Enhancing Countries’ Fitness with Recommender Systems on

Research ArticleEnhancing Countriesrsquo Fitness with Recommender Systems onthe International Trade Network

Hao Liao 1 Xiao-Min Huang1 Xing-Tong Wu1 Ming-Kai Liu1 Alexandre Vidmer 1

Ming-Yang Zhou 1 and Yi-Cheng Zhang12

1National Engineering Laboratory for Big Data System Computing Technology Guangdong Province Key Laboratory ofPopular High Performance Computers College of Computer Science and Software Engineering Shenzhen UniversityShenzhen 518060 China2Department of Physics University of Fribourg 1700 Fribourg Switzerland

Correspondence should be addressed to Ming-Yang Zhou zhoumy2010gmailcom

Received 17 May 2018 Revised 23 August 2018 Accepted 4 October 2018 Published 18 October 2018

Guest Editor Miguel Fuentes

Copyright copy 2018 Hao Liao et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Prediction is one of the major challenges in complex systems The prediction methods have shown to be effective predictors of theevolution of networks These methods can help policy makers to solve practical problems successfully and make better strategy forthe future In thiswork we focus on exporting countriesrsquo data of the International TradeNetwork A recommendation system is thenused to identify the products that correspond to the production capacity of each individual country but are somehow overlookedby the country Then we simulate the evolution of the countryrsquos fitness if it would have followed the recommendations The resultof this work is the combination of these twomethods to provide insights to countries on how to enhance the diversification of theirexported products in a scientific way and improve national competitiveness significantly especially for developing countries

1 Introduction

International trade plays a considerable role in the exchangechannels between countries [1 2] It is also becoming moreimportant as time goes on In 1960 international tradeaccounted for roughly 25 of a countryrsquos total Gross Domes-tic Product (GDP) Nowadays it accounts for nearly 60of countries GDP [3] Historically various classic economicmodels were developed to evaluate the dissimilarity of wealthresulting from the exportation of diverse goods [4] Modelsbased on the gravity equation were also developed andshowed to be adequate to explain many of the features ofthe international trade [5] Another approach the ProductSpace attempted to illustrate how the nations will developin the future by projecting the exports data onto a two-dimensional map and observing the diffusion of the exportprocess [6] Economic models mainly consist of commodityprofits geographical relations comprehensive productivityeconomic structure [7] and a series of macroeconomicelements In practice numerous complex external factorseg national policies religious beliefs and the countryrsquos

current production capacity are key components in theinternational trade Here we also recognize that plenty ofsociologists have constructed grand theories on the empiricalstudy of global economic development [8ndash10]Thesemethodsand theories were developed by David Snyder and EdwardL Kick [11] it was the first study of international trade andworld economic growth using a network framework in theAmerican Journal of Sociology 1979 In [12] the authorsemphasized the importance of the global trade and thestructure of the modern world system was addressed bymultiple-network analysis The complex network approachwas also used in [13] and it was shown that the Interna-tional Trade Network and the World Wide Web both havecollaborative characteristics [14] Indeed the InternationalTrade Network is a complex network in terms of structureWith this is in mind we apply recommendation algorithmsthat are usually applied on e-commerce systems in orderto predict the evolution of the International Trade Network[15ndash17]

Twomethods were proposed to assign scores to countriesand products using the complex network approachThe basis

HindawiComplexityVolume 2018 Article ID 5806827 12 pageshttpsdoiorg10115520185806827

2 Complexity

of these methods is to analyze the relation between countriesand their exports and then to rank the countries accordingto their economic competitiveness and the exported goodwith the economic advantage they bring to the exportingcountries The first method the Method of Reflection (MR)proposed the Economic Complexity Index (ECI) to accountfor the production characteristics of countries The countriesare ranked according to their exporting capacity The authorspointed out that the method is able to predict the futureeconomic expansion of countries and that the scores obtainedwith MR indicate which products should be exported inorder to maximize the countriesrsquo performance [18] In [19]a method based on the Markov chain was proposed Themethod showed the need to take into account the nonlinearinteractions between exported commodities and nationaldiversity This led to the development of the Fitness andComplexity metric [20] It is an iterative method based onthe nonlinearity of the system This method was shown tobe conceptually more grounded than the previous ones anda better predictor of the economic evolution [21 22] Thismethod was applied to forecast the GDP growth in a recentwork The authors reported that their estimates were onaverage 25 percent more accurate than were those made bythe International Monetary Fund [23]

In this paper we startwith a detailed definition of the usedalgorithms namely the Probabilistic Spreading algorithm[24] the Heat Spreading algorithm [25] the Degree Increasealgorithm [26] and the Time-Aware Probabilistic Spreadingalgorithms [27] We then apply these four algorithms to theInternational Trade Network and compare their performanceon two different aspects The first one is the evaluation of theaccuracy of the recommendation which is a standard evalu-ation of the recommendation algorithms The second aspectis the evaluation of the algorithms on their ability to rec-ommend products that would improve the countriesrsquo fitnessThis is obtained by the combination of the recommendationresults with the Fitness and Complexity scores to simulatethe changes in rankings and fitness values of countries afterexporting recommended products The experimental resultsconfirm the validity of the recommendation algorithm onthis task and show the validity of our approach to tackle thisproblem

2 Materials and Methods

21 International Trade Network

2001 to 2015 This dataset was cleaned using harmoniza-tion techniques in [28] and the similar categories weremerged together Additionally the countries that had noentries recorded for exportation between 2001 and 2015were removed After cleaning procedure the InternationalTrade Network was comprised of 192 countries and 786commodities We use the bipartite network approach to rep-resent the data In this approach one set of nodes representsthe countries and the second set of nodes represents thecommodities If a country is considered as an exporter ofa commodity a link connects the countryrsquos node and thecommodity node

