On the convergence of the Fitness-Complexity algorithm
We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q . The algorithm was originally based on the adjacency...
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| Published in: | The European physical journal. ST, Special topics Vol. 225; no. 10; pp. 1893 - 1911 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Berlin/Heidelberg
Springer Berlin Heidelberg
01.10.2016
Springer Nature B.V |
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| ISSN: | 1951-6355, 1951-6401 |
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| Abstract | We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness
F
and Complexity
Q
. The algorithm was originally based on the adjacency matrix
M
of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of
F
and
Q
. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied. |
|---|---|
| AbstractList | We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q. The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q. Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied. We investigate the convergence properties of an algorithm which has been recently proposed to measure the competitiveness of countries and the quality of their exported products. These quantities are called respectively Fitness F and Complexity Q . The algorithm was originally based on the adjacency matrix M of the bipartite network connecting countries with the products they export, but can be applied to any bipartite network. The structure of the adjacency matrix turns to be essential to determine which countries and products converge to non zero values of F and Q . Also the speed of convergence to zero depends on the matrix structure. A major role is played by the shape of the ordered matrix and, in particular, only those matrices whose diagonal does not cross the empty part are guaranteed to have non zero values as outputs when the algorithm reaches the fixed point. We prove this result analytically for simplified structures of the matrix, and numerically for real cases. Finally, we propose some practical indications to take into account our results when the algorithm is applied. |
| Author | Zaccaria, Andrea Pugliese, Emanuele Pietronero, Luciano |
| Author_xml | – sequence: 1 givenname: Emanuele surname: Pugliese fullname: Pugliese, Emanuele organization: Istituto dei Sistemi Complessi, via dei Taurini 19, Sapienza Università di Roma, Piazzale Aldo Moro 2 – sequence: 2 givenname: Andrea surname: Zaccaria fullname: Zaccaria, Andrea email: and.zaccaria@gmail.com organization: Istituto dei Sistemi Complessi, via dei Taurini 19, Sapienza Università di Roma, Piazzale Aldo Moro 2 – sequence: 3 givenname: Luciano surname: Pietronero fullname: Pietronero, Luciano organization: Istituto dei Sistemi Complessi, via dei Taurini 19, Sapienza Università di Roma, Piazzale Aldo Moro 2 |
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| References | TacchellaA.CristelliM.CaldarelliG.GabrielliA.PietroneroL.Sci. Rep.201227232012NatSR...2E.723T10.1038/srep00723 D. Ricardo, On the Principles of Political Economy and Taxation (John Murray, 1817) R.J. Barro, X. Sala-i Martin, Economic Growth (MIT Press, 2004) ZaccariaA.CristelliM.KupersR.TacchellaA.PietroneroL.J. Econom. Interact. Coord.20161115110.1007/s11403-015-0145-9 G. Caldarelli, Scale-free Networks: Complex Cebs in Nature and Technology (Oxford University Press, 2004) S. Brin, L. Page, in Computer Networks and ISDN Systems (1998), p. 107 HidalgoC.HausmannR.Proc. Natl. Acad. Sci. USA,2009106105702009PNAS..10610570H10.1073/pnas.0900943106 ZaccariaA.CristelliM.TacchellaA.PietroneroL.PLoS ONE20149e1137702014PLoSO...9k3770Z10.1371/journal.pone.0113770 CristelliM.GabrielliA.TacchellaA.CaldarelliG.PietroneroL.PLoS ONE20138e707262013PLoSO...870726C10.1371/journal.pone.0070726 CristelliM.TacchellaA.L. Pietronero. PLoS ONE201510e011717410.1371/journal.pone.0117174 M. Cristelli, A. Tacchella, A. Zaccaria, L. Pietronero, Growth Scenarios for Sub-Saharan Countries in the Framework of Economic Complexity (2015) https://mpra.ub.uni-muenchen.de/71594 E. Pugliese, G.L. Chiarotti, A. Zaccaria, L. Pietronero, Complex economies have a lateral escape from the poverty trap [arXiv:1511.08622] (2015) BalassaB.Manchester