Entropy techniques for robust management decision making in high-dimensional data
Abstract
Entropy, a key measure of chaos or diversity, has recently found intriguing applications in the realm of management science. Traditional entropy-based approaches for data analysis, however, prove inadequate when dealing with high-dimensional datasets. In this paper, a novel uncertainty coefficient based on entropy is proposed for categorical data, together with a pattern discovery method suitable for management applications. Furthermore, we present a robust fractal-inspired technique for estimating covariance matrices in multivariate data. The efficacy of this method is thoroughly examined using three real datasets with economic relevance. The results demonstrate the superior performance of our approach, even in scenarios involving a limited number of variables. This suggests that managerial decision-making processes should reflect the inherent fractal structure present in the given multivariate data. The work emphasizes the importance of considering fractal characteristics in managerial decision-making, thereby advancing the applicability and effectiveness of entropy-based methods in management science.
References
Agresti, A. (2002). Categorical data analysis. 2nd edn. Hoboken, NJ: Wiley.
Akhmet, M., Fen, M.O., & Alejaily, E.M. (2020). Dynamics with chaos and fractals. Cham, Switzerland: Springer.
Al-Hadeethi, H., Abdulla, S., Diykh, M., Deo, R.C., & Green, J.H. (2022) An eigenvalue-based covariance matrix bootstrap model integrated with support vector machines for multichannel EEG signals analysis, Front. Neuroinform. 15, 808339.
Boas, A.V., André, J., Cerqueira, S.M., & Santos, C.P. (2023). A DMPs-based approach for human-robust collaboration task quality management. IEEE International Conference on Autonomous Robust Systems and Competitions ICARSC 2023, 226‒231.
Broniatowski, M. (2021). Minimum divergence estimators, maximum likelihood and the generalized bootstrap. Entropy, 23, 185.
Che, Y., Deng, Y., & Yuan, Y.H. (2022). Maximum-entropy-based decision-making trial and evaluation laboratory and its application in emergency management. Journal of Organizational and End User Computing, 34, 1‒16.
Chen, Y., Jiao, J., & Farahi, A. (2023). Disparities in affecting factors of housing price: A machine learning approach to the effects of housing status, public transit, and density factors on single-family housing price. Cities, 140, 104432.
Chhikara, P. Jain, N., Tekchandani, R., & Kumar, N. (2022). Data dimensionality reduction techniques for Industry 4.0: Research results, challenges, and future research directions. Software Practice and Experience, 52, 658‒688.
Czyż , T. & Hauke, J. (2015). Entropy in regional analysis. Quaestiones Geographicae, 34, 69‒78.
Darian-Smith, E. (2022). Global burning: Rising antidemocracy and the climate crisis. Stanford, CA: Stanford University Press.
Delgado-Bonal, A. & Marshak, A. (2019). Approximate entropy and sample entroy: A comprehensive tutorial. Entropy, 21, 541.
Fedajev, A., Radulescu, M., Babucea, A.G., Mihajlovic, V. (2021). Real convergence in EU: Is there a difference between the effects of the pandemic and the global economic crisis? Politická ekonomie, 69, 571‒594.
Gleick, J. (2008). Chaos: Making a new science. NY: Viking Press.
Güney, Y., Tuaç, Y., Özdemir, S., & Arslan, O. (2021). Robust estimation and variable selection in heteroscedastic regression model using least favorable distribution. Computational Statistics, 36, 805‒827.
Himeur, Y., Elnour, M., Fadli, F., Meskin, N., Petri, I., et al. (2023). AI-big data analytics for building automation and management systems: A survey, actual challenges and future perspectives. Artificial Intelligence Review, 56, 4929‒5021.
Jiřina, M. & Jiřina, M. (2015). Classification using the Zipfian kernel. Journal of Classification, 32, 305‒326.
Kahneman, D. (2011). Thinking, fast and slow. NY: Farrar, Straus and Giroux.
Kalina, J. (2024). Regularized least weighted squares estimator in linear regression. Communications in Statistics‒Simulation and Computation. Accepted.
Kalina, J. (2022). Decision making reflecting the fractalization of the society. Serbian Journal of Management, 17, 207‒218.
Kalina, J. & Tichavský, J. (2022). The minimum weighted covariance determinant estimator for high-dimensional data. Advances in Data Analysis and Classification, 16, 977‒999.
Keziou, A. & Regnault, P. (2017). Semiparametric estimation of mutual information and related criteria: Optimal test of independence. IEEE Transactions on Information Theory, 63, 57‒71.
Krstić, S & Fedajev, A. (2020). The role and importance of large companies in the economy of the Republic of Serbia. Serbian Journal of Management, 15, 335‒352.
Le, J., Liao, X., Zhang, L., & Mao, T. (2021). Distributionally robust chance constrained planning model for energy storage plants based on Kullback-Leibler divergence. Energy Reports, 7, 5203‒5213.
