3]. The current developments in globalization can be mostly attributed to the integration of advanced and less developed economies through immigration, trade barrier reduction, and additional economic reforms, along with foreign direct investment [4,5].

Infrastructure is a fundamental requirement for economic growth and has a big influence on the local economic structure [6]. The term “urban infrastructure economic benefit” refers to the benefits of using city infrastructures, which involve encouraging consumption, raising income, boosting exports, and more [7]. The significance of city communications in the progression of economic advancement has grown with the development of urban scale and the swift development of the urban economy [8]. Worldwide, numerous significant cities place a strong emphasis on building urban infrastructure and are crucial for forecasting economic development. In today’s society, the impact of urban infrastructure on economic growth is becoming more and more evident [9]. Urban infrastructure is required to keep the urban economy functioning effectively [10]. It offers the essential services needed for urban economic activity. However, several cities have a shorter history of building urban infrastructure, which has resulted in numerous issues related to its development, leading to low levels of use and poor operational efficiency [11]. Urban economies rely on well-developed infrastructure, including transportation networks, utilities, communication systems, and public services. Infrastructure development is crucial for supporting economic activities and ensuring the smooth functioning of the urban economy [12].

Increasing the economic advantages provided by urban infrastructure is a widespread issue in many nations, particularly emerging nations [13]. In addition to economic growth, other economic activities are impacted by the urban structures of cities [14]. This breaks down the economic system into four categories such as government purchases, investments, consumption, and external demand [15]. These categories are considered based on the macroeconomic theory of national economic identity. Urban infrastructure projects have a reciprocal impact on each other and contribute significantly to economic benefits within cities [16]. A complete analysis of the economic benefit of urban communication is suggested using an integrated methodology. Analyzing the world cities’ economies will lead to inaccurate decisions due to incomplete data [17]. It also accounts for the social and environmental impacts of economic activities, providing a limited perspective. A deep knowledge-based economic prediction model is computationally intensive and requires significant resources in terms of processing power, memory, and time. Implementing and maintaining such models is challenging with limited resources. Therefore, an automated economic analysis strategy is introduced for the world cities to tackle this problem.

The significant contributions of the designed world cities economics analysis model are provided below.

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To implement an adaptive deep learning-based world cities economics analysis framework for analyzing the data in real-time that enables timely responses to provide changes in economic conditions.
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To develop a heuristic algorithm known as IHSOA from the conventional HSOA by updating the random attribute for tuning the parameters from ADCapNet-AM to enhance the efficiency of the proposed model.
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To design a deep learning model ADCapNet-AM, which is the combination of both capsule network and attention mechanism with parameter optimization using IHSOA for the economic prediction of world cities.
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To evaluate the designed economic prediction model with other existing models to reveal the efficacy of the proposed framework.

The remaining sections of this research work are described below. Literature survey and problems of existing world cities’ economic prediction models are described in Section 2. The architectural view and dataset description of the designed model are explained in Section 3. Preprocessing and feature extraction techniques of the proposed mechanism for parameter tuning are described in Section 4. Adaptive deep networks with attention mechanisms for analyzing the world cities’ economics are explained in Section 5. In Section 6, the results of the designed model are explained. In Section 7, the overall summary of this research work is described.
2. Literature survey

2.1 Related works

In 2012, Shirov et al. [18] examined the constraints placed on human resources as a result of the Russian economy growth. It was determined how much productivity has contributed to recent economic growth. The main element influenced by labor productivity in the Russian economy was made public. The potential production dynamics in the high-tech industry were also reviewed.

In 2018, Suna et al. [19] proposed an integrated approach to analyze the effects of Chinese autonomous municipalities at different levels. The economic benefits of urban infrastructure were divided into four effects: spending, investment, administration purchase, and outside demand. Initially, the economic advantage of urban infrastructure was assessed. Next, a coupling synchronization degree model was constructed to assess the development along with different impacts. Finally, a panel regression model was used to study the impact of synchronized development between four factors on the degree of economic benefit from urban infrastructure. Based on the findings, the integrated growth level of the four effects could help to accelerate the enhancement of urban communication. The suggested approach achieved a good job of examining the financial benefits of urban infrastructure.

In 2022, He and Li [20] developed a Deep Neural Network (DNN)-based economic forecasting framework for smart cities’ long-term economic development. Cities need traffic management to ensure that goods and people may travel around the city without restriction. Finding a public parking spot was challenging in smart cities due to the large number of cars trying to enter congested regions. It was inconvenient for divers and citizens. To address the problem, many traffic management organizations have deployed ANN and intelligent parking systems with contemporary car systems. When compared to existing techniques, the current experimental results of the deep knowledge-based economic forecasting model improve traffic inference, traffic flow exactness prediction, and smart parking.

In 2021, Andres et al. [21] implemented an advanced machine learning artificial DNN technique to forecast the knowledge economy index for 71 rising and promising nations between 1995 and 2017. When used in conjunction with a K-closest neighbor algorithm-based data imputation process, a DNN could handle missing data issues more effectively than other techniques. The proposed model produced a low quadratic and absolute error after a 10-fold validation. The model had a high degree of predictive capacity, and the results were reliable and effective. On taken into account, this research had closed gaps resulting from lacking data, enabling successful policy approaches. When compared to existing approaches, the newly developed model would perform well.

