Creation of a Spatiotemporal Algorithm and Application to COVID-19 Data
Abstract
:1. Introduction
2. Spatiotemporal Data Analysis and Clustering
2.1. Training the Algorithm for Spatiotemporal Data
2.2. Key Parameters of the Developed Algorithm
2.3. Best Matching Unit and Prototype Vectors
Algorithm 1: Spatiotemporal Clustering Algorithm (proposed in this study and inspired by the works of Aaron et al. [29,30]). |
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2.4. Summary of the Algorithm and Detailed Steps
3. Application to COVID-19 Dataset and Results
3.1. COVID-19 Dataset
3.2. Clustering Results and Discussion
3.2.1. Construction and Composition of the Different Classes
3.2.2. Evolution of COVID-19 in France, Italy, Sweden, and the United States
4. Advantages and Utility of the Constructed Algorithm
Theoretical Comparison of Clustering Methods
5. Time and Space Complexity Analysis
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Parameter | Explanation |
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M | Number of study periods. Represents the number of distinct temporal periods considered in the analysis. |
S | Number of populations. Represents the number of distinct populations (e.g., countries) considered in the analysis. |
D | Data Set. Collection of N data objects characterized by , where s denotes a population and m denotes a period. |
X | Data Representation. Vector of variables associated with each data point in D, enabling comparisons and similarity calculations. |
K | Desired number of groups. Represents the desired final number of clusters or prototypes aimed to be formed within the data. |
Ultimate Superclasses. Subset of P obtained using ascending hierarchical method, representing the final groups. | |
Learning Rate. Percentage by which the algorithm learns during each iteration, influencing modification of prototype vectors. | |
Temporal Neighborhood Function. Governs intensity with which neurons having different times than BMU approach a data point. | |
Spatial Neighborhood Function. Determines intensity with which neurons with same period as BMU approach a data point. | |
Temporal Radius. Defines extent of temporal influence, allowing adjustments in temporal neighborhood function. | |
Spatial Radius. Controls spatial influence on clustering, impacting spatial neighborhood function. | |
Total Spatial Iterations. Represents total number of spatial iterations, influencing cluster evolution over space. | |
Total Temporal Iterations. Represents total temporal iterations within each spatial iteration, allowing exploration of temporal patterns. | |
Clustering Target. Desired final number of clusters or prototypes aimed to be formed within the data. | |
Initial Spatial Radius. Initial spatial radius for neighborhood functions. | |
Final Spatial Radius. Final spatial radius for neighborhood functions. | |
Initial Temporal Radius. Initial temporal radius for neighborhood functions. | |
Final Temporal Radius. Final temporal radius for neighborhood functions. | |
E | Number of Randomly Selected Populations. Represents number of randomly selected populations from the dataset. |
Prototype Vector. Serves as the prototype vector associated with neuron k, evolving during clustering to capture cluster characteristics. | |
BMU | Best Matching Unit. Identifies the neuron with the prototype vector closest to the data point, pivotal in clustering. |
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Bou Sakr, N.; Mansour, G.; Salhi, Y. Creation of a Spatiotemporal Algorithm and Application to COVID-19 Data. COVID 2024, 4, 1291-1314. https://doi.org/10.3390/covid4080092
Bou Sakr N, Mansour G, Salhi Y. Creation of a Spatiotemporal Algorithm and Application to COVID-19 Data. COVID. 2024; 4(8):1291-1314. https://doi.org/10.3390/covid4080092
Chicago/Turabian StyleBou Sakr, Natalia, Gihane Mansour, and Yahia Salhi. 2024. "Creation of a Spatiotemporal Algorithm and Application to COVID-19 Data" COVID 4, no. 8: 1291-1314. https://doi.org/10.3390/covid4080092