A Projection Pursuit Dynamic Cluster Model for Tourism Safety Early Warning and Its Implications for Sustainable Tourism
Abstract
:1. Introduction
2. Establishment of Tourism Safety Early Warning Evaluation Index System and Collection of Sample Data
2.1. Establishment of Tourism Safety Early Warning Evaluation Index System
- (1)
- The frequency of disasters at a destination: the frequency of hydrometeorological disasters (), the frequency of earthquakes and geological disasters (), and the frequency of epidemic diseases ().
- (2)
- The safety degree of tourism facilities: the service saturation of tourism facilities () and the degree of traffic safety ().
- (4)
- The regional stability of a destination: the political stability (), the social unemployment rate (), the social safety stability (), the rate of consumer price index increase (), and the potential index of host–guest cultural conflict ().
2.2. Criteria for Judging Individual Indicators of Tourism Safety Early Warning and the Collection of Sample Data
3. Introduction to the Principle of the Projection Pursuit Classification Model
- (1)
- Setting ( and are the maximum and minimum values of ). If is closest to the positive integer , then is classified as the category (). In this way, we classify all sample points into categories , record them as , and record the cluster kernels as .
- (2)
- Iteratively calculate the weights and thus obtain the projected value of the th sample . We classify all the sample points in into the categories according to the principle of proximity (the shortest absolute distance between the point and the kernels) and record them as
- (2)
- Form new cluster kernels , where , is the number of sample points in .
- (4)
- Repeat above steps (2)~(3) to obtain the dynamic clustering result sequence , . To set we obtain the sum of absolute distances between the intra-category sample points of each category after the th iteration as follows:
4. Empirical Research on Tourism Safety Early Warning
4.1. Empirical Research by Yang et al. [43]
4.2. Empirical Study with Sample Data by Wang and Li [44]
4.3. The Empirical Study with Sample Data by Zhu et al. [45]
5. Result and Discussion
5.1. Analysis of the PPDC Modeling Results of the Data [43,44,45]
5.2. The Evaluation Indicators Affecting the Levels of Tourism Safety Risk and the Importance of the Three Major Aspects
5.3. Measures and Suggestions to Reduce Tourism Safety Risks
5.4. Characteristics of the PPDC Model, Comparison with the other Conventional Evaluation Methods, and the Applicability Analysis
- (1)
- PPDC model. From a methodological point of view, the idea of a PPDC model is entirely consistent with the way of thinking of human beings for a comprehensive evaluation. Hence, a PPDC model is very suitable for the evaluation, classification, and ranking of tourism safety evaluation and early warning. First, the PPDC model can be applied to the modeling with a high-dimensional, non-linear, non-normal distribution sample data, particularly small samples. In contrast, PCA and FA are only suitable for cases with a strong linear correlation between evaluation indicators (or KMO is greater than 0.60) and obeying normal distribution. It overcomes the defect of the “curse of dimensionality” of PCA, FA, and BPNN models, which are mainly suitable for large sample data [28,48,51,53,54]. Second, according to the theorem proposed by Lou and Qiao [31], it is easy to judge whether the optimization process has obtained the proper, globally optimal solution, and the modeling difficulty is moderate. Third, the PPDC model is characterized by clear mathematical meaning, a linear relationship between the sample projected value (tourism safety score) and the evaluation indicators, and being highly convenient for subsequent applications, facilitating the direct determination of the importance and ranking of each evaluation indicator. Fourth, in the optimization process of the PPDC model, the weights of the evaluation indicator and the projected values of the sample are obtained simultaneously. There is no need to use other methods to determine the indicator weight and the sample’s expectation in advance, like the BPNN model, avoiding the influence of human factors to the greatest extent. Fifth, the empirical research shows that the results of the PPDC model are in good agreement with expert opinions, indicating sufficient accuracy of the PPDC model. Sixth, the PPDC model can integrate expert knowledge or decision-maker preference into its constraints to establish a PPDC model based on decision-maker preference. In contrast, all other comprehensive evaluation methods do not have this trait. Of course, when we build a PPDC model, we should determine a suitable number of classifications and reasonable initial clustering kernels.
