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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2504.12990 |
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| _version_ | 1866908739081076736 |
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| author | Becchi, Matteo Pavan, Giovanni Maria |
| author_facet | Becchi, Matteo Pavan, Giovanni Maria |
| contents | In the analysis of any type of system, granting maximum information extraction from its data is non-trivial. Confidence in successful information extraction typically builds on prior knowledge of the studied system or on the user's experience. However, a robust and objective criterion for ensuring maximum information extraction from data is difficult to define. Here, we introduce a data-driven approach that employs Shannon entropy as a transferable metric to assess and quantify Maximum Information Extraction (MInE) from data via their clustering into statistically-relevant micro-domains. The method is general and can be applied virtually to any type of data or system. We demonstrate its efficiency by analyzing, as a first example, time-series data extracted from molecular dynamics simulations of water and ice coexisting at the solid/liquid transition temperature. The method allows quantifying the information contained in the data distributions (time-independent component) and the additional information gain attainable by analyzing data as time-series (i.e., accounting for the information contained in data time-correlations). The different micro-domains that can be effectively resolved and classified in the system are characterized by own entropy, which are found consistent with experimentally known thermodynamic parameters. A second test case demonstrates how the MInE approach is also effective for high-dimensional datasets and clearly shows how including little informative, but noisy, extra components/features in high-dimensional analyses may be not only useless, but even detrimental to maximum information extraction. This provides a robust parameter-free approach and quantitative metrics for data-analysis, and for the study of any type of system from its data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12990 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximum Information Extraction Via Clustering and Minimization of Shannon Entropy Becchi, Matteo Pavan, Giovanni Maria Data Analysis, Statistics and Probability In the analysis of any type of system, granting maximum information extraction from its data is non-trivial. Confidence in successful information extraction typically builds on prior knowledge of the studied system or on the user's experience. However, a robust and objective criterion for ensuring maximum information extraction from data is difficult to define. Here, we introduce a data-driven approach that employs Shannon entropy as a transferable metric to assess and quantify Maximum Information Extraction (MInE) from data via their clustering into statistically-relevant micro-domains. The method is general and can be applied virtually to any type of data or system. We demonstrate its efficiency by analyzing, as a first example, time-series data extracted from molecular dynamics simulations of water and ice coexisting at the solid/liquid transition temperature. The method allows quantifying the information contained in the data distributions (time-independent component) and the additional information gain attainable by analyzing data as time-series (i.e., accounting for the information contained in data time-correlations). The different micro-domains that can be effectively resolved and classified in the system are characterized by own entropy, which are found consistent with experimentally known thermodynamic parameters. A second test case demonstrates how the MInE approach is also effective for high-dimensional datasets and clearly shows how including little informative, but noisy, extra components/features in high-dimensional analyses may be not only useless, but even detrimental to maximum information extraction. This provides a robust parameter-free approach and quantitative metrics for data-analysis, and for the study of any type of system from its data. |
| title | Maximum Information Extraction Via Clustering and Minimization of Shannon Entropy |
| topic | Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2504.12990 |