RCA The data of the International Trade Network includescountry nodes and commodity nodes These two types ofnodes form a bipartite network One important aspect of ournetwork representation is that it is binary Either two nodesare connected or they are not We then need a criterion todefine if a country can be considered as an exporter of acommodity or not Indeed even if countries cannot producea specific commodity they might export a very small amountof it Therefore it should not be considered as an exporterof the commodity In order to quantify the advantage of acountry on a commodity we use the ldquoRevealed ComparativeAdvantagerdquo (RCA) as a clear constraint to determine whethera country can be considered as an exporter of certaincommodities [29]

119877119862119860 119894120572 = 119890119894120572sum119895 119890119895120572sum120573 119890119894120573sum119895120573 119890119895120573 (1)

where 119890119894120572 is the total amount of export 120572 for country 119894 Ifthe country 119894 is regarded as an exporter of the commodity120572 the export amount of the commodity 120572 should occupy alarger proportion in the total amount of the export goods ofthe country 119894 We set the RCA value to 1 and the country-commodity will have links when this pair of nodes satisfiesthe condition of 119877119862119860 119894120572 ge 1 These nodes and links togetherconstitute the bipartite network of the international tradeactivities

22 Methods

221 Recommendation System Recommendation systemsaim at recommending the most adequate items for usersIn comparison with traditional link prediction the focus isput on individual nodes rather than individual links In ourcase the main focus of the recommendation process is thecountries nodes For each country node in the system thealgorithms compute a score for every product in the networkIf the country is already considered as an exporter of an itemthe score corresponding to the product is set to 0 (ie aproduct that is already exported is not recommended) Therecommendation list for each country is composed by the top119871 products with the highest score for the particular countryWe now describe the algorithms used in this work Note that119871 is set to 20 in this work and it has been shown to have noimpact on the significance of the accuracy [17]

In order to compare the performance of the five recom-mender algorithms we choose a year 119879 and predict whichadditional product the countries export at year 119879 + 5 (thetesting set) based solely on the data up to year 119879 (the trainingset)

Probabilistic Spreading (ProbS) For target user 119894 the initialresources are first distributed evenly on the item side and thenpropagated to the user side through a random walk process[24] In the same way the resources are then returned to theitem side Both steps are used to allocate resources amongneighbors and then spread to the other side Finally the scoreof each item for country 119894 is obtained The initial resource

Complexity 3

vector is represented as 119891(119894) and its elements are representedas 119891(119894)120572 = 119886119894120572 The final resource values 119904(119894)120572 can be written as

119904(119894)120572 =119868sum120573=1

119882120572120573119891(119894)120573 (2)

The elements of the redistribution matrix119882 are derived fromProbabilistic Spreading process

119882120572120573 = 1119896120573119880sum119895=1

119886119895120572119886119895120573119896119895 (3)

where 119868 denotes the number of products and 119880 the numberof countries 119886119895120572119886119895120573 represents path from item 120573 to item120572 through country 119895 in two random walks The ProbSalgorithm employs a column-normalized transition matrixThe partition of 119896120573 and 119896119895 corresponds to the uniformpartition of resources between all links from nodes 120573 and 119895[30]

Heat Spreading (HeatS) The HeatS spreading algorithmevolved from the Probabilistic Spreading algorithm Thesetwo methods are similar in structure and both use randomwalk processes to the redistribute initial resources Comparedwith the ProbS algorithm resources spread more evenlyin the HeatS spreading method and items with only fewconnections usually benefit from a higher score than with theProbS algorithm [25]

The initial resource vector is set to 119891(119894) according to userrsquositem collection the elements 119891(119894)120572 = 119886119894120572 can be regarded as thetemperature value of the item Unlike the ProbS algorithmwhich uses column normalization transformation matrixthe HeatS algorithm uses row normalization The spreadingprocess is represented by a matrix as follows where 1198821015840 =119882119879

1198821015840120572120573 = 1119896120572119880sum119895=1

119886119895120572119886119895120573119896119895 (4)

Resource received by the user 119894 is equal to the averageresource owned by the userrsquos collected item Similarly itemside receives resources transmitted from the user through theaveraging process The itemrsquos score is calculated as

ℎ(119894)120572 =119868sum120573=1

1198821015840120572120573119891(119894)120573 (5)

Degree Increase (DI) The time information is often over-looked in the evolution of complex networks In fact timeplays a crucial role in the evolution of information networks[31ndash33] The combination of recommendation systems withtime dynamics improves the recommendation and allowsperforming better predictions It has been proven that theDegree Increase (DI) method can accurately predict theprevalence of items in the future The increase in popularityof item 120572 within time window 120591 is

Δ119896120572 (119905 120591) = 119896120572 (119905) minus 119896120572 (119905 minus 120591) (6)

where item degree 119896120572(119905) = sum119894 119860 119894120572(119905) corresponds to thenumber of users who have collected item 120572 The final itemscore is expressed as

Δ1198961015840120572 (119905 120591) = Δ119896120572 (119905 120591) + 120576119896120572 (119905) (7)

In practice the value of 120576must be small enough to ensure thatthe ranking of commodity popularity growth Δ119896120572(119905 120591) doesnot change

Time-Aware Probabilistic Spreading (TProbS) The ProbSmethod is characterized by the fact that spread of resourcesis cumulative that is the more popular items are more likelyto get high scores and get recommended to users The Time-Aware Probabilistic Spreading method integrates the ProbSmethod with the DI method It is written mathematically as

119906(119894)120572 = 119904(119894)120572 (Δ1198961015840120572 (119905 120591)119896120572 (119905) )

120579

(8)

where the parameter 120579 is an additional parameter to definethe length of past time window

222 Fitness and Complexity Metrics The Fitness and Com-plexity metrics are used to measure the competitiveness ofcountries and the quality of exported productsThe algorithmconsists of two nonlinear coupling equations [20 34] whicheventually reach a fixed value through iterative methods andthe equations are defined as

119865119899119894 =119868sum120572=1

119886119894120572119876119899minus1120572 (9)