In 2019, Gupta et al. [22] recommended a cryptocurrency-based economic analysis model that has gained popularity over the past several years. Numerous researches were conducted on the prediction of bitcoin prices using a variety of metrics such as social media and bitcoin elements. This study compared several factors influencing the forecast of the price of bitcoin using the Root Mean Square Error (RMSE) and a variety of neural networks, including “Convolutional Neural Networks (CNN), Long Short Term Memory (LSTM), and Gated Recurrent Units (GRU)”. Here, experimental analysis proved that the proposed analysis model performed well when balanced with other models.

In 2020, Wang et al. [23] developed a discrete choice model, which was capable of providing economic data. Here, the proposed model especially with high sample sizes could automatically acquire utility features and uncover patterns of behavior that were not specified by domain experts. However, because of autonomous learning capacity, and elevated sensitivity to hyperparameters the model non-identification has occurred. The economic information derived from the deep network could be incorrect when the sample size was limited. The numerical challenge of maintaining both the estimation and assessment errors of a network was crucial and optimizing to find the optimal solution was also a challenging task. Based on the experimental outcome, the proposed model could improve the reliability of the economic communication extracted from the deep network.

In 2022, Cheng and Huang [24] developed a DNN for analyzing the world economy based on Gross Domestic Product (GDP). Based on this proposed model, the overall production of goods and services over some time was evaluated to analyze the economic growth among cities. The experimental result showed that the western and central regions were experiencing tremendous expansion. The coefficient of variation for the difference in GDP between the major industrial provinces was approximately 1 before 2013 and then decreased.

In 2022, Park et al. [25] developed a deepLSTM-based framework, which was better for decision-making and economic assessment. Based on sequential data, a generated model was utilized to predict the economic growth rate and crisis within the economic cycle. Here, with the help of Artificial Intelligence (AI) machine knowledge, the economic patterns of each city were assessed. The resultant outcomes were balanced with other traditional predictive models to analyze the efficiency of the designed model. The private debt in urbanized countries and government debt in rising countries were the main factors that limited economic growth.

Table 1
Features and challenges of the traditional prediction model for analyzing the world cities economics.

Author [citation]	Methodology	Features	Challenges
Shirov et al. [18]	Methodological approaches	This method is suitable for real-time analysis and helps to ensure accuracy.	This method performs a time-consuming data collection and analysis process.
Suna et al. [19]	Coupling coordination degree model	This method helps to provide effective urban development planning. It helps to understand the spatial differentiation between the social economy and the ecological environment.	It increases the interdependence among the modules which makes the system more complex and difficult to understand.
He and Li [20]	DNN	It can handle large and complicated data and attain state-of-the-art efficacy on a wide range of problems.	This method needs a large amount of data and analytical resources to train the network. It is more expensive.
Andres et al. [21]	K-closest neighbor algorithm	It is easy to implement and versatile for several calculations.	This algorithm leads to storage issues in case of large datasets and the speed of processing is also slow.
Gupta et al. [22]	Crypto economy	It is a cheaper and faster model. It provides financial services worldwide, which promotes economic growth in an impoverished region.	Data loss and cyber attacks are crucial challenges in the crypto economy.
Wang et al. [23]	Discrete choice model	This method can reduce sources of bias and provide a border approach to economic assessment.	This method requires the most significant data in case of complex choice scenarios.
Cheng and Huang [24]	DNN	It is flexible in modeling complex data. It is more efficient and laborious shortcomings of the manual feature design.	Overfitting issues are high in this model.
Park et al. [25]	LSTM	Sequential and long-range dependencies data are handled by using this method.	Large data input is needed, which is a time-consuming and difficult process.

2.2 Problem statement

The economic prediction framework helps to predict the unemployment, productivity, outcome, and other key factors that will develop the country’s overall economy. But, this model depends on accurate and relevant data. If the data used for training the model gets biased then the forecasting model will also lead to flaws. The features and challenges of the existing traditional economic prediction model are generated in Table 1. The methodological approach [18] is well-suited for real-time analysis and ensuring accuracy but it has time-consuming data collection and analysis process. The coupling coordination degree model [19] provides effective urban development planning. Even though high coupling increases the interdependence among the modules it makes the system more complex and difficult to understand. DNN [20] can handle large and complicated data and attain state-of-the-art efficacy on a wide range of problems. Still, this method needs a large amount of data and analytical resources to train the network. The k-closest neighbor algorithm [21] is easy to implement and versatile for different calculations. Moreover, this algorithm leads to storage issues in case of large datasets and the speed of processing is also slow. Crypto economy [22] provides financial services worldwide, which promote economic growth in an impoverished region and it is a cheaper and faster model. However, data loss and cyber attacks are crucial challenges in the crypto economy. The discrete choice model [23] can reduce sources of bias and provide a border approach to economic assessment. However, this method requires the most significant data in case of complex choice scenarios. DNN [24] is more efficient and laborious shortcomings of the manual feature design and is flexible in modeling complex data. Yet, Overfitting issues are high in this model. LSTM [25] is utilized to handle sequential and long-range dependencies of data. However, large data input is needed, which is a time-consuming and difficult process. To overcome these difficulties, an innovative deep learning-based analyzing the world cities economics framework is implemented.

