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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (31 December 2022) | Viewed by 28712

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Special Issue Editors

Dr. Chaman Verma

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Guest Editor

Faculty of Informatics, University of Eötvös Loránd, 1053 Budapest, Hungary
Interests: data mining; data science; teaching–learning-based technologies; Internet of Things (IoT); deep learning; AI; multimedia systems; statistical analysis

Dr. Maria Simona Raboaca

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Guest Editor

ICSI Energy Department, National Research and Development Institute for Cryogenics and Isotopic Technologies, 240050 Ramnicu Valcea, Romania
Interests: renewable resources; hydrogen energy; fuel cell technology; hybrid energy system; smart stand‐alone systems; electric vehicle charging station; blockchain technology
Special Issues, Collections and Topics in MDPI journals

Dr. Zoltán Illés

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Faculty of Informatics, University of Eötvös Loránd, 1053 Budapest, Hungary
Interests: real-time; operating systems; computer systems; OS scripting; embedded systems; web; signalR; asynchronous web communication; C#; Internet of Things (IoT)

Special Issue Information

Dear Colleagues,

Statistical analysis and machine learning models are efficient in dealing with complex prediction models due to their outstanding performance in handling large-scale data sets with uniform characteristics and noisy data. The application of statistics and machine learning algorithms has impacted the lives of researchers, educationists, and industrialists. Machine learning statistical models are embedded in various technologies: edge, cloud, IoT, and block-chain. The invention of new machine algorithms and statistical models significantly contributes to the development of various real-time applications. This special section provides an excellent international forum for sharing knowledge and results regarding statistical theory and models; machine learning algorithm application; and other mathematics models for several sectors, such as health, education, transportation, and agriculture. This Special Issue also covers novel and scientific aspects for future real-time application development and emerging technologies with various mathematics-based AI approaches, and seeks original and unpublished research articles, including theoretical studies, practical applications, and predictive models, to contribute novel findings to the research community.

Dr. Chaman Verma
Dr. Maria Simona Raboaca
Dr. Zoltán Illés
Guest Editors

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Keywords

statistical analysis
IoT
machine learning
feature selection
real-time

Published Papers (14 papers)

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21 pages, 4640 KiB

Open AccessArticle

ConvGRU-RMWP: A Regional Multi-Step Model for Wave Height Prediction

by Youjun Sun, Huajun Zhang, Shulin Hu, Jun Shi, Jianning Geng and Yixin Su

Mathematics 2023, 11(9), 2013; https://doi.org/10.3390/math11092013 - 24 Apr 2023

Cited by 1 | Viewed by 1235

Abstract

Accurate large-scale regional wave height prediction is important for the safety of ocean sailing. A regional multi-step wave height prediction model (ConvGRU-RMWP) based on ConvGRU is designed for the two problems of difficult spatial feature resolution and low accuracy of multi-step prediction in ocean navigation wave height prediction. For multi-step prediction, a multi-input multi-output prediction strategy is used, and wave direction and wave period are used as exogenous variables, which are combined with historical wave height data to expand the sample space. For spatial features, a convolutional gated recurrent neural network with an Encoder-Forecaster structure is used to extract and resolve multi-level spatial information. In contrast to time series forecasting methods that consider only backward and forward dependencies in the time dimension and a single assessment of the properties of the predictor variables themselves, this paper additionally considers spatial correlations and implied correlations among the meteorological variables. This model uses the wave height information of the past 24 h to predict the wave height information for the next 12 h. The prediction results in both space and time show that the model can effectively extract spatial and temporal correlations and obtain good multi-step wave height prediction results. The proposed method has a lower prediction error than the other five prediction methods and verifies the applicability of this model for three selected sea areas along the global crude oil transportation route, all of which have a lower prediction error. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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17 pages, 5989 KiB

Open AccessArticle

ResInformer: Residual Transformer-Based Artificial Time-Series Forecasting Model for PM2.5 Concentration in Three Major Chinese Cities

by Mohammed A. A. Al-qaness, Abdelghani Dahou, Ahmed A. Ewees, Laith Abualigah, Jianzhu Huai, Mohamed Abd Elaziz and Ahmed M. Helmi