- (2)
- BPNN model. Artificial neural networks are the most popular machine learning algorithm chosen to perform a risk assessment and safety early warning [55,56,57,58,59,60], particularly the BPNN model. Establishing a BPNN model with generalization ability and practical value must follow the required principles and steps [28,51,53,54,61]. First, the BPNN model is only suitable for modeling with large sample data, and it faces the defect of the “curse of dimensionality”. Second, it is necessary to use the “trial-and-error” method to manually determine the reasonable number of hidden layer nodes and other parameters and to judge whether there is “over-training” and other phenomena in the training process, and this method is highly subjective. For the given sample data, it is impossible to obtain exactly the same two models by establishing BPNN models twice before and after, suggesting the existence of ambiguity. Third, the BPNN model, as a non-linear model, cannot be directly used to judge the relationship between the model results and evaluation indicators, to judge the importance of indicators, and to propose measures and suggestions to reduce tourism safety risks, which greatly reduces the theoretical and practical significance of tourism safety evaluation and early warning. Therefore, the BPNN model is only used when other methods cannot achieve or face difficulty achieving satisfactory results and the conditions for BPNN modeling are met. Ref. [51] put forward a rule of thumb: you should aim to have at least five times as many cases (training samples) as connection weights in the network and preferably ten times as many for establishing a reliable and effective BPNN model [61]. The number of data in [43,44,45] is 48, 10, and 10, and the network topology used is 19-14-1 (the connection weights are 295), 10-5-4 (the connection weights 79), and 10-5-4, respectively. There are no validation samples used to monitor the training process; it is impossible to judge whether over-training has occurred. In the case of over-training occurring, even if the error of the training dataset is minimal, and even if the RMSE of the test dataset is casually small, the established model has no generalization ability and practical value. Scholars should pay more attention to this problem. The number of connection weights is obviously greater than the number of the samples in Refs. [43,44,45]. The rule of thumb is not obeyed, and the established BPNN models in Refs. [43,44,45] cannot have generalization ability and practice value [51,53,54,61]. The possible results in establishing a BPNN model with the data used by Yang et al. [46] are detailed given and discussed by Lou et al. [29]. Although Refs. [43,44,45] all described that they obtained the correct results, the established BPNN models still have no generalization ability, and their results are not reliable and accurate.
- (3)
- TOPSIS and GRA models based on Information Entropy (Lou et al., [29]), variation coefficient [62], and other weighing methods. The rationality of the results of these models directly depends on the rationality of the weighing, which is one of the critical contents of the comprehensive evaluation. This notwithstanding, the TOPSIS and the GRA methods are non-linear evaluation models and cannot be used to judge the relative importance of evaluation indicator and its ranking directly. Furthermore, TOPSIS and GRA models cannot be directly applied to clustering research, and other methods must be used to classify the results. The ranking of the verification samples T41-T48 through the PPDC model is entirely in agreement with that of TOPSIS [29].
- (4)
- Variable fuzzy set (VFS) method [26,27,28]. The VFS method requires the determination of the weights and relative membership function of each evaluation indicator in advance. Accompanied by the ambiguity feature, it is a non-linear evaluation method that cannot be used to judge the importance and ranking of the evaluation indicator directly. The rankings of sample T42 in Luo [33,34] are inconsistent.
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Parte, L.; Alberca, P. Business performance and sustainability in cultural and rural tourism destinations. Mathematics 2021, 9, 892. [Google Scholar] [CrossRef]
- Perez-Rodrıguez, J.V.; Rachinger, H.; Santana-Gallego, M. Does tourism promote economic growth? A fractionally integrated heterogeneous panel data analysis. Tour. Econ. 2022, 28, 1355–1376. [Google Scholar] [CrossRef]
- Wang, Y.; Tziamalis, A. International tourism and income inequality: The role of economic and financial development. Tour. Econ. 2023, 29, 1–29. [Google Scholar] [CrossRef]
- Vukovic, D.B.; Maiti, M.; Petrovic, M.D. Tourism employment and economic growth: Dynamic panel threshold analysis. Mathematics 2023, 11, 1112. [Google Scholar] [CrossRef]
- Jaisinghani, D.; Kaur, M.; Joshi, M.; Sharma, S.; Ahmed, A.D. Impact of political risk and economic growth on the tourism industry: Evidence from a dynamic threshold panel model. Tour. Econ. 2023. [Google Scholar] [CrossRef]
- Boluk, K.A.; Rasoolimanesh, S.M. Introduction to the Special Issue on “Deepening Our Understandings of the Roles and Responsibilities of the Tourism Industry towards the United Nations Sustainable Development Goals (SDGs)”. Tour. Manag. Perspect. 2022, 41, 100944. [Google Scholar] [CrossRef]
- UNWTO. UNWTO Discussion Paper on Sustainable Tourism for Development. 2015. Available online: http://media.unwto.org/content/unwto-news-1-special-international-year-sustainable-tourism-development-edition (accessed on 9 September 2023).
