A New Approach to Customer Classification According to a Hybrid Non-linear Bayesian and Quantum Approach

الموضوعات :

Nazanin Kashani Kikoo ¹ , مهناز ربیعی ² , Kiamars Fathi ³

1 - Ph.D. student, Department of Information Technology Management, South Tehran Branch, Islamic Azad University, Tehran, Iran,
2 - معاون پژوهشی دانشگاه آزاد واحد الکترونیکی
3 - Islamic Azad University South Branch

تاريخ الإرسال : 29 الإثنين , صفر, 1446 تاريخ التأكيد : 21 السبت , جمادى الأولى, 1446 تاريخ الإصدار : 30 الثلاثاء , جمادى الثانية, 1446

الکلمات المفتاحية: Banking services, Customer relationship management, Fuzzy clustering and data mining, Quantum.,

ملخص المقالة :

The present study explains a customer classification model according to Bayesian-quantum approaches. This study is applied-exploratory research. This study investigated the information of 98,604 customers of one of Iran's banks. Four approaches were used including data mining, fuzzy, quantum, and nonlinear Bayesian averaging. In this study, information on 22 indicators related to customers was entered into nonlinear Bayesian models. According to the error rate, the BMA model had the highest accuracy. According to the results, four features including account balance, total deposit balance, total current facility balance, and volume of financial transactions were used as the primary features for customer classification. The results showed that the C-MEANS approach has higher accuracy than K-MEANS. Then, according to the C-MEANS approach, 16 clusters were identified and the characteristics of each 16 clusters were analyzed. Thus, the selected variables of the Bayesian averaging approach were used in estimating quantum models. According to the results, the harmonic oscillator approach had higher accuracy than the geometric Brownian motion and Heston approaches. The harmonic oscillator approach of the quantum model has high accuracy in all groups and has higher accuracy in the categories where customers are more loyal.

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نص كامل:

Kashani Kikoo et al., A New Approach to Customer Classification According to a Hybrid Non-linear Bayesian ….

A New Approach to Customer Classification According to a Hybrid Non-linear Bayesian and Quantum Approach

Nazanin Kashani Kikoo ¹, Mahnaz Rabeei *², Kiamars Fathi Hafshejani ³

Received: 02 Sep 2024/ Revised: 30 Oct 2024/ Accepted: 23 Nov 2024/ Published: 31 Dec 2024
© Islamic Azad University (IAU) 2024

Abstract

Keywords: Banking services, Customer relationship management, Fuzzy clustering and data mining, Quantum.

[1] Ph.D. student, Department of Information Technology Management, South Tehran Branch, Islamic Azad University, Tehran, Iran,

[2] Corresponding Author: Department of Economics, Modeling and Optimization Research Center in Engineering Sciences, South Tehran Branch, Islamic Azad University, Tehran, Iran, Email: Dr_mahnaz_rabiei@azad.ac.ir

[3] Department of Industrial Management, South Tehran Branch, Islamic Azad University, Tehran, Iran.

Introduction

The customer is the most important asset in the banking business. Banks worldwide are trying to make their businesses customer-centric (Kalaivani & Sumathi, 2019). Thus, customer orientation according to a deep understanding of customer needs with the help of customer behavior analysis, service customization, offering products to meet the needs of different customers, providing outstanding services, flexibility in customer orientation (KhatamiFirouzabadi et al., 2018), easy access and relationship orientation to retain customers (Aslam et al., 2022), preventing deviation from deeper penetration in the market, preventing asset value decline, and increasing profitability with existing customers is a vital issue (Safabakhsh, & Asayesh, 2023). Innovation in the banking industry has always been of special importance thanks to its dynamic nature (Kinge et al., 2022). The emergence of the Internet was vital in this regard (Vidal & Kristjanpoller, 2020). The importance of data and information increased with the advent of the Internet and artificial intelligence (Theodoridis & Tsadiras, 2022). The data and information quality plays a critical role in making sound decisions by managers (Zoynul Abedin et al., 2023). Thus, the process of converting data into information is crucial (Liu et al. 2022; Yuan et al., 2022; Aslam et al., 2022), Thus, data mining is a new science for data exploration (Kalaivani & Sumathi, 2019; De Caigny et al., 2020; Jain et al., 2021; Chen et al., 2021; Alam et al. 2021).

Data mining plays a vital role in banks' capability to meet customer needs as it reduces customer churn (Clerkin & Hanson, 2021; Berggrun et al., 2020; Liu et al., 2022). It is possible to extract the characteristics specific to each customer group from content-free data (Yuan et al., 2022; Aslam et al., 2022). Identifying these characteristics leads to better customer segmentation and better service provision (Long et al., 2019; Abedin et al., 2020; Zhang et al. 2021). Thus, the primary goal of this article is to classify bank customers according to the characteristics of each group and the importance of each of these characteristics in the profitability of the bank in each group (Keramati et al. 2016; Yuan et al., 2022).