Mathematics 2023, 11(2), 476; https://0-doi-org.brum.beds.ac.uk/10.3390/math11020476 - 16 Jan 2023

Cited by 7 | Viewed by 2615

Abstract

Many Chinese cities have severe air pollution due to the rapid development of the Chinese economy, urbanization, and industrialization. Particulate matter (PM2.5) is a significant component of air pollutants. It is related to cardiopulmonary and other systemic diseases because of its ability to penetrate the human respiratory system. Forecasting air PM2.5 is a critical task that helps governments and local authorities to make necessary plans and actions. Thus, in the current study, we develop a new deep learning approach to forecast the concentration of PM2.5 in three major cities in China, Beijing, Shijiazhuang, and Wuhan. The developed model is based on the Informer architecture, where the attention distillation block is improved with a residual block-inspired structure from efficient networks, and we named the model ResInformer. We use air quality index datasets that cover 98 months collected from 1 January 2014 to 17 February 2022 to train and test the model. We also test the proposed model for 20 months. The evaluation outcomes show that the ResInformer and ResInformerStack perform better than the original model and yield better forecasting results. This study’s methodology is easily adapted for similar efforts of fast computational modeling. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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16 pages, 1006 KiB

Open AccessArticle

Applying the Push-Pull Mooring to Explore Consumers’ Shift from Physical to Online Purchases of Face Masks

by Sung-Wen Yu, Jun-Yan Liu, Chien-Liang Lin and Yu-Sheng Su

Mathematics 2022, 10(24), 4761; https://0-doi-org.brum.beds.ac.uk/10.3390/math10244761 - 15 Dec 2022

Cited by 1 | Viewed by 2137

Abstract

In response to the emergency management caused by COVID-19, Taiwan began to impose a name-based rationing system for the purchase of face masks by having consumers visit physical stores and preorder them online. By doing so, the risk of face mask shortages caused by panic buying was reduced. To understand consumers’ willingness to switch from buying face masks at physical stores to preordering them online, we used a push-pull-mooring (PPM) model to measure related dimensions. We administered an online questionnaire survey and collected 233 valid responses. In the present study, perceived risk (including time risk, psychological risk and social risk) was treated as a second-order formative indicator, while pull effect was measured by the variables of critical mass and alternative attraction. Mooring effect was measured by switching cost. Through structural equation modeling (SEM), perceived risk, as well as critical mass and alternative attraction, had a significant effect on switching intention, while switching cost had no significant relationship with switching intention. This study investigated whether perceived risk (time risk, psychological risk and social risk), critical mass, alternative attraction and switching cost can serve as references for purchase behaviors amid future emergency management, through the prism of population migration theory, and proposed recommendations for their promotion and implementation. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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11 pages, 672 KiB

Open AccessArticle

A New Zero-Inflated Negative Binomial Multilevel Model for Forecasting the Demand of Disaster Relief Supplies in the State of Sao Paulo, Brazil

by Camila Pareja Yale, Hugo Tsugunobu Yoshida Yoshizaki and Luiz Paulo Fávero

Mathematics 2022, 10(22), 4352; https://0-doi-org.brum.beds.ac.uk/10.3390/math10224352 - 19 Nov 2022

Cited by 1 | Viewed by 1209

Abstract

This article presents the results of the implementation of a forecasting model, to predict the relief materials needed for assisting in decisions prior to natural disasters, thus filling a gap in the exploration of Generalized Linear Mixed Models (GLMM) in a humanitarian context. Demand information from the State of Sao Paulo, Brazil was used to develop the Zero Inflated Negative Binomial Multilevel (ZINBM) model, which gets to handle the excess of zeros in the count data and considers the nested structure of the data set. Strategies for selecting predictor variables were based on the understanding of the needs for relief supplies; consequently, they were derived from vulnerability indicators, demographic factors, and occurrences of climatic anomalies. The model presents coefficients that are statistically significant, and the results show the importance of considering the nested structure of the data and the zero-inflated nature of the outcome variable. To validate the fitness of the ZINBM model, it was compared against the Poisson, Negative Binomial (NB), Zero Inflated Poisson (ZIP), and Zero Inflated Negative Binomial (ZINB) models. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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25 pages, 466 KiB