- Wang, X.; Zhang, M.; Jie, S.; Zhang, M.; Zhang, Z. Exploring the coordinated evolution mechanism of regional sustainable development and tourism in China’s “Beautiful China” initiative. Land 2023, 12, 1003. [Google Scholar] [CrossRef]
- Destek, M.A.; Aydin, S. An empirical note on tourism and sustainable development nexus. Environ. Sci. Pollut. Res. 2022, 29, 34515–34527. [Google Scholar] [CrossRef] [PubMed]
- Dwyer, L. Tourism development to enhance resident well-being: A strong sustainability perspective. Sustainability 2023, 15, 3321. [Google Scholar] [CrossRef]
- Farrukh, B.; Younis, I.; Cheng, L.S. The impact of natural resource management, innovation, and tourism development on environmental sustainability in low-income countries. Resour. Policy 2023, 86, 104088. [Google Scholar] [CrossRef]
- Kronenberg, K.; Fuchs, M. Aligning tourism’s socio-economic impact with the United Nations’ sustainable development goals. Tour. Manag. Perspect. 2021, 39, 100831. [Google Scholar] [CrossRef]
- León-Gómez, A.; Ruiz-Palomo, D.; Fernández-Gámez, M.A.; García-Revilla, M.R. Sustainable tourism development and economic growth: Bibliometric review and analysis. Sustainability 2021, 13, 2270. [Google Scholar] [CrossRef]
- Nagendrakumar, N.; Alwis, K.N.N.; Eshani, U.A.K.; Kaushalya, S.B.U. The impact of sustainability practices on the going concern of the travel and tourism industry: Evidence from developed and developing countries. Sustainability 2022, 14, 17046. [Google Scholar] [CrossRef]
- Umurzakov, U.; Tosheva, S.; Salahodjaev, R. Tourism and Sustainable Economic Development: Evidence from Belt and Road Countries. J. Knowl. Econ. 2023, 14, 503–516. [Google Scholar] [CrossRef]
- Vrana, V. Sustainable tourism development and innovation: Recent advances and challenges. Sustainability 2023, 15, 7224. [Google Scholar] [CrossRef]
- Herrera, M.R.G. Tourism Safety and Security with a Sustainability Vision, Ciudad Juarez (Mexico). In Advances in Tourism, Technology and Systems; Abreu, A., Carvalho, J.V., Liberato, D., Galdames, I.S., Eds.; Springer Nature Singapore Pte Ltd.: Singapore, 2023. [Google Scholar]
- Buhalis, D.; Costa, C. Tourism Management Dynamics: Trends, Management and Tools; Elsevier Butterworth-Heinemann: Oxford, UK, 2006. [Google Scholar]
- Mansfeld, Y.; Pizam, A. Tourism, Security and Safety—From Theory to Practice; Elsevier Inc.: Amsterdam, The Netherlands, 2006. [Google Scholar]
- Steene, A.N. Tourism safety and security. Tour. Econ. 2000, 6, 105–108. [Google Scholar] [CrossRef]
- Timothy, D.J. Safety and Security Issues in Tourism. In Tourism Management Dynamics: Trends, Management and Tools; Buhalis, D., Costa, C., Eds.; Elsevier: Oxford, UK, 2006. [Google Scholar]
- Santana-Gallego, M.; Fourie, J. Tourism falls apart: How insecurity affects African tourism. Tour. Econ. 2022, 28, 995–1008. [Google Scholar] [CrossRef]
- Caldeira, A.M.; Seabra, C.; AlAshry, M.S. Contrasting the COVID-19 effects on tourism safety perceptions and coping behavior among young people during two pandemic waves: Evidence from Egypt. Sustainability 2022, 14, 7492. [Google Scholar] [CrossRef]
- Agarwal, S.; Page, S.J.; Rob Mawby, R. Tourist security, terrorism risk management and tourist safety. Ann. Tour. Res. 2021, 89, 103207. [Google Scholar] [CrossRef]
- Beirman, D. Tourism crisis and safety management. In The SAGE Hanagement; Cooper, C., Volo, S., Gartner, W.C., Scott, N., Eds.; SAGE Publications Ltd.: London, UK, 2018. [Google Scholar]
- Xia, J.C.; Sun, P.P. A research on the construction of tourism industry security evaluation index system. J. Urban Stud. 2022, 43, 1–9. [Google Scholar]
- Xie, C.W. Study on the construction of tourism security pre-warning system in China. China Saf. Sci. J. 2010, 20, 170–176. [Google Scholar]
- Lou, W.G.; Qiao, L. A neural network-based financial risk early warning model and it’s empirical research. Financ. Forum 2011, 16, 52–61. [Google Scholar]