3. Proposed intelligent deep learning network for analyzing the world cities economics: Structural view and dataset description

3.1 Architecture of proposed world cities economics analysis model

The world economy is a collaboration of countries that are tied together by economic activity. GDP is a primary indicator of economic performance. It evaluates the total economic output of a city, including the value of goods and services produced. Cities with high GDP are often considered economic powerhouses. Employment opportunities and job marketing are crucial aspects of a city’s economy. High-employment cities tend to attract a diverse and skilled workforce [26]. The presence of research institutions, tech startups, and investments in research and development indicate cities’ commitment to modernization. Cities that serve as global financial centers play a crucial role in the world economy. Even though cities with high real estate values and living costs may face challenges related to affordability and with the increasing awareness of environmental issues in cities are evaluated [27]. The dynamics of world city economies are changed based on global economic trends, geopolitical factors, and technical growth. Hence, world economic analysis is a complex task. Therefore, adaptive deep knowledge-based analysis of the world cities economics framework is designed and implemented. The architectural layout of the proposed world cities economics analysis model is provided in Fig. 1.

Figure 1.

Architectural view of proposed world cities economic analysis model using a deep learning technique.

A new adaptive deep knowledge-based model is developed for analyzing the world cities’ economics for handling large datasets and is generalized well to diverse economic contexts. This scalability is essential when analyzing economic data at a global scale. The data needed for this research work are accumulated from the standard benchmark. Further, the gathered data are involved in the data pre-processing phase. Here, data cleaning, data scaling, and Nan value removal methods are applied to achieve better predictions without any false rate. Next, pre-processed data are fed to the feature extraction phase where the Restricted Boltzmann Machine (RBM) model is applied because RBMs are capable of handling noisy data and extracting meaningful features, which make the network robust in scenarios. Finally, the extracted features are fed to the prediction stage. Here, the ADCapNet-AM network is designed, which is the formulation of a deep capsule network and attention mechanism that aims to reduce the redundancy in data representation by using capsules to represent specific entities. The efficiency of the designed model is boosted by optimizing parameters like “hidden neuron count, epoch size, and step per epoch count” from the ADCapNet-AM network using IHSOA. Fine-tuning aims to minimize error rates like Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and Mean Absolute Error (MAE). Evaluate the outcome of the designed model with other validated datasets to ensure the effectiveness of the designed model. Thus, the designed ADCapNet-AM-based world cities economics analysis model achieves better prediction outcomes.

3.2 Collection of world cities economic dataset

The designed world cities economic analysis framework gathers the data from the standard database and the descriptions related to these datasets are mentioned below.

Dataset 1: The database utilized for this research work is the “World Economic Outlook Database” which is available at https://www.imf.org/en/Publications/SPROLLs/world-conomic-outlook-databases#sort=%40imfdate%20descending and it is accessed on 2024-02-05. This dataset contains macroeconomic data series from the International Monetary Fund (IMF). The database contains analysis and projection of economic developments globally and for individual cities.

Database 2: The second database needed for this research work is “city statistic economy”, which is available at the link https://stats.oecd.org/index.aspx?queryid=119047 and it was accessed on 2024-02-05. This dataset allows users to retrieve aggregate statistics for a subset of the entities in the database, which is used for analyzing the world cities’ economic analysis.

The collected data from the above link are represented as $R_{k}^{c a p}$ , where $k = 1, 2, \dots, K$ . The term $K$ indicates the total amount of data collected.

4. Preprocessing and feature extraction stages with description of the proposed optimization mechanism for parameter optimization

4.1 Data preprocessing

The process of transforming raw data $R_{k}^{c a p}$ into clean data is done in the data preprocessing phase. The dataset is processed to check for missing values, noisy data, and other inconsistencies. In this designed model, preprocessing is performed by using data cleaning, data scaling, and null value removal methods.

Data cleaning: Raw data $R_{k}^{c a p}$ is applied as input. This approach helped to identify and eliminate mistakes from data to raise the quality of data. Data quality techniques effectively clean the data by resolving inconsistencies, finding or eliminating outliers, smoothing noisy data, and replacing the missing values. There are multiple methods for resolving issues with missing data. Certain analysis methods are extremely durable and unaffected by missing data. Eliminating the records with missing data is an alternative strategy [28]. However, it may produce data misinterpretation and it forecasts new values using an alternate strategy. In this data preprocessing phase, duplicated records are removed to ensure the integrity of data. Next, normalize the numerical features for a consistent scale. Finally, transformation is applied to address the skewness in numerical features and cleaned data $R_{p}^{c a p}$ is achieved as an outcome.

Data scaling: Cleaned data $R_{p}^{c a p}$ is used for the data scaling process, which is utilized to combine or transform the data into ranges and formats that are suitable for prediction models. Min-max algorithm is used in the data scaling process [29].

Min-max algorithm: Original data are linearly transformed using the min-max algorithm. The minimum and maximum variable in sample data is represented as $C_{m n}$ and $C_{m x}$ . Scaling algorithm maps a value $X$ using the formula in Eq. (1).

X = (\frac{X - C_{m n}}{C_{m x} - C_{m n}}) + C_{m n}

(1)

The variables in the training sample vary in the interval $[- 1, 1]$ based on the linear mapping. Furthermore, scaling the input data is necessary for NN models to facilitate a faster and more robust learning process. Scaled data $R_{g}^{s c l}$ is achieved as an outcome.