Open AccessArticle

Binned Term Count: An Alternative to Term Frequency for Text Categorization

by Farhan Shehzad, Abdur Rehman, Kashif Javed, Khalid A. Alnowibet, Haroon A. Babri and Hafiz Tayyab Rauf

Mathematics 2022, 10(21), 4124; https://0-doi-org.brum.beds.ac.uk/10.3390/math10214124 - 04 Nov 2022

Cited by 3 | Viewed by 1240

Abstract

In text categorization, a well-known problem related to document length is that larger term counts in longer documents cause classification algorithms to become biased. The effect of document length can be eliminated by normalizing term counts, thus reducing the bias towards longer documents. This gives us term frequency (TF), which in conjunction with inverse document frequency (IDF) became the most commonly used term weighting scheme to capture the importance of a term in a document and corpus. However, normalization may cause term frequency of a term in a related document to become equal or smaller than its term frequency in an unrelated document, thus perturbing a term’s strength from its true worth. In this paper, we solve this problem by introducing a non-linear mapping of term frequency. This alternative to TF is called binned term count (BTC). The newly proposed term frequency factor trims large term counts before normalization, thus moderating the normalization effect on large documents. To investigate the effectiveness of BTC, we compare it against the original TF and its more recently proposed alternative named modified term frequency (MTF). In our experiments, each of these term frequency factors (BTC, TF, and MTF) is combined with four well-known collection frequency factors (IDF), RF, IGM, and MONO and the performance of each of the resulting term weighting schemes is evaluated on three standard datasets (Reuters (R8-21578), 20-Newsgroups, and WebKB) using support vector machines and K-nearest neighbor classifiers. To determine whether BTC is statistically better than TF and MTF, we have applied the paired two-sided t-test on the macro

F_{1}

results. Overall, BTC is found to be 52% statistically significant than TF and MTF. Furthermore, the highest macro

F_{1}

value on the three datasets was achieved by BTC-based term weighting schemes. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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23 pages, 1544 KiB

Open AccessArticle

Improved Recurrent Neural Network Schema for Validating Digital Signatures in VANET

by Arpit Jain, Jaspreet Singh, Sandeep Kumar, Țurcanu Florin-Emilian, Mihaltan Traian Candin and Premkumar Chithaluru

Mathematics 2022, 10(20), 3895; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203895 - 20 Oct 2022

Cited by 17 | Viewed by 1507

Abstract

Vehicular ad hoc networks (VANETs) allow communication between stationary or moving vehicles with the assistance of wireless technology. Among various existing issues in smart VANETs, secure communication is the key challenge in VANETs with a 5G network. Smart vehicles must communicate with a broad range of advanced road systems including traffic control and smart payment systems. Many security mechanisms are used in VANETs to ensure safe transmission; one such mechanism is cryptographic digital signatures based on public key infrastructure (PKI). In this mechanism, secret private keys are used for digital signatures to validate the identity of the message along with the sender. However, the validation of the digital signatures in fast-moving vehicles is extremely difficult. Based on an improved perceptron model of an artificial neural network (ANN), this paper proposes an efficient technique for digital signature verification. Still, manual signatures are extensively used for authentication across the world. However, manual signatures are still not employed for security in automotive and mobile networks. The process of converting manual signatures to pseudo-digital-signatures was simulated using the improved Elman backpropagation (I-EBP) model. A digital signature was employed during network connection to authenticate the legitimacy of the sender’s communications. Because it contained information about the vehicle on the road, there was scope for improvement in protecting the data from attackers. Compared to existing schemes, the proposed technique achieved significant gains in computational overhead, aggregate verification delay, and aggregate signature size. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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18 pages, 4700 KiB