- Lou, W.G.; Wang, G.L.; Feng, G.Z. Evaluation of travel security early warnings by applying TOPSIS with information entropy weighting and positive research. Tour. Trib. 2013, 28, 66–74. [Google Scholar]
- Yu, Y.H.; Lou, W.G. Comprehensive evaluation and empirical research on the academic quality of physical education and sports journals. J. Beijing Sport Univ. 2015, 38, 46–54. [Google Scholar]
- Yu, X.H.; Lou, W.G.; Yu, X.R. The Comprehensive Evaluation and Empirical Research on the Development of China’s Provincial Inclusive Finance. Financ. Forum 2016, 21, 18–32. [Google Scholar]
- Su, W.H. Review and recognition on the research of multi-indicators comprehensive evaluation in China. Stat. Res. 2012, 29, 98–107. [Google Scholar]
- Luo, J.F. Application of variable fuzzy method in early warning of tourism safety. J. Saf. Sci. Technol. 2014, 10, 181–186. [Google Scholar]
- Luo, J.F. Set pair analysis-variable fuzzy method for tourism safety early warning. China Saf. Sci. J. 2015, 25, 151–156. [Google Scholar]
- Luo, J.F. Weighted variable fuzzy method of the tourism safety early warning. J. Wuhan Univ. Technol. Inf. Manag. Eng. 2017, 39, 510–513, 518. [Google Scholar]
- Zou, Y.G.; Zheng, X.M. Tourism destination safety evaluation based on the catastrophe theory. J. Saf. Sci. Technol. 2014, 10, 175–181. [Google Scholar]
- Friedman, J.H.; Tukey, J.W. A projection pursuit algorithm for exploratory data analysis. IEEE Trans. Comput. 1974, C-23, 881–890. [Google Scholar] [CrossRef]
- Lou, W.G.; Qiao, L. New theory exploration of projection pursuit clustering model and its positive research. J. Appl. Stat. Manag. 2015, 34, 47–58. [Google Scholar]
- Hamm, D.; Su, C.H. Managing tourism safety and risk: Using the Delphi expert consensus method in developing the event tourism security self-beliefs scale. J. Hosp. Tour. Manag. 2021, 49, 364–374. [Google Scholar] [CrossRef]
- Rauf, A.; Abbas, A.M.A.; Rafiq, A.; Shakir, S.; Abid, S. The Impact of political instability, food prices, and crime rate on tourism: A way toward sustainable tourism in Pakistan. Sustainability 2022, 14, 16993. [Google Scholar] [CrossRef]
- Ni, C.J.; Wang, S.J.; Cui, P. Projection pursuit dynamic cluster model and its application in groundwater classification. J. Sichuan Univ. Eng. Sci. Ed. 2006, 38, 29–33. [Google Scholar]
- Yu, X.H.; Luo, W.G.; Kang, H.Y. Dynamic clustering projection pursuit modeling for credit risk assessment of the corporates on supply chain and its positive research. Math. Pract. Theory 2018, 48, 32–40. [Google Scholar]
- Yang, J.B.; Huang, Y.L.; Li, F.; Chen, Y. Application of BP neural network in travel security early warning information system. Resour. Dev. Mark. 2007, 23, 108–111. [Google Scholar]
- Wang, H.B.; Li, X.F. Application of BP neural network in tourism crisis early warning system. Sci. Technol. Manag. Res. 2012, 32, 209–213. [Google Scholar]
- Zhu, X.; Wang, J.; Wu, G.Q. Research on the construction and application of indicators for early warning of tourism security. Tech-Econ. Manag. 2010, S1, 133–136. [Google Scholar]
- Ren, R.E.; Wang, H.W. Multivariate Statistical Data Analysis—Theory, Methods, Examples; National Defense Industry Press: Beijing, China, 1999. [Google Scholar]
- Tang, Q.Y. Data Processing System (DPS): Experimental Design, Statistical Analysis and Data Mining; Science Press: Beijing, China, 2010. [Google Scholar]
- Lou, W.G. Projection Pursuit Theory Based on Swarm Intelligence Optimization Algorithm: New Progress, Application and Software; Fudan University Press: Shanghai, China, 2021. [Google Scholar]
- Zhang, W.F.; Liu, H.Y. MATLAB implementation of the improved group search optimizer algorithm. Comput. Inf. Technol. 2010, 18, 44–46. [Google Scholar]
- Lee, E.K.; Cook, D. A projection pursuit index for large p small n data. Stat. Comput. 2010, 20, 381–392. [Google Scholar] [CrossRef]
- STATSOFT Inc. Electronic Statistics Textbook. Tulsa. 2011. Available online: http://www.statsoft.com/textbook (accessed on 8 June 2023).