School1965339910.1111/j.1467-9957.1965.tb00050.x G. Gaulier, S. Zignago, Baci: International trade database at the product-level. Centre d’Etudes Prospectives et d’Informations Internationales (2010), http://www.cepii.fr/anglaisgraph/workpap/pdf/2010/wp2010-23.pdf R.C. Feenstra, R.E. Lipsey, H. Deng, A.C. Ma, H. Mo, World trade flows: 1962–2000. Technical report (National Bureau of Economic Research, 2005) M. Cristelli (50118_CR14) 2015; 10 A. Tacchella (50118_CR1) 2012; 2 50118_CR15 A. Zaccaria (50118_CR12) 2014; 9 B. Balassa (50118_CR4) 1965; 33 50118_CR10 50118_CR13 M. Cristelli (50118_CR5) 2013; 8 50118_CR3 50118_CR2 50118_CR8 50118_CR7 50118_CR6 C. Hidalgo (50118_CR9) 2009; 106 A. Zaccaria (50118_CR11) 2016; 11 |
| References_xml | – reference: R.C. Feenstra, R.E. Lipsey, H. Deng, A.C. Ma, H. Mo, World trade flows: 1962–2000. Technical report (National Bureau of Economic Research, 2005) – reference: G. Gaulier, S. Zignago, Baci: International trade database at the product-level. Centre d’Etudes Prospectives et d’Informations Internationales (2010), http://www.cepii.fr/anglaisgraph/workpap/pdf/2010/wp2010-23.pdf – reference: HidalgoC.HausmannR.Proc. Natl. Acad. Sci. USA,2009106105702009PNAS..10610570H10.1073/pnas.0900943106 – reference: ZaccariaA.CristelliM.KupersR.TacchellaA.PietroneroL.J. Econom. Interact. Coord.20161115110.1007/s11403-015-0145-9 – reference: E. Pugliese, G.L. Chiarotti, A. Zaccaria, L. Pietronero, Complex economies have a lateral escape from the poverty trap [arXiv:1511.08622] (2015) – reference: D. Ricardo, On the Principles of Political Economy and Taxation (John Murray, 1817) – reference: CristelliM.TacchellaA.L. Pietronero. PLoS ONE201510e011717410.1371/journal.pone.0117174 – reference: M. Cristelli, A. Tacchella, A. Zaccaria, L. Pietronero, Growth Scenarios for Sub-Saharan Countries in the Framework of Economic Complexity (2015) https://mpra.ub.uni-muenchen.de/71594/ – reference: TacchellaA.CristelliM.CaldarelliG.GabrielliA.PietroneroL.Sci. Rep.201227232012NatSR...2E.723T10.1038/srep00723 – reference: G. Caldarelli, Scale-free Networks: Complex Cebs in Nature and Technology (Oxford University Press, 2004) – reference: BalassaB.Manchester School1965339910.1111/j.1467-9957.1965.tb00050.x – reference: CristelliM.GabrielliA.TacchellaA.CaldarelliG.PietroneroL.PLoS ONE20138e707262013PLoSO...870726C10.1371/journal.pone.0070726 – reference: R.J. Barro, X. Sala-i Martin, Economic Growth (MIT Press, 2004) – reference: S. Brin, L. Page, in Computer Networks and ISDN Systems (1998), p. 107 – reference: ZaccariaA.CristelliM.TacchellaA.PietroneroL.PLoS ONE20149e1137702014PLoSO...9k3770Z10.1371/journal.pone.0113770 – ident: 50118_CR2 doi: 10.3386/w11040 – ident: 50118_CR8 doi: 10.1016/S0169-7552(98)00110-X – volume: 106 start-page: 10570 year: 2009 ident: 50118_CR9 publication-title: Proc. Natl. Acad. Sci. USA, doi: 10.1073/pnas.0900943106 – volume: 2 start-page: 723 year: 2012 ident: 50118_CR1 publication-title: Sci. Rep. doi: 10.1038/srep00723 – ident: 50118_CR3 doi: 10.2139/ssrn.1994500 – volume: 33 start-page: 99 year: 1965 ident: 50118_CR4 publication-title: Manchester School doi: 10.1111/j.1467-9957.1965.tb00050.x – volume: 10 start-page: e0117174 year: 2015 ident: 50118_CR14 publication-title: L. Pietronero. PLoS ONE doi: 10.1371/journal.pone.0117174 – volume: 9 start-page: e113770 year: 2014 ident: 50118_CR12 publication-title: PLoS ONE doi: 10.1371/journal.pone.0113770 – volume: 8 start-page: e70726 year: 2013 ident: 50118_CR5 publication-title: PLoS ONE doi: 10.1371/journal.pone.0070726 – ident: 50118_CR6 doi: 10.3386/w9682 – ident: 50118_CR7 – ident: 50118_CR13 – volume: 11 start-page: 151 year: 2016 ident: 50118_CR11 publication-title: J. Econom. Interact. Coord. doi: 10.1007/s11403-015-0145-9 – ident: 50118_CR15 – ident: 50118_CR10 |
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| SubjectTerms | Algorithms Atomic Classical and Continuum Physics Complex Complexity Condensed Matter Physics Convergence Fitness Inter-networked Economic and Social Systems Materials Science Measurement Science and Instrumentation Molecular Optical and Plasma Physics Physics Physics and Astronomy Regular Article |
| Title | On the convergence of the Fitness-Complexity algorithm |
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