A new world trade ranking method using link analysis

JIANG Chun-heng, LIN Wen-bin

(1.School of Mathematics, Southwest Jiaotong University, Chengdu 610031, P.R.C.;

2.School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, P.R.C.)

A new world trade ranking method using link analysis

JIANG Chun-heng1, LIN Wen-bin2

(1.School of Mathematics, Southwest Jiaotong University, Chengdu 610031, P.R.C.;

2.School of Physical Science and Technology, Southwest Jiaotong University, Chengdu 610031, P.R.C.)

World trade requires multifaceted tools for measurement and analysis. This work proposes one new method for world trade ranking of countries, where both the import and export are brought into considered. With the concept of world trade network (WTN), link analysis is utilized to evaluate the influence of countries within the global multilateral trade network. With the proposed method, each country in the network will receives one non-negative score for ranking. Empirical experiments on real trade data indicates that the proposed method provides an effective tool for world trade measurement and analysis.

world trade network; ranking algorithm; link analysis; PageRank; HITS

1 Introduction

Trading plays a vital role for international interactions among countries. The analysis and understanding of world trade is of primary importance for modern international economics [1]. Usually, the world trade ranking of countries is done in terms of the export and/or import measured in US dollar. However, this approach biases towards the developed nations and is unfavorable to the under-developed countries. To avoid this problem, a natural idea is to present the trade flow of goods and services between two countries, using a directed line that linked two vertices representing the two trading countries. Moreover, the value of the flow can also be attached to the line. Thus, a directed graph called World Trade Network (WTN) can be constructed with all nations in global included. Although the notion of world trade network is not new, and economists have conceived the international trade as a network since long ago [2], there are still numerous efforts are devoted to explore the topology properties of trade network in the past decades [3, 4, 5].

This paper focuses on the ranking of countries involving in the global trading. The ranking problem is also the core of information retrieval, and especially for web search. To efficiently find the most relevant information in the sea of information, various ranking methods have been developed. These ranking methods can be categorized into two classes, one for content analysis, and the other one for link analysis. In the latter category, the methods such as PageRank [6], HITS [7], TrustRank [8], are all built upon the assumption that, web pages are connected via the hyper-links and forms a huge web. The link analysis idea has been applied in various directed networks, such as the citation network of scientific papers and journals [9, 10, 11], the semantic network for machine translation [12, 13]. The World Wide Web is similar to the trade network. For this reason, we can introduce those methods on web search into the world trade ranking of countries on the world trade network.

PageRank [6] is one of the most important algorithms used in the ranking system of Google, the most popular search engine in the world. In PageRank algorithm, each web pagehas one scoreand can be modeled mathematically in terms of the random surfer model [14]

Another link analysis method called HITS [7] is invented at the same time. In HITS, each web pagehas both an authority scoreand a hub score. The intuition is that a good authority is pointed to by many good hubs, and a good hub points to many good authorities. This mutually reinforcing relationship can be represented in the following form

The goal of this paper is to customize the two link analysis based methods PageRank and HITS for the world trade ranking of countries. The rest of this paper is organized as follows. In Section 2, we use link analysis to explore the properties of world trade network and develop one new ranking method for countries involved in the network. Then, we conduct empirical experiments to evaluate the proposed method and compare it with other ranking methods in Section 3. Finally, Section 4 arrives at a conclusion of the paper and makes suggestions for further research.

2 A New Ranking Method: TradeRank

The t analysis based methods PageRank and HITS, are suitable to measure the citation relationships between web pages, sites or scientific articles. However, we cannot directly apply them to measure the world trade network for the following reasons. (1) The citation network for both PageRank and HITS are binary, on the other side, the world trade network provides additional information on the links with trade flow. (2) In general, the size of the citation network is much bigger, while the size of the trade network is bound by the number of countries in the world. (3) Furthermore, no country would like to trade around in random, and the random walk theory does not suitable to deal with the bilateral trading. As for HITS, it is one proper tool to model the economic interdependence among countries. We hope to develop one composite measure with both the authority and the hub properties.