- Tabachnick, B.G.; Fidell, L.S. Using Multivariate Statistics; Pearson Education, Inc.: London, UK, 2013. [Google Scholar]
- Zhang, G.; Patuwo, E.; Hu, M. Forecasting with artificial neural networks: The state of the art. Int. J. Forecast. 1998, 14, 35–62. [Google Scholar] [CrossRef]
- Yu, X.H.; Xu, H.Y.; Lou, W.G.; Xu, X.; Shi, V. Examining energy eco-efficiency in China’s logistics industry. Int. J. Prod. Econ. 2023, 258, 108797. [Google Scholar] [CrossRef]
- Feng, L.; Hao, Y.K. Optimization algorithm of tourism security early warning information system based on long short-term memory (LSTM). Comput. Intell. Neurosci. 2021, 2021, 9984003. [Google Scholar] [CrossRef] [PubMed]
- Guo, W. Safety risk assessment of tourism management system based on PSO-BP neural network. Comput. Intell. Neurosci. 2021, 2021, 1980037. [Google Scholar] [CrossRef]
- Hegde, J.; Rokseth, B. Applications of machine learning methods for engineering risk assessment—A review. Saf. Sci. 2020, 122, 104492. [Google Scholar] [CrossRef]
- Niu, T.T. Smart safety early warning model of landslide geological hazard based on BP neural network. Saf. Sci. 2020, 123, 104572. [Google Scholar] [CrossRef]
- Zhang, H.; Li, Y.; Zhang, H. Risk early warning safety model for sports events based on back propagation neural network machine learning. Saf. Sci. 2019, 118, 332–336. [Google Scholar] [CrossRef]
- Zhong, C.H.; Lou, W.G.; Wang, C.T. Neural network-based modeling for risk evaluation and early warning for large-scale sports events. Mathematics 2022, 10, 3228. [Google Scholar] [CrossRef]
- Yu, X.; Lou, W. An exploration of prediction performance based on projection pursuit regression in conjunction with data envelopment analysis: A comparison with artificial neural networks and support vector regression. Mathematics 2023, 11, 4775. [Google Scholar] [CrossRef]
- Pu, X.G.; Liu, L.M. An empirical tudy on the performance evaluation of databases based on Coefficient of variation and grey relational analysis. Libr. Inf. Serv. 2014, 58, 71–78. [Google Scholar]
Safety Status | Frequency of Hydrometeorological Disasters ) * | Frequency of Earthquakes and Geological Disasters ) | Frequency of Epidemic Diseases ) | Service Saturation of Tourism Facilities ) ** | Degree in Traffic Safety ) | Political Stability ) | Unemployment Rate ) | Social Safety Stability ) | Rate of Consumer Price Index Increase ) | ) | Alarming Mode |
---|---|---|---|---|---|---|---|---|---|---|---|
Excellent | 0.10 | 0.10 | 0.10 | 0.80 | 0.45 | 0.70 | 0.05 | 0.70 | 0.05 | 0.10 | Green |
Good | 0.15 | 0.15 | 0.20 | 0.70 | 0.35 | 0.60 | 0.06 | 0.60 | 0.10 | 0.20 | Blue |