119876119899120572 = 1sum119880119894=1 1198861198941205721119865119899minus1119894 (10)

where 119865119899119894 indicates the fitness of country 119894 after 119899 iterationsIn [35] the convergence of the algorithm and its stoppingcondition were demonstrated The higher the fitness valuethe more advantageous the variety and complexity of thegoods exported by the country The study [36] shows that theweak economies can analyze how to get out of the povertytrap and increase the diversification of their exports via fitnessmetrics Complexity 119876119899120572 cannot simply be calculated fromthe average of countriesrsquo fitness Successful countries exportalmost all products and it is unable to infer the complexityof each product from their export data (for example ourdata shows that a total of 786 products were included inthe International Trade Network from 2001 to 2015 and theUnited States exported a total of 775 kinds of products)Therefore the complexity of product should be measured ina nonlinear way namely it is essential to reduce contributionof successful countries Assuming that product 120572 possessestwo exporters 119894 and 119895 with fitness values of 02 and 15respectively the complexity of the product would be 0197If the two exporters 119894 and 119895 have fitness values of 10 and 15the complexity would be 6 These two examples verify thefact that the value of complexity dependsmainly on the worstexporter

4 Complexity

223 Precision and Recall Metrics In general recommen-dation algorithms are compared in their ability to predictthe future In order to evaluate their accuracy we use twometrics namely the Precision and the Recall metrics We arenot interested in the accuracy of the algorithms per se butthe accuracy of the recommendation results is an importantevaluation indicator A higher accuracy indicates that theexporting countries possess the capacity to produce therecommended commodities Indeed the countries shouldbe able to produce the recommended commodities in thenear future otherwise the recommendation process would bemeaningless

Precision For each country the individual Precision is mea-sured as the fraction of recommended products that areeventually exported If 119899119894 is the number of products thatare eventually exported by country 119894 and that are actuallyrecommended then the Precision for country 119894 is 119875119894 = 119899119894119871The Precision 119875 is the average of 119875119894 over every country RecallRecall is similar to Precision but we use the number of newlyexported goods instead of the fixed recommendation list 119871If country 119894 exports 119864119894 additional items in the testing set theindividual Recall reads 119877119894 = 119899119894119864119894 The Recall is the averageof 119877119894 over every country23 Addition of Products to Countriesrsquo Export Basket Afterhaving obtained the recommendation list from the previouslydescribed recommendation methods we add the goods thatare at the top of the recommendation lists to the respectivecountriesrsquo exports baskets Then the fitness value of eachcountry is reevaluated and its change is recorded Howeverthe calculations of fitness are an iterative nonlinear processwhich is coupledwith the complexity of the productsThus inorder to evaluate the changes brought by adding the productsto the countryrsquos export basket only one country is modifiedat a time In other words for a given country 119894 only itsrecommendation list is added to its exports basket and therest of the network is left untouched For instance if wehave a high complexity product to the export basket of alow fitness country the complexity of the product might begreatly reduced which will have a strong impact on the restof the Fitness and Complexity values The simulation processis described as below For each country we add the119871 productsin its recommendation list to its export basket For eachproduct 120572 in the top 119871 part of the recommendation list ofcountry 119894 we add a link between the country 119894 and the product120572 in the data The export volume of product 120572 from country 119894must satisfy the condition of 119877119862119860 ge 13 Results

31 Accuracy of the Recommendation Algorithms The firststep in the comparison of the algorithms is to comparetheir accuracies We perform the predictions from years2001 to 2010 The results are shown in Figure 1 First wesee that the top performing method is the TProbS methodThis is not surprising as this is the one including boththe strength of ProbS and time information The parameter120579 = 02 is constantly the one giving the highest Recall in

our simulation and thus is fixed to this value Obviouslythis lessens the impact of degree increase on the networkwhich is compatible with the expected behavior of countriesdevelopmentThey should not all focus on the same productsbut they still follow the ongoing trends As noted in [17]the HeatS method performs surprisingly well This methodusually performs poorly in online e-commerce networks[25] but has the advantage of recommending products withlower degree DI and Degree both perform poorly which isexpected as they do not take into account the productioncapabilities of countries

32 Tier Division An interesting study is to investigate theimpact of the methods on countries with different fitnessrank It is not certain that a country that belongs to thetop of the fitness list will behave the same to a countrythat belongs at the bottom of the list In order to study thiseffect we divide the countries into three different categoriesaccording to their fitness rank The three categories hold thesame number of countries and thus are denoted as top tiermiddle tier and low tier For each category we computethe average increased ranking and increased fitness after theaddition of the recommended exports The results are shownin Figure 2 The countries that benefit the most from theserecommendations are middle and low tier countries In panel(a) the most interesting result is in HeatS The increasedrankings by following its recommendation are much higherthan those of TProbS This is especially true with top tiercountries as following the recommendation of TProbSwouldeven lower a countryrsquos fitness This comes from the fact thattop tier countries need to innovate and produce goods forwhich there are only a few competitors while for middle andlow tier countries it is sufficient to produce additional itemsNote that we try adding time to HeatS the Recall improvedto the level of TProbS but the improvement of fitness waslower than that of HeatS So we decided to keep only HeatSand TProbS for simplicity

From panel (b) we see that the fitness of top tiercountries is the one improving themost which shows that therecommendation algorithm indeed recommends differentcomplex products in line with the ability of the countryFor top tier countries the difference of fitness between twocountries is large while for lower tier countries the fitnessdifference between two countries is much smaller This factexplains the result that top tier countriesrsquo fitness improvementis significant but their ranking is only slightly improved whilethe low tier countries can increase the ranking a lot in thecase of less improvement in fitness To illustrate better ourrecommendation results we select three countries in eachtier Due to the limit of the page size we only choose thefive products with the highest score according to TProbSand HeatS for each country The products recommended byTProbS and HeatS are shown in Tables 1 and 2 respectivelyBoth tables show the products with different complexity forvarious tier countries