Null value removal: Scaled data $R_{g}^{s c l}$ is fed to null value removal. The null value represents missing or undefined data in the dataset [30]. Removing these data is crucial in the pre-processing phase. Yet, this method removes the entire row or column but it leads to loss of valuable information. Hence, null values are replaced with mean, median, or mode values of the respective feature. Finally, the preprocessed data $R_{w}^{n l}$ is achieved as an outcome.

4.2 DRBM-based feature extraction

Selecting the relevant information from pre-processed data $R_{w}^{n l}$ is a crucial part of a deep knowledge network. Hence, feature extraction reduces the data complexity while retaining the important information. In this proposed model, Deep RBM-based feature extraction is developed because RBMs allow the model to handle uncertainty in the data and make them more robust.

RBM [31] is an unsupervised neural network consisting of a visible and a hidden layer. This network learns to reconstruct the input data by adapting the weights among the layers. The contrastive divergence method is utilized to adjust the weights in a way that the reconstruction of input data is intensified. The collected data are represented in the visible and hidden layers enabling to extraction of relevant features from the visible layer. The neurons of each layer are interconnected, which is bidirectional and allows the data to be transmitted in both directions [32].

The neurons in the visible layer are denoted as $v_{1}, v_{2}, \dots v_{w}$ , here $w$ is represented as the total number of neurons in the invisible layer. The neurons in the hidden layer are represented as $h_{1}, h_{2}, \dots h_{m}$ , where $m$ is indicated as the total amount of neurons in the hidden layer. It is a probabilistic model used in deep knowledge networks to identify the complex relationship among the data [33]. The probabilistic distribution among $v$ and $h$ is defined based on entropy function and the numerical form is provided in Eq. (2).

\begin{matrix} E_{p} (v, h) = - h^{y} E v - g^{Y} v - j^{Y} h \end{matrix}

(2)

\begin{matrix} E_{p} (v, h) = - \sum_{k = 1}^{d, n} v_{p} h_{p} E_{p} - \sum_{k = 1}^{n} g_{p} v_{p} - \sum_{h = 1}^{n} g_{p} l_{p} \end{matrix}

(3)

By using this entropy function, it is probable to allocate a probability to each neuron. The probability of the visible layer is the sum of all probabilities of all vectors from the hidden neuron count and their mathematical form is described in Eq. (4).

Q (v) = \frac{\sum_{j} e^{- E (v, h)}}{\sum_{v, h} e^{- E (v, h)}}

(4)

In the RBM structure, the neighboring neurons of the same layers are not interconnected [34]. It effectively performs dimensional reduction by capturing the most relevant features and discarding less significant data. The most relevant feature generated is represented as $F R_{l}^{e x}$ .

4.3 Proposed IHSOA

Purpose: The proposed optimization model IHSOA is designed to enhance the performance of the ADCapNet-AM network by optimizing key hyperparameters such as the hidden neuron count, epoch size, and step per epoch count. This optimization aims to minimize error metrics, including MSE, RMSE, and MAE. The proposed IHSOA algorithm is derived from the conventional HSOA.

The HSOA can be easily parallelized, significantly reducing computation time and making it highly suitable for large-scale optimization problems. It is effective in navigating complex optimization landscapes with multiple global optima, ensuring a higher probability of finding the best solution. However, HSOA is computationally intensive, demanding significant processing power, especially for complex problems. It often requires a large number of function evaluations to achieve the optimal solution, which can be time-consuming.

Novelty: The integration of IHSOA with the ADCapNet-AM network is a novel approach that specifically addresses the above-mentioned challenges. This novelty lies in the improvement of the conventional HSOA. This includes updating the random variable used in the optimization process, which enhances the algorithm’s performance in terms of speed and accuracy. This adaptive mechanism, provided in Eq. (5), helps in dynamically adjusting the search process, leading to better optimization results.

q = - 1 - C_{i t} * (\frac{(- 2)}{M_{i t}})

(5)

Here, the term $q$ is indicated as a random variable, $C_{i t}$ shows the current fitness value, and $M_{i t}$ is defined as the maximum iteration value. The adaptive formulation is placed in Eq. (14).

In this algorithm, each solution representing a set of hyperparameters being optimized is encoded within the population. Solution encoding involves encoding the hyperparameters in every individual within the population. Through iterative evaluation and selection, the best solution is identified from the population. The value obtained from this process is referred to as the optimized value. The evaluation function assesses the performance of each encoded solution, guiding the search process toward the optimal hyperparameters.

HSOA [35]: It is a nature-based optimized algorithm that stimulates the natural behavior of squid. Generally, Humboldt squid is large and reach up to a length of 2 m. It has 10 appendages, each equipped with suckers and a sharp teeth-like structure that allow the squid to grasp prey. The strategy of squid feeding, swimming, mating, and locomotion are used in this optimization algorithm. The normal behavior of squid varies from other animals, thus making it a unique predator. The usual behavior of squid helps to find an optimal solution for an optimization problem.

HSOA follows hunting, moving, and mating strategy and the mathematically modeled using five processes “attacking the fish, escape of fish, successful attack, attack on small squid, and mating of squid”.