Open AccessArticle

Cryptanalysis and Improved Image Encryption Scheme Using Elliptic Curve and Affine Hill Cipher

by Parveiz Nazir Lone, Deep Singh, Veronika Stoffová, Deep Chandra Mishra, Umar Hussain Mir and Neerendra Kumar

Mathematics 2022, 10(20), 3878; https://0-doi-org.brum.beds.ac.uk/10.3390/math10203878 - 19 Oct 2022

Cited by 15 | Viewed by 1604

Abstract

In the present era of digital communication, secure data transfer is a challenging task in the case of open networks. Low-key-strength encryption techniques incur enormous security threats. Therefore, efficient cryptosystems are highly necessary for the fast and secure transmission of multimedia data. In this article, cryptanalysis is performed on an existing encryption scheme designed using elliptic curve cryptography (ECC) and a Hill cipher. The work shows that the scheme is vulnerable to brute force attacks and lacks both Shannon’s primitive operations of cryptography and Kerckchoff’s principle. To circumvent these limitations, an efficient modification to the existing scheme is proposed using an affine Hill cipher in combination with ECC and a 3D chaotic map. The efficiency of the modified scheme is demonstrated through experimental results and numerical simulations. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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30 pages, 3396 KiB

Open AccessArticle

Covariance Matrix Adaptation Evolution Strategy for Improving Machine Learning Approaches in Streamflow Prediction

by Rana Muhammad Adnan Ikram, Leonardo Goliatt, Ozgur Kisi, Slavisa Trajkovic and Shamsuddin Shahid

Mathematics 2022, 10(16), 2971; https://0-doi-org.brum.beds.ac.uk/10.3390/math10162971 - 17 Aug 2022

Cited by 25 | Viewed by 1797

Abstract

Precise streamflow estimation plays a key role in optimal water resource use, reservoirs operations, and designing and planning future hydropower projects. Machine learning models were successfully utilized to estimate streamflow in recent years In this study, a new approach, covariance matrix adaptation evolution strategy (CMAES), was utilized to improve the accuracy of seven machine learning models, namely extreme learning machine (ELM), elastic net (EN), Gaussian processes regression (GPR), support vector regression (SVR), least square SVR (LSSVR), extreme gradient boosting (XGB), and radial basis function neural network (RBFNN), in predicting streamflow. The CMAES was used for proper tuning of control parameters of these selected machine learning models. Seven input combinations were decided to estimate streamflow based on previous lagged temperature and streamflow data values. For numerical prediction accuracy comparison of these machine learning models, six statistical indexes are used, i.e., relative root mean squared error (RRMSE), mean absolute error (MAE), mean absolute percentage error (MAPE), Nash–Sutcliffe efficiency (NSE), and the Kling–Gupta efficiency agreement index (KGE). In contrast, this study uses scatter plots, radar charts, and Taylor diagrams for graphically predicted accuracy comparison. Results show that SVR provided more accurate results than the other methods, especially for the temperature input cases. In contrast, in some streamflow input cases, the LSSVR and GPR were better than the SVR. The SVR tuned by CMAES with temperature and streamflow inputs produced the least RRMSE (0.266), MAE (263.44), and MAPE (12.44) in streamflow estimation. The EN method was found to be the worst model in streamflow prediction. Uncertainty analysis also endorsed the superiority of the SVR over other machine learning methods by having low uncertainty values. Overall, the SVR model based on either temperature or streamflow as inputs, tuned by CMAES, is highly recommended for streamflow estimation. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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15 pages, 1039 KiB

Open AccessArticle

Convolutional Neural Network-Based Parkinson Disease Classification Using SPECT Imaging Data

by Jigna Hathaliya, Raj Parekh, Nisarg Patel, Rajesh Gupta, Sudeep Tanwar, Fayez Alqahtani, Magdy Elghatwary, Ovidiu Ivanov, Maria Simona Raboaca and Bogdan-Constantin Neagu

Mathematics 2022, 10(15), 2566; https://0-doi-org.brum.beds.ac.uk/10.3390/math10152566 - 23 Jul 2022