33 Evolution of Countriesrsquo Fitness In order to directly studythe effect of each algorithm on the countryrsquos fitness value werandomly select 30 countries in the middle tier and compare

Complexity 5

Table 1 The top five recommended products by TProbS algorithms for three randomly selected countries in different tiers

Tier Country Recommended products (top 5)

Low tier

Vanuatu

CigarettesFruit fresh or driedPlants and parts of trees used in perfumery in pharmacy etcSawlogs and veneer logs of non-coniferous speciesNon-alcoholic beverages

Tonga

Spices except pepper and pimentoSugar confectionery and preparations non-chocolateFish dried salted or in brine smoked fishCementWood simply shaped

Dominica

Meal and flour of wheat and flour of meslinCask drums etc of iron steel aluminium for packing goodsPacking containers box files etc of paper used in officesBeer made from maltPlastic packing containers lids stoppers and other closures

Middle tier

Norway

Animals live (including zoo animals pets insects etc)Fuel wood and wood charcoalBovine and equine hides raw whether or not splitBones ivory horns coral shells and similar productsSoaps organic products and preparations for use as soap

Mauritius

SkirtsVegetable products roots and tubers fresh driedLeather of other hides or skinsFootwearOther outer garments

Kyrgyzstan

Oil seeds and oleaginous fruitsFish fresh or chilled excluding filletEggs birds and egg yolks fresh dried or preserved in shellFruit or vegetable juicesJams jellies marmalades etc as cooked preparations

Top tier

Germany

Iron steel aluminium reservoirs tanks etc capacity 300 lt plusNon-domestic refrigerators and refrigerating equipment partsInsulated electric wire cable bars etcBottles etc of glassRailway or tramway sleepers

Italy

Refined sugar etcFuel wood and wood charcoalSugar confectionery and preparationsManufactures of mineral materials (other than ceramic)cotton not elastic nor rubberized

Switzerland

Structures and parts of of iron steel plates rods and the likeManufactures of mineral materials (other than ceramic)Other furniture and parts thereofOrganic surface-active agentsMiscellaneous articles of base metal

6 Complexity

Table 2 The top five recommended products by HeatS algorithms for three randomly selected countries in different tiers


Low tier

Vanuatu

Sugars beet and cane raw solidNatural rubber latex natural rubber and gumsJute other textile bast fibers raw processed but not spunOres and concentrates of uranium and thoriumNuts edible fresh or dried

Tonga

Manila hemp raw or processed but not spunCoconut (copra) oilCocoa beans raw roastedWaxes of animal or vegetable originPalm nuts and kernels

Dominica

Potassium salts natural crudeDistilled alcoholic beveragesSurveying navigational compasses etc instruments nonelectricalFigs fresh or driedBeer made from malt

Middle tier

Norway

Crustaceans and molluscs fresh chilled frozen saltedAsbestosRadio-active chemical elements isotopes etcShips boats and other vesselsIron ore agglomerates

Mauritius

Fabrics wovenFish dried salted or in brine smoked fishArticles of apparel clothing accessories of plastic or rubberHousehold appliances decorative article etc of base metalHeadgear and fitting thereof

Kyrgyzstan

Meat of sheep and goats fresh chilled or frozenIron ore and concentrates not agglomeratedCoffee green roasted coffee substitutes containing coffeeCut flowers and foliageRailway or tramway sleepers (ties) of wood

Top tier

Germany

Photographic and cinematographic apparatus and equipmentOrgano-sulfur compoundsParts of the pumps and compressorOrthopedic appliances hearing aids artificial parts of the bodyPhenols and phenol-alcohols and their derivatives

Italy

Digital central storage units separately consignedChildrenrsquos toys indoor games etcOptical instruments and apparatusFabrics of glass fiber (including narrow pile fabrics lace etc)Printing presses

Switzerland

Electro-medical equipmentChemical products and preparationsParts of steam power unitsSpectacles and spectacle framesOther chemical derivatives of cellulose vulcanized fiber

Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on

DI Degree ProbS TProbSHeatSMethods

(a)

000

002

004

006

008

010

Reca

ll

DI HeatS ProbS TProbSDegree Methods

(b)

Figure 1 A comparison of Recall and Precision for the five algorithms The recommendation is performed at year 119879 for year 119879 + 5 with119879 ranging from year 2001 to 2010 The results shown are averaged over this time period For TProbS we set a value of 120579 = 02 The Degreemethod simply ranks the products according to their degree All subsequent experiments were based on this recommendation

low tiermiddle tiertop tier

minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g

DI HeatS ProbS TProbSDegreeMethods

(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)

Figure 2 Panel (a) is the average increase of fitness ranking for the three different tiers of countries for the time period 2008ndash2015 Thenumber of goods added for each country is set to 119871 = 20 Panel (b) is the average increased fitness value of those three tiers

8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess

Figure 3 Panel (a) shows fitness values as a function of the length of the recommendation list 119871 The results are average over 30 randomlyselected countries and over the 15 years spanned by the data Time evolution of fitness for the thirty selected middle tier countries that areshown in panel (b) The length of the recommendation list is set to 119871 = 20

the evolution in the average fitness of these countries forthe different methods We compare the normal evolution ofcountries and the one recommended by these algorithmsTheresults are shown in Figure 3 (panel (a)) For any length ofthe recommendation list 119871 HeatS is the top performing by agreat margin compared to other methods For all methodsranking is consistent for every choice of 119871 and so the choiceof the value is not meaningful as long as it is reasonablysmall compared to the total number of items By lookingat the evolution with the length of the recommendationlist 119871 we find that the results are consistent and if thecountry should follow the recommendation even if it canadd only few products to its export basket Following therecommendation made by HeatS seems to be adequate interms of technological requirements (ie the countries havethe required technology) as well as the best path to increasethe countryrsquos fitness In Figure 3 (panel (b)) the results areshown for different years and for fixed 119871 Though somemethods are better in a specific year than others it is clearthat HeatS is always the top performing method followed byDegree andDI and thenTProbSThis is good news as it showsthe robustness of our method both in the isolated case and inthe real evolution of countriesrsquo exports