Attack of school fish: The attacking strategy is used to stimulate the attack of fish using the formula in Eq. (6).

\begin{aligned} Z D_{n e w, p}^{f} = C_{b} + B_{h r t} \cdot (- Z H_{n e w, q 1}^{f} - L o l S j j_{q 2}^{f}) \end{aligned}

(6)

Here, the position of the squid at $f^{th}$ aspect is indicated by $Z D_{n e w, p}^{f}$ and the locomotion velocity of the squid is signified as $B_{h r t}$ . The random integers $q 1$ and $q 2$ are used in statistics to consider randomness and probability, which vary in the range of $[1 - s i z e o f p o p u l a t i o n]$ .

Successful attack: After obtaining the updated spot for squid, the current position of squid is superseded with the new one using the formula in Eq. (7).

Z D_{p}^{f} = {\begin{cases} Z D_{p} = Z D_{n e w, p} & if H_{k, n e w p} < H_{d,} p \\ escape strategy & otherwise \end{cases}

(7)

Here, the current and the new fitness function of $p^{th}$ dimension are indicated as $H_{k, n e w p}$ and $H_{d p}$ , respectively.

Extraordinary Escape strategy: If the school fish gets attacked then, these fish escape to a randomly selected location. The velocity and location of newly updated fish are generated using the formula in Eq. (8).

Z D_{n e w, p} = {\begin{cases} Z D_{p} + \underset{\to}{q} (y b e s t - Z D_{p}) \cdot B g & if g < 0.1 \cdot {max}_{f} \\ Z H_{p} + t m \cdot (A r c Z_{q_{1}} - L o l s j j_{q 2}) \cdot B g & otherwise \end{cases}

(8)

The current iteration and maximum iteration of evaluation are denoted as $f$ and $max_{f}$ respectively. Here, the term $Z D_{n e w, p}$ is indicated as the new position of $p^{th}$ fish and $q$ is indicated as a random vector. If the function is evaluated in its initial generation, the fishes move towards the best position otherwise move towards the random position.

Attacking stronger squid: If the fish and squid do not find any best optimal solution in the existing step, then the stronger squid position is updated. The larger squid eats the smaller one and then moves towards the new position. During this phase, a new position is updated using the formula in Eq. (9).

Z M_{n e w, p}^{f} = Z D_{n e w, p}^{f} + B_{h r t 2} \cdot (Z D_{n e w, p}^{f} - Z_{n}^{f})

(9)

Here, the second parameter vector is indicated as $B_{h r t 2}$ . During this phase, larger squid are moved towards and smaller squid remain in the optimal position.

The strategy used for the Squid Matting process: This process is performed to generate the position of squid based on a deferential evolutionary algorithm. The numerical form used to execute this phase is provided in Eq. (10).

E_{g} = (\begin{array}{l} ϖ \cdot C D + (1 - ϖ \cdot q B_{s}) \cdot δ + (1 - λ) \cdot p (q 1) \\ + E \cdot p (q 2) - p A (q 3) \end{array})

(10)

Here, the weights of the searching process are denoted as $ϖ$ , $δ$ and $λ$ respectively. The value of $E$ is measured using the formula in Eq. (11).

E = M x {β \cdot π (1 - β), 1 - π}

(11)

The values of $π$ and $β$ are estimated using the formula in Eqs (12) and (13).

\begin{matrix} π = η_{π} + v_{1} \cdot c \end{matrix}

(12)

\begin{matrix} β = η_{β} + v_{2} \cdot \overset{⇀}{t} m \end{matrix}

(13)

It is noted that the value of the parameter $β$ must be greater than zero and I is measured using the formula in Eq. (14).

β = η_{β} + 0.1 \tan (π . q)

(14)

In the conventional HSOA, the random number $q$ typically varies within a fixed range, such as $[0, 1]$ . This fixed range may lead to suboptimal solutions because it does not adapt to the progress of the optimization process, potentially causing the algorithm to either converge prematurely or miss the global optimum. To address these issues, an adaptive mechanism for updating the random number is introduced. This mechanism dynamically adjusts the range of the random number based on the current iteration and the maximum number of iterations. This adaptive approach is described by Eq. (5).

The pseudocode of the proposed IHSOA is given in Algorithm 1 and the flowchart of IHSOA is given in Fig. 2.

Figure 2.

Flowchart of IHSOA.

5. Adaptive deep learning with attention mechanism for analyzing world cities economics

5.1 Deep capsule network

Deep capsule networks are the type of dynamic routing mechanisms, allowing them to adapt to changes in input patterns of neural networks that can capture hierarchical relationships among data which is used in dynamic routing mechanisms, allowing them to adapt to changes in input patterns. Capsule Networks utilize dynamic routing mechanisms to establish relationships between capsules, facilitating the routing of information based on spatial hierarchies. This dynamic routing can lead to more robust feature extraction, especially in prediction models. In traditional CNNs, pooling layers are commonly used to downsample spatial dimensions. However, in a capsule network, the spatial information is preserved throughout the network without a pooling layer. Capsule networks aim to reduce the redundancy in data representation by using capsules to represent specific entities. This can result in more compact and informative representations, potentially leading to better generalization. The dynamic routing mechanism and the ability to capture hierarchical features contributed to the network to achieve efficient prediction outcomes. Yet, it suffers from heavy parameter learning and has poor performance on large or complex datasets. Hence, a deep capsule network with an attention mechanism is intended in this designed world cities economics analyzing model.

Capsule network [36] is designed to alleviate the limitations of traditional neural networks, particularly in managing hierarchical relationships within data. Self-attention layer is added to enable the parallel processing of data and its calculation formula with the input layer is provided in Eq. (15).