Ledoit, O. & Wolf, M. (2022). The power of (non-)linear shrinking: A review and guide to covariance matrix estimation. Journal of Financial Econometrics, 20, 187‒218.
Lee, C.H., Cook, S., Lee, J.S., & Han, B. (2016). Comparison of two meta-analysis methods: Inverse-variance-weighted average and weighted sum of Z-scores. Genomics & Informatics, 14, 173‒180.
Li, B. & Zhang, R. (2021). A new mean-variance-entropy model for uncertain portfolio optimization with liquidity and diversification. Chaos, Solitons, & Fractals, 146, 110842.
Li, M., Wang, Y., Yu, P., Sun, Z., & Chen, Z. (2023). Online adaptive energy management strategy for fuel cell hybrid vehicles based on improved cluster and regression learner. Energy Conversion and Management, 292, 117388.
Lin, L, Bao, H., & Dinh, N. (2021). Uncertainty quantification and software risk analysis for digital twins in the nearly autonomous management and control systems: A review. Annals of Nuclear Energy, 160, 108362.
Love, P.E.D., Ika, L.A., & Pinto, J.K. (2022). Homo heuristicus: From risk management to managing uncertainty in large-scale infrastructure projects. IEEE Transactions on Engineering Management, 71, 1940-1949.
Martins, T.M. & Neves, R.F. (2020). Applying genetic algorithms with speciation for optimization of grid template detection in financial markets. Expert Systems with Applications, 147, 113191.
Mosteanu, N.R. (2019). Intelligent tool to prevent economic crisis‒fractals. A possible solution to assess the management of financial risk. Quality‒Access to Success, 20, 13‒17.
Pamučar, D.S., Božanić, D., & Ranđelović, A. (2017). Multi-criteria decision making: An example of sensitivity analysis. Serbian Journal of Management, 12, 1‒27.
Punetha, N. & Jain, G. (2023). Integrated Shannon entropy and COPRAS optimal model-based recommendation network. Evolutionary Intelligence, 17 (1), 1-13
Reddy, G.T., Reddy, M.P.K., Lakshmanna, K., Kaluri, R., Rajput, D.S., et al. (2020). Analysis of dimensionality reduction techniques on Big Data. IEEE Access, 8, 54776‒54788.
Rezazadeh, F., Rezazadeh, S., & Rezazadeh, M. (2023). Fractal organizations and employee-organization relationship dynamics. In Faghih, N. (ed.), Time and Fractals. Contributions to Management Science. Cham, Switzerland: Springer.
Rousseeuw, P.J. & Leroy, A.M. (1987). Robust regression and outlier detection. NY: Wiley.
Sadik, S., Et-tolba, M., & Nsiri, B. (2023). A novel regularization-based optimization approach to sparse mean-reverting portfolios selection. Optimization and Engineering, 24, 2549-2577.
Slanina, F. (2013). Essentials of econophysics modelling. Oxford, England: Oxford University Press.
Subramanian, I., Verma, S., Kumar, S., Jere, A., Anamika, K. (2020). Multi-omics data integration, interpretation, and its application. Bioinformatics and Biology Insights, 2020, 14, 1177932219899051.
Šmidovnik, T. & Grošelj, P. (2023). Solution for convergence problem in DEMATEL method: DEMATEL of finite sum of influences. Symmetry, 15 (7), 1357.
Tatsuoka, K.S., & Tyler, D.E. (2000). On the uniqueness of S-functionals and M-functionals under nonelliptical distributions. Annals of Statistics, 28, 1219‒1243.
Tilfani, O., Ferreira, P., & El Boukfaoui, M.Y. (2020). Multiscale optimal portfolios using CAPM fractal regression: Estimation for emerging stock markets. Post-Communist Economies, 32, 77‒112.
Vourdas, A. (2020). Uncertainty relations in terms of the Gini index for finite quantum systems. Europhysics Letters, 130, 20003.
Vujicić, M.D., Papić, M.Z., & Blajević, M.D. (2017). Comparative analysis of objective techniques for criteria weighing in two MCDM methods on example of an air conditioner selection. Tehnika, 67, 422‒429.
Wielicka-Gańczarczyk, K. & Jonek-Kowalska, I. (2023). Perceptions and attitudes toward risks of city administration employees in the context of smart city management. Smart Cities, 6, 1325‒1344.
Xiao, B., Yang, W., Wu, J., Walker, P.D., & Zhang, N. (2022). Energy management strategy via maximum entropy reinforcement learning for an extended range logistic vehicle. Energy, 253, 124105.
Zamani, M.G., Nikoo, M.R., Niknazar, F., Al-Rawas, G., Al-Wardy, M., & Gandomi, A.H. (2023). A multi-model data fusion methodology for reservoir water quality based on machine learning algorithms and Bayesian maximum entropy. Journal of Cleaner Production, 416, 137885.
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