We are also interested in the individual behavior of thefitness evolution We randomly select four countries andstudy the effect of the method on the evolution of the fitnessvalues The comparison of the five methods as a functionof L and the original fitness is shown in Figure 4 AgainHeatS is the top performing method except for KazakhstanFor this country DI and Degree are the top performingmethods due to the low fitness of this country The originalfitness values corresponding to the four countries Croatia

Kazakhstan Poland andColombia are 20563 07234 37678and 10714 respectively While we saw in Figure 3 that HeatSis always best on average it is different when consideringindividual countries with especially low production Theimpact of the recommendation on the increased ranking ofthe four countries is shown in Figure 5 We see in Figure 5(panel (b)) that even if HeatS is not the best method thedifference in ranking is quite small while in other panels itclearly outperforms other methods

34 Real Production Ability In the previous results we fixeda parameter119871 and assigned the same number of newproductsto every country However in reality some countries producemany new products in a specific year while some othersstruggle more To reflect this we use a dynamic lengthof the recommendation 119871 119894 where 119871 119894 is the length of therecommendation list for country 119894 equal to its number ofnew products between times 119879 + 5 and 119879 We build aldquovirtual networkrdquo corresponding exactly to the real one at119879 + 5 except for one country 119894 for which we replace thelinks that appear between 119879 and 119879 + 5 by those of therecommendation list This ensures that the network is ofconstant sizeThe results for HeatS are shown in Figure 6Wesee that HeatS improves greatly the fitness of most countriesthat follow its recommendation Only a few countries seetheir fitness decreasing compared to their original evolutionAs a comparison we see in Figure 7 that TProbS is of no usefor top tier countries but for middle and especially low tiercountries they might benefit from it While lower than forHeatS the recommendations of TProbS are made of morewidespread technologies and so might be easier to follow forthe low fitness countries

Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia

Figure 4 Detailed view of the fitness as a function of the length of the recommendation list 119871 for four randomly selected countries Theoriginal fitness values of four countries Croatia Kazakhstan Poland and Colombia are 20563 07234 37678 and 10714 respectively

4 Conclusion

In this study we extended the traditional recommendationswhich are usually applied on social networks to the inter-national trade Thanks to recent advances in measuring thepotential countriesrsquo evolution based solely on the networkstructure we designed amethodwhich aims to help countriesto find a suitable evolution path among all the possible onesThe study suffers two main limitations The first one is thatthe exports categories are roughly defined Only about 786categories are present in the dataset This leads to somecategories containing very varied products such as iron basedgoodsThe second one is that there are important restrictionsor conversely support to the trade between countries Forinstance USA Canada and Mexico recently signed an

agreement to open the market of dairy and car parts On theopposite side countries might limit their sensitive exportssuch as military goods to specific countries While the firstlimitation is difficult to address due to the data limitationsthe second one can be added by weighting differently therelationships between countries on specific products

At the same time the recommendation proved to graspthe countries technological evolution by being able to cor-rectly predict the future and the method of Fitness andComplexity has been shown in [37ndash39] to uncover hiddenfeatures of the countriesrsquo evolution It is important to notethat the recommendation method should agree with thesimilar capabilities of a country [40] Those two ingredientstogether mixed with our results show remarkable evidencethat our methods as supplementary message could help to

10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia

Figure 5 Comparison of the increased rankings of the four selected countries The increased ranking of each method is averaged overdifferent lengths of the recommendation list 119871

minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country

Figure 6 Difference of fitness resulting from following recommendation of HeatS and real evolution The countries are sorted according totheir fitness value country 0 being the one with the highest average fitness Each bar represents a countryThe recommendation is performedat year 119879 for year 119879+ 5 with 119879 ranging from year 2001 to 2010 143 countries of the 181 countries would see their fitness improve by followingthe recommendation of HeatS

Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country

Figure 7 Difference of fitness resulting from following recom-mendation of TProbS and real evolution The countries are sortedaccording to their fitness value country 0 being the one withthe highest average fitness Each bar represents a country Therecommendation is performed at year 119879 for year 119879 + 5 with 119879ranging from year 2001 to 2010 120 countries of the 181 countrieswould see their fitness improve by following the recommendationof TProbS

design objective metrics in order to facilitate the work ofpolicy makers and encourage the development of technologytowards the better economic goal

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

We acknowledge financial support from the NationalNatural Science Foundation of China grants number61803266 11547040 61873171 and 61703281 the GuangdongProvince Natural Science Foundation of China grantsnumber 2016A030310051 and 2017A030310374 the Foun-dation for Distinguished Young Talents in Higher Educationof Guangdong grant number 2015KONCX143 the ShenzhenFundamental Research Foundation grants numberJCYJ20150529164656096 and JCYJ20170302153955969the Natural Science Foundation of SZU grant number2016-24 and the Guangdong Pre-National Project grantnumber 2014GKXM054

References

[1] A Almog T Squartini and D Garlaschelli ldquoThe double roleof GDP in shaping the structure of the International TradeNetworkrdquo International Journal of Computational Economicsand Econometrics vol 7 2015

[2] H Liao M S Mariani M s Medo Y-C Zhang and M-YZhou ldquoRanking in evolving complex networksrdquoPhysics Reportsvol 689 pp 1ndash54 2017

[3] The World Bank Trade data retrieved from World Banknational accounts data (2018) httpsdataworldbankorgindicatorNETRDGNFSZS

[4] D Hummels and P J Klenow ldquoThe variety and quality of anationrsquos exportsrdquo American Economic Review vol 95 no 3 pp704ndash723 2005

[5] G Fagiolo ldquoThe international-trade network Gravity equationsand topological propertiesrdquo Journal of Economic Interaction andCoordination vol 5 no 1 pp 1ndash25 2010