Fair | 0.20 | 0.20 | 0.30 | 0.60 | 0.25 | 0.50 | 0.08 | 0.50 | 0.20 | 0.30 | Orange |
Poor | >0.20 | >0.20 | >0.30 | <0.60 | >0.25 | <0.50 | >0.08 | <0.50 | >0.20 | >0.30 | Red |
Samples | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
T1 | 0.93 | 0.92 | 0.93 | 0.94 | 0.52 | 0.75 | 0.28 | 0.75 | 0.97 | 0.90 |
T2 | 0.95 | 0.93 | 0.94 | 0.87 | 0.51 | 0.72 | 0.27 | 0.70 | 0.96 | 0.89 |
T3 | 0.96 | 0.94 | 0.96 | 0.93 | 0.53 | 0.69 | 0.29 | 0.72 | 0.95 | 0.84 |
T4 | 0.95 | 0.95 | 0.92 | 0.88 | 0.51 | 0.77 | 0.26 | 0.74 | 0.96 | 0.85 |
T5 | 0.94 | 0.90 | 0.90 | 0.87 | 0.47 | 0.74 | 0.27 | 0.71 | 0.99 | 0.90 |
T6 | 0.91 | 0.91 | 0.92 | 0.95 | 0.50 | 0.71 | 0.28 | 0.73 | 0.98 | 0.91 |
T7 | 0.92 | 0.93 | 0.91 | 0.92 | 0.49 | 0.73 | 0.26 | 0.68 | 0.95 | 0.88 |
T8 | 0.94 | 0.89 | 0.94 | 0.86 | 0.46 | 0.68 | 0.25 | 0.72 | 0.96 | 0.89 |
T9 | 0.93 | 0.92 | 0.97 | 0.94 | 0.48 | 0.73 | 0.28 | 0.77 | 0.97 | 0.87 |
T10 | 0.95 | 0.91 | 0.95 | 0.89 | 0.43 | 0.69 | 0.27 | 0.69 | 0.98 | 0.86 |
T11 | 0.88 | 0.89 | 0.85 | 0.88 | 0.42 | 0.65 | 0.25 | 0.65 | 0.94 | 0.82 |
T12 | 0.87 | 0.90 | 0.88 | 0.86 | 0.41 | 0.66 | 0.24 | 0.63 | 0.95 | 0.83 |
T13 | 0.89 | 0.88 | 0.87 | 0.68 | 0.4 | 0.64 | 0.25 | 0.60 | 0.93 | 0.85 |
T14 | 0.90 | 0.87 | 0.86 | 0.82 | 0.38 | 0.67 | 0.26 | 0.66 | 0.91 | 0.81 |
T15 | 0.88 | 0.86 | 0.84 | 0.80 | 0.44 | 0.58 | 0.24 | 0.58 | 0.90 | 0.77 |
T16 | 0.89 | 0.87 | 0.79 | 0.87 | 0.35 | 0.59 | 0.25 | 0.68 | 0.89 | 0.84 |
T17 | 0.92 | 0.84 | 0.83 | 0.89 | 0.39 | 0.61 | 0.24 | 0.64 | 0.92 | 0.78 |
T18 | 0.86 | 0.90 | 0.82 | 0.85 | 0.38 | 0.63 | 0.26 | 0.61 | 0.93 | 0.79 |
T19 | 0.88 | 0.89 | 0.90 | 0.89 | 0.36 | 0.68 | 0.25 | 0.67 | 0.90 | 0.82 |
T20 | 0.91 | 0.85 | 0.81 | 0.88 | 0.37 | 0.60 | 0.24 | 0.62 | 0.94 | 0.8 |
T21 | 0.85 | 0.85 | 0.8 | 0.76 | 0.30 | 0.54 | 0.23 | 0.57 | 0.91 | 0.75 |
T22 | 0.87 | 0.86 | 0.71 | 0.75 | 0.33 | 0.52 | 0.22 | 0.51 | 0.88 | 0.76 |
T23 | 0.86 | 0.82 | 0.72 | 0.68 | 0.32 | 0.56 | 0.24 | 0.56 | 0.85 | 0.77 |
T24 | 0.81 | 0.84 | 0.79 | 0.79 | 0.36 | 0.58 | 0.24 | 0.52 | 0.88 | 0.72 |
T25 | 0.83 | 0.81 | 0.74 | 0.76 | 0.29 | 0.57 | 0.22 | 0.58 | 0.84 | 0.74 |
T26 | 0.82 | 0.82 | 0.82 | 0.82 | 0.28 | 0.54 | 0.23 | 0.54 | 0.82 | 0.71 |
T27 | 0.85 | 0.79 | 0.75 | 0.77 | 0.30 | 0.60 | 0.24 | 0.60 | 0.85 | 0.76 |
T28 | 0.84 | 0.81 | 0.78 | 0.78 | 0.35 | 0.51 | 0.22 | 0.49 | 0.83 | 0.78 |
T29 | 0.85 | 0.80 | 0.77 | 0.84 | 0.34 | 0.53 | 0.25 | 0.55 | 0.89 | 0.74 |
T30 | 0.83 | 0.83 | 0.69 | 0.77 | 0.31 | 0.59 | 0.23 | 0.59 | 0.86 | 0.75 |
T31 | 0.80 | 0.80 | 0.60 | 0.7 | 0.20 | 0.45 | 0.21 | 0.45 | 0.81 | 0.70 |
T32 | 0.78 | 0.75 | 0.55 | 0.72 | 0.22 | 0.44 | 0.20 | 0.42 | 0.78 | 0.69 |
