Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms
We uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn–Knopp algorithm, widely used in diverse domains ranging from computer science and mathematics to economics. Despite minor formal differences between the two methods, both...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2024-01-01
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| Series: | Journal of Physics: Complexity |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/2632-072X/ad2697 |
| _version_ | 1827348969358884864 |
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| author | D Mazzilli M S Mariani F Morone A Patelli |
| author_facet | D Mazzilli M S Mariani F Morone A Patelli |
| author_sort | D Mazzilli |
| collection | DOAJ |
| description | We uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn–Knopp algorithm, widely used in diverse domains ranging from computer science and mathematics to economics. Despite minor formal differences between the two methods, both converge to the same fixed-point solution up to normalization. The discovered connection allows us to derive a rigorous interpretation of the Fitness and the Complexity metrics as the potentials of a suitable energy function. Under this interpretation, high-energy products are unfeasible for low-fitness countries, which explains why the algorithm is effective at displaying nested patterns in bipartite networks. We also show that the proposed interpretation reveals the scale invariance of the Fitness-Complexity algorithm, which has practical implications for the algorithm’s implementation in different datasets. Further, analysis of empirical trade data under the new perspective reveals three categories of countries that might benefit from different development strategies. |
| first_indexed | 2024-03-08T00:22:15Z |
| format | Article |
| id | doaj.art-bbc8979dffb44de8949b30bbb686f004 |
| institution | Directory Open Access Journal |
| issn | 2632-072X |
| language | English |
| last_indexed | 2024-03-08T00:22:15Z |
| publishDate | 2024-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | Journal of Physics: Complexity |
| spelling | doaj.art-bbc8979dffb44de8949b30bbb686f0042024-02-16T06:13:58ZengIOP PublishingJournal of Physics: Complexity2632-072X2024-01-015101501010.1088/2632-072X/ad2697Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithmsD Mazzilli0https://orcid.org/0000-0001-7948-7584M S Mariani1https://orcid.org/0000-0003-1032-5821F Morone2https://orcid.org/0000-0002-8830-1179A Patelli3https://orcid.org/0000-0002-1864-9612Enrico Fermi Research Center , via Panisperna 89a, 00184 Rome, ItalyInstitute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China , Chengdu 610054, People’s Republic of China; URPP Social Networks, University of Zurich , CH-8050 Zurich, SwitzerlandDepartment of Physics, New York University , New York, NY 10003, United States of AmericaEnrico Fermi Research Center , via Panisperna 89a, 00184 Rome, ItalyWe uncover the connection between the Fitness-Complexity algorithm, developed in the economic complexity field, and the Sinkhorn–Knopp algorithm, widely used in diverse domains ranging from computer science and mathematics to economics. Despite minor formal differences between the two methods, both converge to the same fixed-point solution up to normalization. The discovered connection allows us to derive a rigorous interpretation of the Fitness and the Complexity metrics as the potentials of a suitable energy function. Under this interpretation, high-energy products are unfeasible for low-fitness countries, which explains why the algorithm is effective at displaying nested patterns in bipartite networks. We also show that the proposed interpretation reveals the scale invariance of the Fitness-Complexity algorithm, which has practical implications for the algorithm’s implementation in different datasets. Further, analysis of empirical trade data under the new perspective reveals three categories of countries that might benefit from different development strategies.https://doi.org/10.1088/2632-072X/ad2697SinkhornFitness and Complexityeconomic ComplexitySinkhorn-KnoppOptimal Transport |
| spellingShingle | D Mazzilli M S Mariani F Morone A Patelli Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms Journal of Physics: Complexity Sinkhorn Fitness and Complexity economic Complexity Sinkhorn-Knopp Optimal Transport |
| title | Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms |
| title_full | Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms |
| title_fullStr | Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms |
| title_full_unstemmed | Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms |
| title_short | Equivalence between the Fitness-Complexity and the Sinkhorn-Knopp algorithms |
| title_sort | equivalence between the fitness complexity and the sinkhorn knopp algorithms |
| topic | Sinkhorn Fitness and Complexity economic Complexity Sinkhorn-Knopp Optimal Transport |
| url | https://doi.org/10.1088/2632-072X/ad2697 |
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