[6] C A Hidalgo B Winger A-L Barabasi and R HausmannldquoThe product space conditions the development of nationsrdquoScience vol 317 no 5837 pp 482ndash487 2007

[7] M V Tomasello N Perra C J Tessone M Karsai and FSchweitzer ldquoThe role of endogenous and exogenous mecha-nisms in the formationofRampDnetworksrdquo Scientific Reports vol4 pp 5679-5679 2014

[8] A Portes and J Sensenbrenner ldquoEmbeddedness and immi-gration notes on the social determinants of economic actionrdquoAmerican Journal of Sociology vol 98 no 6 pp 1320ndash1350 1993

[9] I WallersteinThemodern world-system I Capitalist agricultureand the origins of the European world-economy in the sixteenthcentury vol 1 Univ of California Press 2011

[10] S Sassen Cities in a world economy Sage Publications 2018[11] D Snyder and E L Kick ldquoStructural position in the world

system and economic growth 1955-1970 a multiple-networkanalysis of transnational interactionsrdquo American Journal ofSociology vol 84 no 5 pp 1096ndash1126 1979

[12] E L Kick L A McKinney S McDonald and A Jorgenson ldquoAmultiple-network analysis of the world system of nations 1995-1999rdquo Sage Handbook of Social Network Analysis pp 311ndash3272011

[13] M A Serrano and M Boguna ldquoTopology of the world tradewebrdquo Physical Review E Statistical Nonlinear and Soft MatterPhysics vol 68 no 2 p 015101 2003

[14] D Garcia C J Tessone P Mavrodiev and N Perony ldquoThe dig-ital traces of bubbles Feedback cycles between socio-economicsignals in the Bitcoin economyrdquo Journal of the Royal SocietyInterface vol 11 no 99 article no 0623 2014

[15] L Lu and T Zhou ldquoLink prediction in complex networks asurveyrdquoPhysica A StatisticalMechanics and its Applications vol390 no 6 pp 1150ndash1170 2011

[16] D Liben-Nowell and J Kleinberg The link-prediction problemfor social networks John Wiley amp Sons Inc 2007

[17] A Vidmer A Zeng M Medo and Y-C Zhang ldquoPrediction incomplex systems The case of the international trade networkrdquoPhysica A StatisticalMechanics and its Applications vol 436 pp188ndash199 2015

[18] C AHidalgo andRHausmann ldquoThe building blocks of econo-mic complexityrdquo Proceedings of the National Acadamy of Sci-ences of the United States of America vol 106 no 26 pp 10570ndash10575 2009

[19] G Caldarelli M Cristelli A Gabrielli L Pietronero A ScalaandA Tacchella ldquoA network analysis of countriesrsquo export flowsfirm grounds for the building blocks of the economyrdquo PLoSONE vol 7 no 10 Article ID e47278 2012

[20] A Tacchella M Cristelli G Caldarelli A Gabrielli and LPietronero ldquoA new metrics for countriesrsquo fitness and productsrsquocomplexityrdquo Scientific Reports vol 2 pp 723ndash730 2012

[21] L Pietronero M Cristelli A Gabrielli D Mazzilli et alldquoEconomic complexity ldquobuttarla in caciarardquo vs a constructiveapproachrdquo httpsarxivorgabs170905272

12 Complexity

[22] M Cristelli A Gabrielli A Tacchella G Caldarelli and LPietronero ldquoMeasuring the intangibles A metrics for the eco-nomic complexity of countries and productsrdquo PloS one vol 8no 8 p e70726 2013

[23] A Tacchella D Mazzilli and L Pietronero ldquoA dynamical sys-tems approach to gross domestic product forecastingrdquo NaturePhysics vol 14 no 8 pp 861ndash865 2018

[24] T Zhou J Ren M Medo and Y Zhang ldquoBipartite networkprojection and personal recommendationrdquo Physical Review EStatistical Nonlinear and Soft Matter Physics vol 76 no 4Article ID 046115 2007

[25] T Zhou Z Kuscsik J Liu M Medo J R Wakeling and YZhang ldquoSolving the apparent diversity-accuracy dilemma ofrecommender systemsrdquo Proceedings of the National Acadamy ofSciences of the United States of America vol 107 no 10 pp 4511ndash4515 2010

[26] A Zeng S Gualdi M Medo and Y-C Zhang ldquoTrend pre-diction in temporal bipartite networks the case of MovielensNetflix and Diggrdquo Advances in Complex Systems A Multidisci-plinary Journal vol 16 no 4-5 1350024 15 pages 2013

[27] A Vidmer andMMedo ldquoThe essential role of time in network-based recommendationrdquo EPL (Europhysics Letters) vol 116 no3 p 30007 2016

[28] GGaulier and S Zignago ldquoBACI International TradeDatabaseat the Product-Level (the 1994-2007 Version)rdquo SSRN ElectronicJournal Working Papers 2010-2023 CEPII (October 2010)URLhttpwwwcepiifrCEPIIfrpublicationswpabstractaspNoDoc=2726

[29] B Balassa ldquoTrade Liberalisation and ldquoRevealedrdquo ComparativeAdvantagerdquo The Manchester School vol 33 no 2 pp 99ndash1231965

[30] F Yu A Zeng S Gillard andMMedo ldquoNetwork-based recom-mendation algorithms a reviewrdquo Physica A Statistical Mechan-ics and its Applications vol 452 pp 192ndash208 2016

[31] R Crane and D Sornette ldquoRobust dynamic classes revealed bymeasuring the response function of a social systemrdquoProceedingsof the National Acadamy of Sciences of the United States ofAmerica vol 105 no 41 pp 15649ndash15653 2008

[32] G Szabo and B A Huberman ldquoPredicting the popularity ofonline contentrdquoCommunications of the ACM vol 53 no 8 pp80ndash88 2010