Y_{(m^{l}, m^{l + 1}, f^{l + 1})}^{l} = y_{m}^{r l} \times E_{(m^{l}, m^{l + 1})}

(15)

Here, the total number of layers is indicated as $l$ and the dimension of the capsule is denoted as $f$ . The term $E_{(m^{l}, m^{l + 1})}$ is denoted as the weights of the matrix at $l^{th}$ layer. The output layer $E_{(m^{l}, m^{l + 1})}$ is evaluated using the formula in Eq. (16).

D_{m}^{l + 1} = Y_{(m^{l + 1})}^{l 1} \times (V_{(m^{l + 1})}^{l} + H_{m^{l + 1}}^{l})

(16)

Here, the term $H_{m^{l + 1}}^{l}$ is denoted as log prior’s matrix, which contains all coupling coefficient weights. The basic structural design of the capsule network is given in Fig. 3.

Figure 3.

The basic architecture of the capsule network.

5.2 Deep capsule network with attention mechanism

Capsule networks and attention networks represent pioneering architectures in the realm of deep learning. Combining these two approaches offers numerous advantages: hybrid networks augment the comprehension of complex structures by enabling capsules to dynamically focus on pertinent components. This synergy harnesses the strengths of both methodologies, promising advancements in understanding and processing intricate data patterns. Attention mechanisms lessen the computational cost and memory usage by selecting and processing only important parts of the input features.

Here, the asymmetric matrix $S^{l}$ is determined based on the numerical form mentioned in Eq. (17).

S_{(m^{l + 1})}^{l} = \frac{Y_{(m^{l + 1})}^{l 1}}{\sqrt{f^{l}}}

(17)

The hyperparameter $f$ helps to balance the coupling coefficient and log priors. Finally, the output of the capsule network is calculated by the activation function and the formula is provided in Eq. (18).

B_{m}^{l} = S q (d_{m}) = (1 - \frac{1}{e^{∥ d_{m} ∥}}) \frac{d_{m}}{‖ d_{m}^{l} ‖}

(18)

Capsule networks are efficient in their ability to handle variations of data, while attention networks are better in selectively processing informative regions. Together, they can improve robustness by allowing capsules to attend to relevant features and adapt to variations in data.

Figure 4.

Recommended ADCapNet-AM-based world cities economics analysis framework.

5.3 Implementation of ADCapNet-AM for world cities economics analysis

The proposed ADCapNet-AM model is the combination of both a capsule network and an attention mechanism, which is utilized for analyzing the world cities’ economics. The extracted features are applied to the ADCapNet-AM model for world cities’ economic analysis. Here, attention mechanisms enable selective information routing by assigning different weights to different parts of the input. When integrated with capsule networks, this selective routing helped to focus on crucial features and relationships, leading to more effective information flow within the network. Capsule Networks aim to reduce redundancy by representing specific features. Attention Networks can further enhance this by allowing the network to focus on the most relevant features, leading to more compact and informative. The efficiency of the designed model is enhanced by optimizing the variables like “hidden neuron count, epoch size, and step per epoch count” from the ADCapNet-AM network using IHSOA. ADCapNet-AM-based approaches incorporate a wide range of data sources and variables. This allows for the integration of empirical data into this model, enhancing their accuracy and relevance to real-world economic scenarios. Three hyperparameters were optimized hence the size of a solution is 3. The aim of this optimization is the minimization of error rates like “MSE, RMSE, and MAE”. The objective function of the designed ADCapNet-AM-based world cities economics analysis model is provided in Eq. (19).

O_{f n} = \underset{{E R_{g}^{A c p}, P Y_{k l}^{A c p}, G F_{h}^{A c p}}}{\arg min} (M s E + R m S e + M a E)

(19)

Here, the term $E R_{g}^{A c p}$ is represented as optimized hidden neuron count that varies in the range of $[5 - 225]$ , $P Y_{k l}^{A c p}$ is indicated as optimized epoch size, which varies in the range of $[5 - 50]$ , and $G F_{h}^{A c p}$ is specified as optimized step per epoch count varies in the range of $[500 - 1000]$ . The formulas used for measuring the error rate are mentioned below.

Root Mean Square Error (RmSe) is measured using the formula in Eq. (20).

R m S e = \sqrt{\sum_{k = 1}^{g} \frac{({\overset{⌢}{R}}_{s} - R_{s})}{w}}

(20)

Mean Absolute Error (MaE), is measured using the formula in Eq. (21).

M a E = \frac{1}{w} \sum_{k = u}^{g} | R_{s} - {\overset{⌢}{R}}_{s} |

(21)

Mean Squared Error (MsE), is measured using the formula in Eq. (2).

M s E = \frac{1}{w} \sum_{k = u}^{g} | R_{s} - {\overset{⌢}{R}}_{s} |

(22)

Here, the entire observation count is expressed as $w$ . The predicted and actual scores are represented as $R_{s}$ and ${\overset{⌢}{R}}_{s}$ correspondingly. The diagrammatic representation of the proposed ADCapNet-AM-based world cities economic analysis framework is illustrated in Fig. 4.

Figure 5.

Cost function analysis of developed world cities economic analysis framework using adaptive deep networks concerning (a) dataset 1, (b) dataset 2.

Figure 6.