T33 | 0.81 | 0.77 | 0.66 | 0.74 | 0.21 | 0.43 | 0.22 | 0.41 | 0.68 | 0.68 |
T34 | 0.77 | 0.76 | 0.76 | 0.71 | 0.25 | 0.46 | 0.18 | 0.46 | 0.72 | 0.66 |
T35 | 0.79 | 0.78 | 0.68 | 0.79 | 0.28 | 0.49 | 0.19 | 0.42 | 0.80 | 0.63 |
T36 | 0.76 | 0.79 | 0.66 | 0.75 | 0.26 | 0.47 | 0.21 | 0.48 | 0.73 | 0.65 |
T37 | 0.78 | 0.81 | 0.67 | 0.73 | 0.27 | 0.50 | 0.22 | 0.47 | 0.62 | 0.64 |
T38 | 0.82 | 0.79 | 0.63 | 0.78 | 0.24 | 0.48 | 0.12 | 0.50 | 0.55 | 0.67 |
T39 | 0.81 | 0.78 | 0.54 | 0.76 | 0.23 | 0.42 | 0.13 | 0.43 | 0.61 | 0.63 |
T40 | 0.80 | 0.76 | 0.72 | 0.66 | 0.22 | 0.51 | 0.12 | 0.49 | 0.72 | 0.65 |
T41 | 0.91 | 0.94 | 0.96 | 0.96 | 0.45 | 0.75 | 0.28 | 0.73 | 0.97 | 0.88 |
T42 | 0.94 | 0.89 | 0.71 | 0.88 | 0.52 | 0.62 | 0.26 | 0.67 | 0.96 | 0.89 |
T43 | 0.92 | 0.89 | 0.85 | 0.83 | 0.38 | 0.68 | 0.25 | 0.69 | 0.94 | 0.86 |
T44 | 0.86 | 0.84 | 0.80 | 0.75 | 0.43 | 0.65 | 0.22 | 0.68 | 0.91 | 0.83 |
T45 | 0.84 | 0.82 | 0.73 | 0.68 | 0.35 | 0.52 | 0.23 | 0.55 | 0.88 | 0.69 |
T46 | 0.83 | 0.79 | 0.68 | 0.57 | 0.28 | 0.58 | 0.21 | 0.50 | 0.85 | 0.77 |
T47 | 0.72 | 0.80 | 0.65 | 0.63 | 0.26 | 0.47 | 0.18 | 0.50 | 0.78 | 0.7 |
T48 | 0.79 | 0.77 | 0.56 | 0.58 | 0.28 | 0.41 | 0.15 | 0.41 | 0.72 | 0.48 |
Samples | Safety Level | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
W1 | 97.56 | 89.37 | 7.36 | 8.15 | 3.45 | 90.24 | 88.62 | 7.47 | 0.67 | 6.38 | no-alarm |
W2 | 77.13 | 79.65 | 12.81 | 13.52 | 5.34 | 80.74 | 75.63 | 13.78 | 1.57 | 18.52 | light-alarm |
W3 | 72.58 | 75.31 | 14.36 | 12.67 | 5.86 | 75.26 | 72.37 | 16.24 | 2.62 | 16.39 | light-alarm |
W4 | 65.37 | 71.45 | 17.82 | 16.23 | 7.38 | 69.31 | 63.18 | 25.62 | 3.54 | 24.63 | medium-alarm |
W5 | 94.76 | 92.84 | 5.27 | 8.63 | 2.58 | 93.18 | 82.23 | 6.59 | 0.58 | 8.12 | no-alarm |
W6 | 42.55 | 58.29 | 35.46 | 42.37 | 12.62 | 60.03 | 55.32 | 30.21 | 4.36 | 41.28 | serious-alarm |
W7 | 58.11 | 68.62 | 16.39 | 18.24 | 6.51 | 59.37 | 67.29 | 24.73 | 3.01 | 27.58 | medium-alarm |
W8 | 78.49 | 77.26 | 13.56 | 14.81 | 5.02 | 77.19 | 76.54 | 17.20 | 2.74 | 17.62 | light-alarm |
W9 | 88.32 | 89.43 | 6.54 | 7.31 | 4.26 | 87.75 | 91.23 | 5.13 | 0.35 | 7.53 | no-alarm |
W10 | 52.74 | 74.83 | 18.47 | 17.53 | 7.73 | 73.84 | 64.51 | 27.32 | 3.22 | 28.19 | medium-alarm |
W11 | 75.64 | 84.52 | 11.24 | 11.85 | 5.47 | 79.31 | 71.23 | 15.63 | 1.83 | 15.37 | light-alarm |
W12 | 37.64 | 61.38 | 47.28 | 38.16 | 15.28 | 66.81 | 58.74 | 31.49 | 4.61 | 39.56 | serious-alarm |
W13 | 83.71 | 93.26 | 8.76 | 6.77 | 3.16 | 89.32 | 84.86 | 8.39 | 0.79 | 9.12 | no-alarm |
No. | y | |||||||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | 0.75 | 0.80 | 0.28 | 0.29 | 0.40 | 0.75 | 0.90 | 0.52 | 0.85 | 0.90 | 0.90 | 0.92 | 0.90 | 0.80 | 0.94 | 0.96 | 0.98 | 0.95 | 0.93 | 0.95 |