There are two kinds of countries in global trade community, the consumer and the producer countries. As their names suggest, the consumer countries such as the United States have thriving demands on products; the producer countries (e.g. China) are expected to supply considerable products. They are the two sides of one coin and most countries import and export products simultaneously. Viewed from their structures in the network, it is easy to distinguish the two classes of countries, and the primary consumers present as authorities, while the producers paly as hubs.

where the first term presents the contribution of the outflow to, and the second term describes the influence of the inflow from. We note that, the percentages of the flows are considerably more important for the strength measure. Hence, both terms are given in the form of percentage. For the country, its export tois one part of the import of, then the outflowis divided by the total importof. On the other side, the inflowis divided by the total exportof. The free parametercontrols the weight of the export. When, the model is completely built upon the export without consideration of the import factor. When, the import factor are ignored. The proposed method brings both the import and export factors into consideration, also the method

attempts to makes full use of the link structure of the trade network, so that to improve the current trade ranking methods.

With the definitions of two diagonal matricesand, the model then can be written in matrix form

Actually, there are few countries do not have any export flow or import flow, producing diagonal zero elements inand. To make all diagonal matrices invertible, all the diagonal zero elements are replaced with one. It's easy to prove that the matrixis one stochastic matrix. The Perron-Frobenius theorem [15] ensures that the matrix has one unique eigenvector with the corresponding eigenvalue 1 be the largest one. As a result, the efficient power method will be adopted for the computation of the strength scores.

3 Experimental Evaluations

Unlike other kinds of ranking problems, there is yet no benchmark standard to enable comparison of different methods. Various ranking methods have been proposed to evaluate trading countries from different aspects of trading. We would like to conduct empirical experiments using real data set to investigate the reason behind our experimental results.

Data Set.The United Nations Conference on Trade and Development (UNCTADStat) is a free online retrieval system based on the United Nations Comtrade Database [16]. The aggregated trade data for all commodities over the time period 1995 -- 2012 are retrieved to build a reduced world trade matrix of size 210. The network is made up of 210 vertices and more than twenty thousands of trade links. To investigate the connectivity of the trading countries, we consider the density of the network, namely the ratio between the number of connected edges and the number of maximum links possible, a measure can be viewed as the probability of taking two countries at random with trade interaction. As for our reduced network, the density has increased from 0.474 in 1995 to the highest 0.621 in 2010, then falls to 0.600 in 2012 as shown in Table 1.

Table 1. Density of the world trade network over the time period 1995 – 2012.

Experiments Results.We carry out experiments to produce various ranking lists of countries using factors such import, export, and the proposed composite measure in TradeRank algorithm. Moreover, we also observe the effect of the free parameteron the change of the ranking results via two values 0.5 and 1.0 for. Finally, these ranking results are further analyzed in pairwise fashion.

Table 2. The ranking lists with respect to the import (IR), the export (ER),wier three representative years 2003, 2008, 2012. Only the top 10 countries (areas) are presented in the ranking lists. Countries are presented with the ISO3 country codes.

Table 2. The ranking lists with respect to the import (IR), the export (ER),wier three representative years 2003, 2008, 2012. Only the top 10 countries (areas) are presented in the ranking lists. Countries are presented with the ISO3 country codes.

Position 1 2 3 4 5 6 7 8 9 10 2003 IR USA DEU GBR FRA CHN JPN ITA NLD CAN HKG ER DEU USA JPN CHN FRA GBR ITA CAN NLD BEL TR(0.5) NZL DEU EST USA IDN AUS GBR POL IND ITA TR(1.0) DEU USA JPN CHN FRA GBR ITA NLD BEL HKG 2008 IR USA DEU CHN FRA JPN GBR NLD ITA BEL HKG ER DEU CHN USA JPN NLD FRA ITA BEL RUS GBR TR(0.5) USA DEU CHN FRA JPN GBR NLD ITA BEL HKG TR(1.0) USA DEU CHN FRA JPN GBR NLD ITA BEL HKG 2012 IR USA CHN DEU JPN FRA GBR NLD HKG KOR ITA ER CHN USA DEU JPN NLD FRA KOR ITA HKG GBR TR(0.5) USA CHN DEU JPN FRA GBR NLD HKG KOR ITA TR(1.0) USA CHN DEU JPN FRA GBR NLD HKG KOR ITA