Comparative analysis of developed world cities economic analysis framework among several existing techniques concerning (a) MAE, (b) MASE, (c) MEP, (d) ONE-NORM, (e) RMSE, (f) SMAPE, (g) TWO-NORM using dataset 1.

Figure 7.

Figure 8.

Comparative analysis of developed world cities economic analysis framework among several existing algorithms concerning (a) MAE, (b) MASE, (c) MEP, (d) ONE-NORM, (e) RMSE, (f) SMAPE, (g) TWO-NORM using dataset 1.

Figure 9.

6. Results and discussion

6.1 Experimental setup

The designed world economic analysis model using deep learning was stimulated in Python. The amount of population needed for this research work is 10, the chromosome length is 3 and the maximum number of iterations is 100. The suggested model was evaluated on different databases to analyze the effectiveness of the developed world cities’ economic analysis model. The traditional techniques and algorithms utilized for the comparison were Ladybug Beetle Optimization (LBO) [37], Barnacles Mating Optimizer (BMO) [38], Grasshopper Optimization Algorithm (GOA) [39], Humboldt Squid Optimization Algorithm (HSOA) [35], and the techniques like Densenet [40], Mobilenet [41], and CNN [42].

Table 2
Comparative outcomes of the proposed world cities economic analysis framework using dataset 1.

Using conventional algorithms
TERMS	LBO-ADCapNet- AM [37]	BMO-ADCapNet- AM [38]	GOA-ADCapNet- AM [39]	HSOA-ADCapNet- AM [35]	IHSOA-ADCapNet-AM
MEP	5.847639	4.828326	4.130901	3.433476	2.682403
SMAPE	0.06683	0.055181	0.04721	0.03924	0.030656
MASE	166.2712	148.5732	124.1869	106.6722	90.23646
MAE	7.949678	6.531009	5.381116	4.594474	3.683208
RMSE	16.86994	15.24633	13.63855	12.80124	11.59263
ONE-NORM	3704.55	3043.45	2507.6	2141.025	1716.375
TWO-NORM	364.172	329.1231	294.4158	276.3408	250.2506
Using conventional techniques
Terms	Densenet [40]	Mobilenet [41]	CNN [42]	ADCapNet-AM [26]	IHSOA-ADCapNet-AM
MEP	5.740343	5.203863	3.540773	3.218884	2.682403
SMAPE	0.065604	0.059473	0.040466	0.036787	0.030656
MASE	160.5244	162.0732	114.7412	97.00869	90.23646
MAE	7.862929	7.414539	4.777468	4.194421	3.683208
RMSE	16.79164	16.60048	13.07735	12.00587	11.59263
ONE-NORM	3664.125	3455.175	2226.3	1954.6	1716.375
TWO-NORM	362.4817	358.3551	282.3012	259.1711	250.2506

6.2 Cost function analysis

The cost function of the world economics analyzing process using deep techniques is specified in Fig. 5. This result shows that the suggested ADCapNet-AM-based world cities economic analysis framework has minimum cost with 82.14% than LBO-ADCapNet-AM, 80% than BMO-ADCapNet-AM, 75% than GOA-ADCapNet-AM, 72.2% than HSOA-ADCapNet-AM at 10^th iteration of dataset 1. Thus, the competence of the designed model is superior by comparing the proposed model with existing models.

6.3 Comparative analysis of the proposed model among existing techniques

The comparative analysis of the world cities economics prediction model using deep techniques over existing techniques based on dataset 1 is specified in Fig. 6 and dataset 2 is illustrated in Fig. 7. Based on Fig. 6b, the MASE of the suggested model is minimized with 41.9% than Densenet, 40% than Mobilenet, 18.1% than CNN, and 15.8% than ADCapNet-AM for the activation function as 2 using dataset 1. This proved the superior efficiency of the proposed economic analysis model over different conventional models.

6.4 Comparative analysis of the proposed model among existing algorithms

The comparative analysis of the world cities economics using deep techniques over existing algorithms using dataset 1 is specified in Fig. 8 and using dataset 2 is illustrated in Fig. 9. Based on Fig. 9c, the MEP value of the suggested model is minimized with 59.6% than LBO-ADCapNet-AM, 50% than BMO-ADCapNet-AM, 47.9% than GOA-ADCapNet-AM, 34.2% than HSOA-ADCapNet-AM for the activation function as 3 using dataset 2. Thus from this analysis, the accomplishment rate of a suggested model using adaptive technique is enhanced than other existing conventional algorithms.

Table 3
Comparative outcomes of the proposed world cities economic analysis framework using dataset 2.

Based on different conventional algorithms
TERMS	LBO-ADCapNet- AM [37]	BMO-ADCapNet- AM [38]	GOA-ADCapNet- AM [39]	HSOA-ADCapNet- AM [35]	IHSOA-ADCapNet-AM
MEP	7.188841	5.257511	4.935622	3.701717	3.165236
SMAPE	0.082158	0.060086	0.056407	0.042305	0.036174
MASE	197.2518	155.599	140.3514	117.3998	97.9775
MAE	10.00059	7.232457	6.516309	5.083369	4.205043
RMSE	19.18829	16.19217	15.15033	13.57468	12.20078
ONE-NORM	4660.275	3370.325	3036.6	2368.85	1959.55
TWO-NORM	414.2183	349.5409	327.0508	293.037	263.3786
Based on different conventional techniques
Terms	Densenet [40]	Mobilenet [41]	CNN [42]	ADCapNet-AM [26]	IHSOA-ADCapNet-AM
MEP	6.276824	6.008584	4.291845	3.809013	3.165236
SMAPE	0.071735	0.06867	0.04905	0.043532	0.036174
MASE	183.0705	171.4568	136.4526	128.3179	97.9775
MAE	8.612822	8.10794	6.086481	5.335032	4.205043
RMSE	17.67659	17.07414	15.08578	14.0157	12.20078
ONE-NORM	4013.575	3778.3	2836.3	2486.125	1959.55
TWO-NORM	381.5852	368.5801	325.6573	302.5575	263.3786