2 | 0.74 | 0.76 | 0.27 | 0.29 | 0.40 | 0.71 | 0.89 | 0.47 | 0.80 | 0.89 | 0.89 | 0.91 | 0.85 | 0.78 | 0.93 | 0.94 | 0.92 | 0.96 | 0.90 | 0.92 |
3 | 0.69 | 0.66 | 0.27 | 0.28 | 0.36 | 0.69 | 0.86 | 0.43 | 0.78 | 0.87 | 0.89 | 0.95 | 0.84 | 0.70 | 0.91 | 0.92 | 0.91 | 0.92 | 0.95 | 0.85 |
4 | 0.65 | 0.61 | 0.25 | 0.26 | 0.32 | 0.65 | 0.85 | 0.42 | 0.75 | 0.85 | 0.78 | 0.88 | 0.75 | 0.65 | 0.91 | 0.88 | 0.90 | 0.89 | 0.85 | 0.77 |
5 | 0.58 | 0.52 | 0.24 | 0.26 | 0.27 | 0.58 | 0.80 | 0.44 | 0.72 | 0.82 | 0.75 | 0.85 | 0.70 | 0.60 | 0.90 | 0.88 | 0.87 | 0.86 | 0.84 | 0.70 |
6 | 0.60 | 0.62 | 0.24 | 0.25 | 0.30 | 0.62 | 0.76 | 0.37 | 0.70 | 0.80 | 0.70 | 0.80 | 0.70 | 0.50 | 0.91 | 0.88 | 0.85 | 0.85 | 0.81 | 0.65 |
7 | 0.54 | 0.56 | 0.23 | 0.25 | 0.25 | 0.57 | 0.74 | 0.30 | 0.65 | 0.75 | 0.68 | 0.79 | 0.68 | 0.40 | 0.88 | 0.85 | 0.85 | 0.83 | 0.80 | 0.58 |
8 | 0.57 | 0.59 | 0.22 | 0.25 | 0.24 | 0.58 | 0.70 | 0.29 | 0.62 | 0.72 | 0.64 | 0.76 | 0.65 | 0.35 | 0.85 | 0.82 | 0.83 | 0.83 | 0.74 | 0.55 |
9 | 0.59 | 0.55 | 0.23 | 0.24 | 0.25 | 0.59 | 0.65 | 0.31 | 0.60 | 0.70 | 0.60 | 0.73 | 0.63 | 0.30 | 0.83 | 0.80 | 0.81 | 0.82 | 0.69 | 0.52 |
10 | 0.45 | 0.49 | 0.21 | 0.19 | 0.20 | 0.45 | 0.62 | 0.28 | 0.58 | 0.65 | 0.55 | 0.69 | 0.48 | 0.21 | 0.80 | 0.79 | 0.81 | 0.82 | 0.59 | 0.49 |
11 | 0.49 | 0.45 | 0.19 | 0.16 | 0.13 | 0.42 | 0.59 | 0.28 | 0.54 | 0.61 | 0.51 | 0.64 | 0.45 | 0.19 | 0.79 | 0.78 | 0.81 | 0.78 | 0.65 | 0.43 |
12 | 0.90 | 0.95 | 0.26 | 0.26 | 0.40 | 0.75 | 0.91 | 0.61 | 0.85 | 0.10 | 0.82 | 0.85 | 0.87 | 0.64 | 0.86 | 0.84 | 0.98 | 0.92 | 0.95 | / |
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhong, C.; Lou, W.; Lai, Y. A Projection Pursuit Dynamic Cluster Model for Tourism Safety Early Warning and Its Implications for Sustainable Tourism. Mathematics 2023, 11, 4919. https://doi.org/10.3390/math11244919
Zhong C, Lou W, Lai Y. A Projection Pursuit Dynamic Cluster Model for Tourism Safety Early Warning and Its Implications for Sustainable Tourism. Mathematics. 2023; 11(24):4919. https://doi.org/10.3390/math11244919
Chicago/Turabian StyleZhong, Chenghao, Wengao Lou, and Yongzeng Lai. 2023. "A Projection Pursuit Dynamic Cluster Model for Tourism Safety Early Warning and Its Implications for Sustainable Tourism" Mathematics 11, no. 24: 4919. https://doi.org/10.3390/math11244919
APA StyleZhong, C., Lou, W., & Lai, Y. (2023). A Projection Pursuit Dynamic Cluster Model for Tourism Safety Early Warning and Its Implications for Sustainable Tourism. Mathematics, 11(24), 4919. https://doi.org/10.3390/math11244919