The ranking results in terms of import, export and TradeRank for three representative years 2003, 2008, and 2012 are summarized in Table 2. Only the top 10 countries or areas in the ranking lists are shown for ease of visualization. We observe that the ranking results with respect to the import and the export are different from each other at majority of the top positions. The United States is always the largest importer country in the world. Germany is the largest exporter in 2003 and 2008, and then the position is replaced by China since 2009. Meanwhile, China also grows to be the second largest importer, the position once occupied by Germany. The ranking lists produced by the proposed

TradeRank indicates that the free parameterseems be insensitive to the network with higher density, both TR(0.5) and TR(1.0) achieve the same results as that obtained by the import-based ranker (IR). In 2003, TR(0.5) provides an interesting ranking results in 2003, while TR(1.0) ranks consistent with the export-based ranker (ER). For example, two top-ranked countries New Zealand, Estonia are exceptions. Although some countries do not have significant total import or export, they may be ranked top of the list for their balanced trading with other countries. The proposed method provides insights about potential gains of a balanced trading relationship.

Fig 1. The Trade Ranking Lists of Twenty Countries (Areas) over the Time Period 1995 – 2012 (left, right).

Furthermore, we report the advancement of trade for all countries that are ranked top 20 in terms of trade strength. As depicted in Fig. 1, the most important countries in the current global trading are U.S., China, Germany, Japan and France. During the past decades, two Asian emerging economies India and China show apparent increasing in trade. For example, China ranks around tenth in 1990s, and then jumps to second position in 2009. Similar patterns could be observed for India, which climbs from thirtieth in 1995 to tenth in 2012. On the other side, some developed countries, such as Japan and Korea are decreasing in terms of trade strength. Also, we explore the relationship of the number of trade partner countries and the trade strength, and discover one interesting pattern that the trade strength of one country is positively correlated with the number of its trade partners as shown in Fig. 2. On the average, those best ranked 50 countries have 190 trade partners. Conversely, the average number falls below 90 for those lowest ranked 50 countries. It implies that the countries that actively develop trade partnership with other countries are likely to gain most from the strongly connected global trade network.

Fig 2. The relationship between the number of trade partners and the trade strength scores of the best ranked 50 countries (blue), the lowest ranked 50 countries (green) and the other middle-ranked countries (red).

4 Conclusion

In this paper we present a link analysis based ranking algorithm called TradeRank to bring orders to countries based on the import, export factors. The proposed algorithm is also empirically studied on the real international trade data set from 1995 to 2012. The experimental results demonstrate that the proposed approach generates reasonable ranking results within the world trade network. We will further investigate the critical factors influencing the trade strength for ranking, as well as the effect of the economic interdependence among countries [18] with some special links in the network removed.

[1] PAUL R KRUGMAN. International economics: Theory and policy[M]. Pearson Education India, 2009.

[2] FOLKE HILGERDT. The case for multilateral trade [J]. The American Economic Review[J]. 1943, 33(2): 393-407.

[3] GIORGIO FAGIOLO, JAVIER REYES, STEFANO SCHIAVO. World-trade web: Topological properties, dynamics, and evolution [J]. Physical Review E, 2009, 79(3): 036115.

[4] JIANKUI HE, MICHAEL W DEEM. Structure and response in the world trade network [J]. Physical review letters, 2010, 105(19): 198701.

[5] LUCA DE BENEDICTIS , LUCIA TAJOLI. The world trade network [J]. The World Economy, 2011, 34(8):1417-1454.