Table 4

Statistical analysis of the proposed world cities economic analysis model using both datasets 1 and 2 among conventional algorithms.

TERMS	LBO-ADCapNet- AM [37]	BMO-ADCapNet- AM [38]	GOA-ADCapNet- AM [39]	HSOA-ADCapNet- AM [35]	IHSOA-ADCapNet-AM
Using dataset 1
Best	1.45436	1.47732	1.3919	1.404949	0.766265
Worst	5.103879	4.285308	2.049928	2.237859	3.937075
Mean	2.116487	1.785003	1.697006	1.606031	0.972583
Median	1.881018	1.47732	1.571487	1.515767	0.766265
Standard deviation	0.890778	0.541589	0.314788	0.274023	0.643501
Using dataset 2
Best	1.326632	1.290388	1.375089	1.319559	0.755705
Worst	5.933887	1.700699	5.566049	4.882136	2.605743
Mean	1.875991	1.421687	1.512476	1.401653	0.940709
Median	1.374979	1.290388	1.375089	1.319559	0.755705
Standard deviation	1.27095	0.1914	0.681879	0.498272	0.555012

6.5 Numerical analysis of the proposed model using dataset 1

The statistical efficacy analysis of the designed world cities economic analysis model using dataset 1 over existing conventional algorithms and techniques is illustrated in Table 2. From the below-provided table results, the MEP value of the recommended model is reduced by 54.12% than LBO-ADCapNet-AM, 44.4% than BMO-ADCapNet-AM, 35.06% than GOA-ADCapNet-AM, and 21.8% than HSOA-ADCapNet-AM using dataset 1. Thus, the proposed model generates superior fitness than another conventional framework.

6.6 Numerical analysis of the proposed model using dataset 2

The numerical effectiveness analysis of the designed world cities economic analysis model using dataset 2 over existing conventional algorithms and classifier is illustrated in Table 3. From the below table results, the SMAPE value of the advanced framework is minimized with 49.5% than Densenet, 47.3% than Mobilenet, 26.2% than CNN, and 16.9% than ADCapNet-AM. It is ensured that the suggested world cities economics analysis model generates better performance than other existing schemes.

6.7 Statistical analysis among various algorithms using dataset 1 and dataset 2

The statistical analysis of the designed world cities economic analysis model among conventional algorithms using Dataset 1 and Dataset 2 is illustrated in Table 4. The standard deviation of the proposed model is 47.3% than LBO-ADCapNet-AM, 48.1% than BMO-ADCapNet-AM, 44.9% than GOA-ADCapNet-AM, and 45.4% than HSOA-ADCapNet-AM using dataset 1. Thus, the developed model has more advanced performance than the other prediction model by analyzing the numerical measure.

7. Conclusion

A new economic prediction of the world cities framework was implemented for analyzing the global economy. Then input data were preprocessed using data cleaning, data scaling, and null value removal methods to reduce the noisy data. The features from preprocessed data were eradicated using the DRBM technique. The extracted deep features were then fed to the ADCapNet-AM-based prediction model, which was the combination of both the capsule network and attention mechanism. Here, the parameters from the ADCapNet-AM network were tuned using IHSOA to increase the efficiency of the proposed framework. The performance of the suggested model was evaluated and balanced with several existing prediction models. Thus, the results illustrated that the proposed world cities economics prediction model achieved better accomplishment than the accessible prediction scheme.

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An automated economics prediction model for world cities using adaptive deep capsule network with attention mechanism

Abstract

Keywords

1. Introduction

2.1 Related works

Table 1 Features and challenges of the traditional prediction model for analyzing the world cities economics.

3. Proposed intelligent deep learning network for analyzing the world cities economics: Structural view and dataset description

3.1 Architecture of proposed world cities economics analysis model

4. Preprocessing and feature extraction stages with description of the proposed optimization mechanism for parameter optimization

4.1 Data preprocessing

5.1 Deep capsule network

6.1 Experimental setup

Table 2 Comparative outcomes of the proposed world cities economic analysis framework using dataset 1.

6.3 Comparative analysis of the proposed model among existing techniques

6.4 Comparative analysis of the proposed model among existing algorithms

Table 3 Comparative outcomes of the proposed world cities economic analysis framework using dataset 2.

6.6 Numerical analysis of the proposed model using dataset 2

6.7 Statistical analysis among various algorithms using dataset 1 and dataset 2

7. Conclusion

References

Table 1
Features and challenges of the traditional prediction model for analyzing the world cities economics.

Table 2
Comparative outcomes of the proposed world cities economic analysis framework using dataset 1.

Table 3
Comparative outcomes of the proposed world cities economic analysis framework using dataset 2.