Results of recent studies indicate that statistical physics and its complex systems, including quantum mechanics, are one of the most robust tools in behavioral analysis. The advantage of quantum models over traditional models is that they often describe the impact of different conditions on customer behavior better. This better description leads to much more accurate modeling. Thus, the primary issue of the present study is to identify the most important customer characteristics and the way they affect bank profitability (Ramezani et al., 2024). Accordingly, the present study is organized in this way. The second section presents the theoretical foundations and domestic and foreign literature review. The third section presents the research methodology, including the models and data used. The fourth section presents the empirical findings from the model estimation. The fifth section presents the conclusions and recommendations.

Theoretical Foundations and Research Background

Converting data into information and using it to gain profit from this information is the most crucial reason for banks' tendency toward innovation. The data mining approach is a new movement in this area (Noei et al., 2023). Data mining leads to greater adaptation of services to customer needs and identification of active and inactive customers (Wojnarski, 2002; Abbasimehr & Shabani, 2021). It also leads to extracting customer behavioral patterns (Baumann et al., 2007; Noshabadi et al. 2023). It improves customer communication (Ghabouli et al., 2023; Chen et al., 2021) and makes the identification of the indicators that cause customer churn possible (Keramati et al. 2016; Kalaivani & Sumathi, 2019). De Caigny et al., 2020 examined customer churn datasets using data mining techniques. It leads to customer retention (De Caigny et al., 2020) and increases customer trust in banks. It also improves data resolution and reduces the consequences of the curse of dimensionality (Kashani Kikoo et al., 2024).

Quantum Theory

As a theory of quantum theory, a quantum agent is like a particle that is under the influence of a quantum potential well. In quantum mechanics, the particle-in-a-box problem, also known as the "infinite potential well", describes the situation of a free particle trapped in a small and impenetrable space, moves in it, and is unable to escape. In classical physics and mechanics, a particle trapped in a large box can take any speed and, in the simplest state, only travels one path until its energy runs out. Quantum behaviors become more apparent as the dimensions of the box decrease to a few nanometers. In this case, the particle can only occupy some positive energy levels and move in those levels. Therefore, it can never have zero energy (there is no zero-energy level). In the quantum state, the probability of finding the particle depends on the distribution function, which depends on the energy levels. Moreover, the particle may never be found at certain points called spatial nodes. The particle in the box problem is one of the quantum mechanical problems that can be solved analytically without the need for complex mathematical relationships. This problem, which is according to the quantized (discrete) nature of energy levels, gives us a good understanding of dealing with more complex problems and describing atomic and molecular systems (Charte et al., 2021). (Figure 1) illustrates a typical example of quantum potential energy created by a quantum particle (such as an atom).

Figure 1. Quantum potential energy created by a quantum particle

Accordingly, the theory of quantum particles in quantum theory is well understood in the field of quantum theory and quantum particles.

Quantum Basic Components

Nowadays, various studies such as (Zadeh & Aliev, 2018) and (Lee, 2020) have indicated how quantum mechanics and quantum field theory can be used to model behaviors. Additionally, the study by (Lee, 2020) investigated how modern and advanced models such as artificial intelligence technologies such as artificial neural networks, fuzzy logic, genetic algorithms, chaos theory, and fractals can be integrated with the quantum model and implement intelligent systems in real-time. (Figure 2) illustrates the quantum concentric circles model. This model consists of the following layers (Lee, 2020):

Layer 1: This layer includes the energy field, the core, and the quantum field, which provide the quantum price field.

Layer 2: The chaotic neural network, which is used to generate financial quantum neural dynamics and support neural oscillators, and chaotic neural networks.

Layer 3: The financial technology artificial intelligence layer, which provides financial technology tools in the field of artificial intelligence. In other words, this layer supports fuzzy logic, genetic algorithms, chaos theory, fractal, and support vector machine models.

Layer 4: It is an applied layer supporting quantum price levels, short-term prediction, long-term trend prediction, and intelligent agent-based trading systems.

Figure 2. Concentric circles model for financial quantum

Source: (Lee, 2020)

Method and Material

This study was an applied and exploratory research. In this study, there were about 98,604 customers. The study models were estimated using Weka and MATLAB software. The following approaches were used in this study (Table 1).

Table 1. Applied models in the study

Row	Model	Definition	Application
Classification of customers	K-Means	K-means	It is an iterative algorithm that divides the unlabeled set into k different clusters such that each cluster belongs to only one group that has similar features.
Classification of customers	Means - C	C-means	In this approach, fuzzy properties are used to classify data.
Considering uncertainty in extracted information	Type-3 fuzzy	Type 3 Fuzzy	Considering the issue of uncertainty in the scoring of factors affecting customer differentiation by experts
Identifying the best characteristics of bank customers	BMA, TVP-DMA, TVP-DMS	Nonlinear Bayesian Models	Selecting the most important characteristics of bank customers
(Modeling approaches)	PCA	Principal Component Analysis	Indexing customer characteristics
Component builder	Quantum	Quantum	Investigating the impact of the most important characteristics of bank customers on profitability

The research variables are presented below according to the extracted characteristics (Table 2).

