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Open AccessArticle

Complexity of Products: The Effect of Data Regularisation

by 1,*,†,‡ and 1,2,3,†,‡
1
Department of Mathematics, King’s College London, The Strand, London WC2R 2LS, UK
2
Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
3
Complexity Science Hub Vienna, Josefstaedter Strasse 39, A 1080 Vienna, Austria
*
Author to whom correspondence should be addressed.
Current address: Department of Mathematics, King’s College London, The Strand, London WC2R 2LS, UK.
These authors contributed equally to this work.
Entropy 2018, 20(11), 814; https://doi.org/10.3390/e20110814
Received: 12 August 2018 / Revised: 12 October 2018 / Accepted: 15 October 2018 / Published: 23 October 2018
(This article belongs to the Special Issue Economic Fitness and Complexity)
Among several developments, the field of Economic Complexity (EC) has notably seen the introduction of two new techniques. One is the Bootstrapped Selective Predictability Scheme (SPSb), which can provide quantitative forecasts of the Gross Domestic Product of countries. The other, Hidden Markov Model (HMM) regularisation, denoises the datasets typically employed in the literature. We contribute to EC along three different directions. First, we prove the convergence of the SPSb algorithm to a well-known statistical learning technique known as Nadaraya-Watson Kernel regression. The latter has significantly lower time complexity, produces deterministic results, and it is interchangeable with SPSb for the purpose of making predictions. Second, we study the effects of HMM regularization on the Product Complexity and logPRODY metrics, for which a model of time evolution has been recently proposed. We find confirmation for the original interpretation of the logPRODY model as describing the change in the global market structure of products with new insights allowing a new interpretation of the Complexity measure, for which we propose a modification. Third, we explore new effects of regularisation on the data. We find that it reduces noise, and observe for the first time that it increases nestedness in the export network adjacency matrix. View Full-Text
Keywords: complex systems; economic complexity; fitness; complexity; regression; nestedness; Hidden Markov Model; regularization complex systems; economic complexity; fitness; complexity; regression; nestedness; Hidden Markov Model; regularization
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Angelini, O.; Di Matteo, T. Complexity of Products: The Effect of Data Regularisation. Entropy 2018, 20, 814.

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  • Externally hosted supplementary file 1
    Doi: 10.5281/zenodo.1451786
    Link: https://doi.org/10.5281/zenodo.1451786
    Description: Code for the calculations. Successive versions here: https://github.com/ganileni/ectools, FALCON wrapper for Python: https://github.com/ganileni/py_falcon (https://doi.org/10.5281/zenodo.1451790)
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