[6] SERGEY BRIN , LAWRENCE PAGE. The anatomy of a large-scale hypertextual web search engine [J]. Computer networks and ISDN systems, 1998, 30(1):107-117.

[7] JON M KLEINBERG. Authoritative sources in a hyperlinked environment [J]. Journal of the ACM (JACM), 1999, 46(5):604–632.

[8] ZOLTáN GY?NGYI, HECTOR GARCIA-MOLINA, JAN PEDERSEN. Combating web spam with trustrank [C]. Proceedings of the Thirtieth international conference on Very large data bases-Volume 30. VLDB Endowment, 2004: 576-587.

[9] P Yu and H Van de Sompel. Networks of scientific papers [J]. Science, 1965, 169:510-515.

[10] SIDNEY REDNER. Citation statistics from more than a century of physical review [EB/OL]. (2004-08-06) [2014-03-10]. http:// arxiv. org/abs/physics/0407137.

[11] NAN MA, JIANCHENG GUAN, YI ZHAO. Bringing pagerank to the citation analysis [J]. Information Processing & Management, 2008, 44(2):800-810.

[12] RADA MIHALCEA, PAUL TARAU, ELIZABETH FIGA. Pagerank on semantic networks, with application to word sense disambiguation [C]. Proceedings of the 20th international conference on Computational Linguistics. Association for Computational Linguistics, 2004: 1126-1129.

[13] ENEKO AGIRRE ,AITOR SOROA. Personalizing pagerank for word sense disambiguation [C]. Proceedings of the 12th Conference of the European Chapter of the Association for Computational Linguistics. Association for Computational Linguistics, 2009: 33-41.

[14] AMY N LANGVILLE , CARL D MEYER. Google’s PageRank and beyond: The science of search engine rankings [M]. Princeton University Press, 2011.

[15] CARL D MEYER. Matrix analysis , applied linear algebra [M], volume 2. SIAM, 2000.

[16] UN COMTRADE. United nations commodity trade statistics database [EB/OL]. (2013-10-02) [2014-3-10]. http://unctadstat. unctad.org/ReportFolders/reportFolders.aspx.

[17] KENNETH N WALTZ. Structural realism after the cold war [J]. International security, 2000, 25(1):5-41.

TP393.092

: A

: 1003-4271(2014)03-0451-05

一種基于鏈接分析的國際貿(mào)易排名新方法

蔣春恒1, 林文斌2
(1.西南交通大學(xué)數(shù)學(xué)學(xué)院, 四川 成都 610031; 2. 西南交通大學(xué)物理學(xué)院、數(shù)學(xué)學(xué)院, 四川 成都 610031)

國際貿(mào)易需要多元化的度量與分析工具. 提出一種新的國際貿(mào)易排名方法, 兼顧貿(mào)易進(jìn)口與出口的影響, 對(duì)參與國際貿(mào)易的國家進(jìn)行排名. 在國際貿(mào)易網(wǎng)絡(luò)的框架下, 使用鏈接分析評(píng)估各個(gè)國家在全球多邊貿(mào)易下的影響力, 為每個(gè)國家賦予權(quán)值并進(jìn)行排名. 真實(shí)貿(mào)易數(shù)據(jù)上的實(shí)證分析表明本文提出的方法提供了一種度量與分析國際貿(mào)易的有效工具.

世界貿(mào)易網(wǎng)絡(luò); 排名算法; 鏈接分析; PageRank, HITS

2014-03-31

蔣春恒(1987-), 男, 漢族, 安徽人, 碩士研究生, 研究方向: 數(shù)據(jù)挖掘, 電子郵箱: chiangchunheng@my. swjtu. edu. cn; 林文斌(1970-), 男, 教授, 博士生導(dǎo)師; 研究方向: 高性能并行計(jì)算、數(shù)據(jù)挖掘、搜索引擎.

New Century Excellent Talents in University (No. NCET-10-0702).

10.3969/j.issn.1003-4271.2014.03.23