[33] Z-M Ren Y-Q Shi and H Liao ldquoCharacterizing popularitydynamics of online videosrdquo Physica A Statistical Mechanics andits Applications vol 453 pp 236ndash241 2016

[34] H Liao and A Vidmer ldquoA Comparative Analysis of thePredictive Abilities of Economic Complexity Metrics UsingInternational Trade Networkrdquo Complexity vol 2018 Article ID2825948 12 pages 2018

[35] E Pugliese A Zaccaria andL Pietronero ldquoOn the convergenceof the Fitness-Complexity algorithmrdquo The European PhysicalJournal Special Topics vol 225 no 10 pp 1893ndash1911 2016

[36] E Pugliese G L Chiarotti A Zaccaria and L PietroneroldquoComplex economies have a lateral escape from the povertytraprdquo PLoS ONE vol 12 no 1 p e0168540 2017

[37] A Tacchella M Cristelli G Caldarelli A Gabrielli and LPietronero ldquoEconomic complexity conceptual grounding of anew metrics for global competitivenessrdquo Journal of EconomicDynamics amp Control vol 37 no 8 pp 1683ndash1691 2013

[38] G Cimini A Gabrielli and F S Labini ldquoThe scientific compet-itiveness of nationsrdquo PLoS ONE vol 9 no 12 p e113470 2014

[39] M S Mariani A Vidmer M Medo and Y-C Zhang ldquoMea-suring economic complexity of countries and products whichmetric to userdquoThe European Physical Journal B vol 88 no 11article 293 pp 1ndash9 2015

[40] E Pugliese G Cimini A Patelli A Zaccaria L Pietroneroand A Gabrielli ldquoUnfolding the innovation system for thedevelopment of countries co-evolution of science technologyand productionrdquo httpsarxivorgabs170705146

Hindawiwwwhindawicom Volume 2018

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International Journal of Mathematics and Mathematical Sciences


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Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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Dierential EquationsInternational Journal of

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Decision SciencesAdvances in


AnalysisInternational Journal of


Stochastic AnalysisInternational Journal of

Submit your manuscripts atwwwhindawicom

2 Complexity

of these methods is to analyze the relation between countriesand their exports and then to rank the countries accordingto their economic competitiveness and the exported goodwith the economic advantage they bring to the exportingcountries The first method the Method of Reflection (MR)proposed the Economic Complexity Index (ECI) to accountfor the production characteristics of countries The countriesare ranked according to their exporting capacity The authorspointed out that the method is able to predict the futureeconomic expansion of countries and that the scores obtainedwith MR indicate which products should be exported inorder to maximize the countriesrsquo performance [18] In [19]a method based on the Markov chain was proposed Themethod showed the need to take into account the nonlinearinteractions between exported commodities and nationaldiversity This led to the development of the Fitness andComplexity metric [20] It is an iterative method based onthe nonlinearity of the system This method was shown tobe conceptually more grounded than the previous ones anda better predictor of the economic evolution [21 22] Thismethod was applied to forecast the GDP growth in a recentwork The authors reported that their estimates were onaverage 25 percent more accurate than were those made bythe International Monetary Fund [23]

In this paper we startwith a detailed definition of the usedalgorithms namely the Probabilistic Spreading algorithm[24] the Heat Spreading algorithm [25] the Degree Increasealgorithm [26] and the Time-Aware Probabilistic Spreadingalgorithms [27] We then apply these four algorithms to theInternational Trade Network and compare their performanceon two different aspects The first one is the evaluation of theaccuracy of the recommendation which is a standard evalu-ation of the recommendation algorithms The second aspectis the evaluation of the algorithms on their ability to rec-ommend products that would improve the countriesrsquo fitnessThis is obtained by the combination of the recommendationresults with the Fitness and Complexity scores to simulatethe changes in rankings and fitness values of countries afterexporting recommended products The experimental resultsconfirm the validity of the recommendation algorithm onthis task and show the validity of our approach to tackle thisproblem

2 Materials and Methods

21 International Trade Network

2001 to 2015 This dataset was cleaned using harmoniza-tion techniques in [28] and the similar categories weremerged together Additionally the countries that had noentries recorded for exportation between 2001 and 2015were removed After cleaning procedure the InternationalTrade Network was comprised of 192 countries and 786commodities We use the bipartite network approach to rep-resent the data In this approach one set of nodes representsthe countries and the second set of nodes represents thecommodities If a country is considered as an exporter ofa commodity a link connects the countryrsquos node and thecommodity node

RCA The data of the International Trade Network includescountry nodes and commodity nodes These two types ofnodes form a bipartite network One important aspect of ournetwork representation is that it is binary Either two nodesare connected or they are not We then need a criterion todefine if a country can be considered as an exporter of acommodity or not Indeed even if countries cannot producea specific commodity they might export a very small amountof it Therefore it should not be considered as an exporterof the commodity In order to quantify the advantage of acountry on a commodity we use the ldquoRevealed ComparativeAdvantagerdquo (RCA) as a clear constraint to determine whethera country can be considered as an exporter of certaincommodities [29]

119877119862119860 119894120572 = 119890119894120572sum119895 119890119895120572sum120573 119890119894120573sum119895120573 119890119895120573 (1)

where 119890119894120572 is the total amount of export 120572 for country 119894 Ifthe country 119894 is regarded as an exporter of the commodity120572 the export amount of the commodity 120572 should occupy alarger proportion in the total amount of the export goods ofthe country 119894 We set the RCA value to 1 and the country-commodity will have links when this pair of nodes satisfiesthe condition of 119877119862119860 119894120572 ge 1 These nodes and links togetherconstitute the bipartite network of the international tradeactivities

22 Methods

221 Recommendation System Recommendation systemsaim at recommending the most adequate items for usersIn comparison with traditional link prediction the focus isput on individual nodes rather than individual links In ourcase the main focus of the recommendation process is thecountries nodes For each country node in the system thealgorithms compute a score for every product in the networkIf the country is already considered as an exporter of an itemthe score corresponding to the product is set to 0 (ie aproduct that is already exported is not recommended) Therecommendation list for each country is composed by the top119871 products with the highest score for the particular countryWe now describe the algorithms used in this work Note that119871 is set to 20 in this work and it has been shown to have noimpact on the significance of the accuracy [17]