Cited by 8 | Viewed by 1910

Abstract

In this paper, we used the single-photon emission computerized tomography (SPECT) imaging technique to visualize the deficiency of dopamine-generated patterns inside the brain. These patterns are used to establish a patient’s disease progression, which helps distinguish the patients into different categories. Furthermore, we used a convolutional neural network (CNN) model to classify the patients based on the dopamine level inside the brain. The dataset used throughout this paper is the Parkinson’s progressive markers initiative (PPMI) dataset. The collected dataset was pre-processed and data amplification was performed to balance the imbalanced dataset. A CNN-based neural network was defined to classify input SPECT images into four categories. The motivation behind the proposed model is to reduce the number of resources consumed while maintaining the performance of the classification model. This will help the healthcare ecosystem run the classification model on mobile devices. The proposed model contains 14 layers with input layers, convolutional layers, max-pool layers, flatten layers, and dense layers with different dimensions. The dense layer classifies the patients into four different categories, including PSD, healthy control, scans without evidence of dopaminergic deficit (SWEDD), and GenReg PSD from the entire SPECT imaging dataset, which is used to establish the disease progression of different patients using SPECT images. The proposed model is trained with a large dataset with 58,692 images for training and 11,738 images for validation, and 7826 for testing. The proposed model outperforms the classification models from the surveyed papers. The proposed model’s accuracy is 0.889, recall is 0.9012, the precision is 0.9104, and the F1-score is 0.9057. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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18 pages, 1357 KiB

Open AccessEditor’s ChoiceArticle

Application of Fuzzy-Based Support Vector Regression to Forecast of International Airport Freight Volumes

by Cheng-Hong Yang, Jen-Chung Shao, Yen-Hsien Liu, Pey-Huah Jou and Yu-Da Lin

Mathematics 2022, 10(14), 2399; https://0-doi-org.brum.beds.ac.uk/10.3390/math10142399 - 08 Jul 2022

Cited by 6 | Viewed by 1606

Abstract

As freight volumes increase, airports are likely to require additional infrastructure development, increased air services, and expanded facilities. Prediction of freight volumes could ensure effective investment. Among the computational intelligence models, support vector regression (SVR) has become the dominant modeling paradigm. In this study, a fuzzy-based SVR (FSVR) model was used to solve the freight volume prediction problem in international airports. The FSVR model can use a fuzzy time series of historical traffic changes for predictions. A fuzzy classification algorithm was used for elements of similar levels in the time series to appropriately divide traffic changes into fuzzy sets, generate membership function values, and establish a fuzzy relationship to produce a fuzzy interpolation with a minimal error. A comparison of the FSVR model with other models revealed that the FSVR model had the lowest mean absolute percentage error (all < 2.5%), mean absolute error, and root mean square error for all types of traffic at all the analyzed airports. Fuzzy sets can handle uncertainty and imprecision in time series. Therefore, the prediction accuracy of the entire time series model is improved by taking advantage of SVR and fuzzy sets. By using the highly accurate FSVR model to predict the future growth of air freight volume, airport management could analyze their existing facilities and service capacity to identify operational bottlenecks and plan future development. The FSVR model is the most accurate forecasting model for air traffic forecasting. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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30 pages, 1059 KiB

Open AccessArticle

Trading Stocks Based on Financial News Using Attention Mechanism

by Saurabh Kamal, Sahil Sharma, Vijay Kumar, Hammam Alshazly, Hany S. Hussein and Thomas Martinetz

Mathematics 2022, 10(12), 2001; https://0-doi-org.brum.beds.ac.uk/10.3390/math10122001 - 10 Jun 2022