Table 2. Characteristics of the extracted variables

Variable type	Variable	Description
Dependent variable	Customer profitability index	Revenues minus costs for each customer are used to calculate the customer profitability index (It should be noted that not all items presented in this index include all customers). Customer revenues Customer low-cost account balance (current in the short term) Revenue from obtaining facilities (interest paid to the bank) Revenue from providing general services to the customer Average of low-cost customer accounts (current in the short term) Revenues from obtaining facilities (interest paid to the bank) revenues from providing general services to the customer revenues from providing specialized banking services (fees) revenues from issuing guarantees and other obligations revenues from handling VIP customer affairs as a proxy revenues from customer affairs Customer expenses revenues received from the bank for long-term investment capital Commission discounts due to the being a VIP customer Expenses due to providing services to VIP customers such as customer club services, airport CIP Expenses for doubtful and non-current receivables Expenses due to failure to fulfill obligations on due date
Explanatory variable	Personal characteristics: Gender	If male, it is one, otherwise, it is zero.
	Personal characteristics: Age	Age ranges from 1 to 85 years
	Account Opening Date	Account opening day
	Account type	Qarz al-Hasan Savings Deposits (Number 0) Short-term Deposits (Number 1) Long-term Deposits (Number 2) Qarz al-Hasan Current Account (Number 3)
	Date of last customer visit	Date of last visit to Internet Banking or in-person visit to the branch
	Account status	Active number one Retard number zero
	Account usage period	Account active period
	Account points	The number of points awarded to the account based on the mean of the account from 1 to 10
	Account balance	Account balance at reporting in million Rials
	The period between the first and last customer visit	Length of using account
	Number of transactions during the period	Number of transfers or deposits to the account
	Checkbook status	There is a checkbook on the account: one, otherwise, zero
	Number of facilities	Number of short-term and long-term facilities
	Facility type	1-Qard-al-Hasan loan; 2. Marriage loan; 3. Housing loan; 4. Mudaraba loan; 5. Loan for the purchase of goods; 6. Loan for the purchase of raw materials; 7. Loan for the purchase of a car; 8. Pensioner loan; 9. Qard-al-Hasan loan for a child; 10. Home repair loan; 11. Self-employment loan; 12. Student loan
	Number of arrears	Number of periods in which the facility payment was not made on its due date
	Volume of financial transactions	Rial amount of transfer or deposit to the account
	Number of deposits	Number of accounts of a person
	Total balance of deposits	Mean deposit balance in the study period
	Number of current facilities	Number of active facilities that the person has in the study period
	Total balance of total current facilities	Current facility balance of the person
	Total arrears	Rial amount of facility installment payment that was not made on its due date
	Date of last claims	Last due date for three consecutive months

Results

Model Estimation

See the article by (Kashani Kikoo et al., 2024) (Table 3) to extract the desired features for customer classification according to the nonlinear Bayesian approach.

Table 3. The second stage of the sampling process and calculations assuming K ̅=5

The first sample includes 2,000 regressions.		The first sample includes 1,000 regressions.		Variable
Posterior probability	Posterior coefficient	Prior probability	Prior coefficient
0.677	0.151	0.530	0.496	Account Balance
0.866	0.224	0.606	0.145	Financial Transaction Volume
0.988	0.224	0.759	0.070	Total Deposit Balance
0.571	0.052	0.226	0.225	Total Current Facility Balance

Source: Researcher's calculations

According to the nonlinear Bayesian approach, the variables of account balance; total deposit balance; total balance of current facilities; and volume of financial transactions were determined as the most important characteristics of customers for their classification.

Determining the Optimal Cluster

After determining the influential indicators of customer clustering, it was necessary to determine the number of clusters. (Table 4) presents the optimal number of clusters, the average silhouette coefficient using two algorithms, K-Means, and fuzzy C-Means.

Table 4. Mean silhouette coefficient using K-Means and fuzzy C-Means algorithms

fuzzy C- Means	k-means	Log number
0.8723	0.8703	2 clusters
0.7935	0.7745	3 clusters
0.7482	0.7355	4 clusters
0.7003	0.7106	5 clusters
0.6839	0.6909	6 clusters
0.6394	0.6705	7 clusters
0.6183	0.5995	8 clusters
0.5934	0.6342	9 clusters
0.5582	0.6982	10 clusters
0.5255	0.7150	11 clusters
0.5184	0.7835	12 clusters
0.7394	0.8245	13 clusters
0.7573	0.7222	14 clusters
0.8284	0.6932	15 clusters
0.9203	0.6533	16 clusters
0.9043	0.6286	17 clusters
0.8432	0.6074	18 clusters
0.7447	0.5873	19 clusters
0.6462	0.5534	20 clusters