In order to compare the performance of the five recom-mender algorithms we choose a year 119879 and predict whichadditional product the countries export at year 119879 + 5 (thetesting set) based solely on the data up to year 119879 (the trainingset)

Probabilistic Spreading (ProbS) For target user 119894 the initialresources are first distributed evenly on the item side and thenpropagated to the user side through a random walk process[24] In the same way the resources are then returned to theitem side Both steps are used to allocate resources amongneighbors and then spread to the other side Finally the scoreof each item for country 119894 is obtained The initial resource

Complexity 3


119904(119894)120572 =119868sum120573=1

119882120572120573119891(119894)120573 (2)


119882120572120573 = 1119896120573119880sum119895=1

119886119895120572119886119895120573119896119895 (3)




1198821015840120572120573 = 1119896120572119880sum119895=1

119886119895120572119886119895120573119896119895 (4)


ℎ(119894)120572 =119868sum120573=1

1198821015840120572120573119891(119894)120573 (5)


Δ119896120572 (119905 120591) = 119896120572 (119905) minus 119896120572 (119905 minus 120591) (6)


Δ1198961015840120572 (119905 120591) = Δ119896120572 (119905 120591) + 120576119896120572 (119905) (7)



119906(119894)120572 = 119904(119894)120572 (Δ1198961015840120572 (119905 120591)119896120572 (119905) )

120579

(8)



119865119899119894 =119868sum120572=1

119886119894120572119876119899minus1120572 (9)

119876119899120572 = 1sum119880119894=1 1198861198941205721119865119899minus1119894 (10)


4 Complexity








Complexity 5



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


6 Complexity



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on


(a)

000

002

004

006

008

010

Reca

ll


(b)



minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g


(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)


8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 3


119904(119894)120572 =119868sum120573=1

119882120572120573119891(119894)120573 (2)


119882120572120573 = 1119896120573119880sum119895=1

119886119895120572119886119895120573119896119895 (3)




1198821015840120572120573 = 1119896120572119880sum119895=1

119886119895120572119886119895120573119896119895 (4)


ℎ(119894)120572 =119868sum120573=1

1198821015840120572120573119891(119894)120573 (5)


Δ119896120572 (119905 120591) = 119896120572 (119905) minus 119896120572 (119905 minus 120591) (6)


Δ1198961015840120572 (119905 120591) = Δ119896120572 (119905 120591) + 120576119896120572 (119905) (7)



119906(119894)120572 = 119904(119894)120572 (Δ1198961015840120572 (119905 120591)119896120572 (119905) )

120579

(8)



119865119899119894 =119868sum120572=1

119886119894120572119876119899minus1120572 (9)

119876119899120572 = 1sum119880119894=1 1198861198941205721119865119899minus1119894 (10)


4 Complexity








Complexity 5



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


6 Complexity



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on


(a)

000

002

004

006

008

010

Reca

ll


(b)



minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g


(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)


8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








4 Complexity








Complexity 5



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


6 Complexity



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on


(a)

000

002

004

006

008

010

Reca

ll


(b)



minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g


(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)


8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 5



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


6 Complexity



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on


(a)

000

002

004

006

008

010

Reca

ll


(b)



minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g


(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)


8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








6 Complexity



Low tier

Vanuatu


Tonga


Dominica


Middle tier

Norway


Mauritius


Kyrgyzstan


Top tier

Germany


Italy


Switzerland


Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on


(a)

000

002

004

006

008

010

Reca

ll


(b)



minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g


(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)


8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 7

000

002

004

006

008

010

012

014 Pr

ecisi

on


(a)

000

002

004

006

008

010

Reca

ll


(b)



minus10

0

10

20

30

40

Incr

ease

d ra

nkin

g


(a)

minus10

minus05

00

05

10

15

20

Incr

ease

d fit

ness



(b)


8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








8 Complexity

originalTProbSProbS

HeatSDIDegree

10 15 205L

06

08

10

12

14

16

18

20

Fitn

ess

originalTProbSProbS

HeatSDIDegree

2011 2012 2013 2014 20152010Year

04

08

12

16

20

Fitn

ess






Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 9

20

25

30

35

40

45

50

55

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(a) Croatia

06

08

10

12

14

16

18

20

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(b) Kazakhstan

30

35

40

45

50

55

60

Fitn

ess

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(c) Poland

09

12

15

18

21

24

27Fi

tnes

s

10 15 205L

DIHeatS

ProbSTProbS

Degree

original

(d) Colombia


4 Conclusion




10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








10 Complexity

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

35

Incr

ease

d ra

nkin

g

(a) Croatia

Methods

DIHeatS

ProbSTProbS

Degree

0

10

20

30

40

Incr

ease

d ra

nkin

g

(b) Kazakhstan

Methods

DIHeatS

ProbSTProbS

Degree

minus4

minus2

0

2

4

6

8

Incr

ease

d ra

nkin

g

(c) Poland

Methods

DIHeatS

ProbSTProbS

Degree

0

5

10

15

20

25

30

Incr

ease

d ra

nkin

g

(d) Colombia


minus02

00

02

04

06

08

H

eat３

-ＬＦ

20 40 60 80 100 120 140 160 1800Country


Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








Complexity 11

minus08

minus06

minus04

minus02

00

02

04

４０ＬＩ＜３-

ＬＦ

20 40 60 80 100 120 140 160 1800Country



Data Availability




Acknowledgments


References






















12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018








12 Complexity



























Journal of












Journal of







Volume 2018






Volume 2018















Journal of












Journal of







Volume 2018






Volume 2018








Documents

Enhancing Countries’ Fitness with Recommender Systems on