Cited by 8 | Viewed by 4046

Abstract

Sentiment analysis of news headlines is an important factor that investors consider when making investing decisions. We claim that the sentiment analysis of financial news headlines impacts stock market values. Hence financial news headline data are collected along with the stock market investment data for a period of time. Using Valence Aware Dictionary and Sentiment Reasoning (VADER) for sentiment analysis, the correlation between the stock market values and sentiments in news headlines is established. In our experiments, the data on stock market prices are collected from Yahoo Finance and Kaggle. Financial news headlines are collected from the Wall Street Journal, Washington Post, and Business-Standard website. To cope with such a massive volume of data and extract useful information, various embedding methods, such as Bag-of-words (BoW) and Term Frequency-Inverse Document Frequency (TF-IDF), are employed. These are then fed into machine learning models such as Naive Bayes and XGBoost as well as deep learning models such as Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM). Various natural language processing, andmachine and deep learning algorithms are considered in our study to achieve the desired outcomes and to attain superior accuracy than the current state-of-the-art. Our experimental study has shown that CNN (80.86%) and LSTM (84%) are the best performing models in relation to machine learning models, such as Support Vector Machine (SVM) (50.3%), Random Forest (67.93%), and Naive Bayes (59.79%). Moreover, two novel methods, BERT and RoBERTa, were applied with the expectation of better performance than all the other models, and they did exceptionally well by achieving an accuracy of 90% and 88%, respectively. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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18 pages, 8413 KiB

Open AccessArticle

Super Resolution for Noisy Images Using Convolutional Neural Networks

by Zaid Bin Mushtaq, Shoaib Mohd Nasti, Chaman Verma, Maria Simona Raboaca, Neerendra Kumar and Samiah Jan Nasti

Mathematics 2022, 10(5), 777; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050777 - 28 Feb 2022

Cited by 3 | Viewed by 3380 | Correction

Abstract

The images in high resolution contain more useful information than the images in low resolution. Thus, high-resolution digital images are preferred over low-resolution images. Image super-resolution is one of the principal techniques for generating high-resolution images. The major advantages of super-resolution methods are that they are economical, independent of the image capture devices, and can be statically used. In this paper, a single-image super-resolution network model based on convolutional neural networks is proposed by combining conventional autoencoder and residual neural network approaches. A convolutional neural network-based dictionary method is used to train low-resolution input images for high-resolution images. In addition, a linear refined unit thresholds the convolutional neural network output to provide a better low-resolution image dictionary. Autoencoders aid in the removal of noise from images and the enhancement of their quality. Secondly, the residual neural network model processes it further to create a high-resolution image. The experimental results demonstrate the outstanding performance of our proposed method compared to other traditional methods. The proposed method produces clearer and more detailed high-resolution images, as they are important in real-life applications. Moreover, it has the advantage of combining convolutional neural network-based dictionary learning, autoencoder image enhancement, and noise removal. Furthermore, residual neural network training with improved preprocessing creates an efficient and versatile single-image super-resolution network. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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37 pages, 3577 KiB

Open AccessArticle

Nearest Descent, In-Tree, and Clustering

by Teng Qiu and Yongjie Li

Mathematics 2022, 10(5), 764; https://0-doi-org.brum.beds.ac.uk/10.3390/math10050764 - 27 Feb 2022

Cited by 2 | Viewed by 1400

Abstract

Clustering aims at discovering the natural groupings in a dataset, prevalent in many disciplines that involve multivariate data analysis. In this paper, we propose a physically inspired graph-theoretical clustering method, which first makes the data points organized into an attractive graph, called In-Tree, via a physically inspired rule, called Nearest Descent (ND). The rule of ND works to select the nearest node in the descending direction of potential as the parent node of each node, which is fundamentally different from the classical Gradient Descent. The constructed In-Tree proves a very good candidate for clustering due to its particular features and properties. In the In-Tree, the original clustering problem is reduced to a problem of removing the inter-cluster edges from this graph. Pleasingly, those inter-cluster edges are usually so distinguishable that they can be easily determined by different automatic edge-cutting methods. We also propose a visualized strategy to validate the effectiveness of the automatic edge-cutting methods. The experimental results reveal that the proposed method is superior to the related clustering methods. The results also reveal the characteristics of different automatic cutting methods and the meaningfulness of the visualized strategy in increasing the reliability of the clustering results in practice. Full article

(This article belongs to the Special Issue Advancements in Machine Learning and Statistical Modeling, and Real-World Applications)

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