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The force-directed spring layout above includes the links from the MST and any edge with a proximity greater than 0.55. To achieve the final Product Space design, the dense clusters were manually untangled and attributes were added in terms of node/link size and color. The basic "skeleton" of the network is developed by imposing on it the strongest links which were not necessarily in the MST by employing a threshold on the proximity values; they chose to include all links of proximity greater than or equal to 0.55. This produced a network of 775 nodes and 1525 links. This threshold was chosen such that the network exhibited an average degree equal to 4, a common convention for effective network visualizations. With the framework complete, a force-directed spring algorithm was used to achieve a more ideal network layout. This algorithm considers each node to be a charged particle and the links are assumed to be springs; the layout is the resulting equilibrium, or relaxed, position of the system. Manual rearranging untangled dense clusters to achieve maximum aesthetic efficacy.
The force-directed spring layout above includes the links from the MST and any edge with a proximity greater than 0.55. To achieve the final Product Space design, the dense clusters were manually untangled and attributes were added in terms of node/link size and color. The basic "skeleton" of the network is developed by imposing on it the strongest links which were not necessarily in the MST by employing a threshold on the proximity values; they chose to include all links of proximity greater than or equal to 0.55. This produced a network of 775 nodes and 1525 links. This threshold was chosen such that the network exhibited an average degree equal to 4, a common convention for effective network visualizations. With the framework complete, a force-directed spring algorithm was used to achieve a more ideal network layout. This algorithm considers each node to be a charged particle and the links are assumed to be springs; the layout is the resulting equilibrium, or relaxed, position of the system. Manual rearranging untangled dense clusters to achieve maximum aesthetic efficacy.
上面的力定向弹簧结构包括来自MST的连接和任何邻近度大于0.55的边缘。为了实现最终的产品空间设计，手动拆解相对稠密的集群，并根据节点/链接的大小和颜色为其添加属性。该网络的”骨架”是最强链接形成的，这些最强链接不局限于中心MST，也会选择包括大于或等于0.55的所有邻近链接。这产生了一个由775个节点和1525个链接组成的网络。阈值的选择使得网络的平均度等于4，这是一个已知的有效的'''<font color="#ff8000">网络可视化 network visualization</font>'''的常见规则。随着框架的完成，用一个力导向的弹簧算法实现更理想的网络布局。该算法将每个节点视为带电粒子，并假定每个连杆为弹簧，布局为系统的平衡位置或松弛位置。手动重新排列整齐的密集集群，以获得最大的美学效果。
===Node and link attributes===
===Node and link attributes===
A system of colors and sizing allows for simultaneous assessment of the network structure with other covariates. The nodes of the Product Space are colored in terms of product classifications performed by Leamer and the size of the nodes reflects the proportion of money moved by that particular industry in world trade. The color of the links reflects the strength of the proximity measurement between two products: dark red and blue indicate high proximity whereas yellow and light blue imply weaker relatedness.
A system of colors and sizing allows for simultaneous assessment of the network structure with other covariates. The nodes of the Product Space are colored in terms of product classifications performed by Leamer and the size of the nodes reflects the proportion of money moved by that particular industry in world trade. The color of the links reflects the strength of the proximity measurement between two products: dark red and blue indicate high proximity whereas yellow and light blue imply weaker relatedness.
颜色和大小与其他协变量同时影响着网络的结构。产品空间的节点按照 Leamer 执行的产品分类进行着色，节点的大小反映了该特定行业在世界贸易中的货币流动比例。链接的颜色反映了两个产品间接近度测量的强度: 暗红色和蓝色表示高邻近度，而黄色和浅蓝色表示较弱的关联度。
In the final Product Space visualization, it is clear that the network exhibits heterogeneity and a core-periphery structure: the core of the network consists of metal products, machinery, and chemicals, whereas the periphery is formed by fishing, tropical, and cereal agriculture. On the left side of the network, there is a strong outlying cluster formed by garments and another belonging to textiles. At the bottom of the network, there exists a large electronics cluster, and at its right mining, forest, and paper products. The clusters of products in this space bear a striking resemblance to Leamer's product classification system, which employed an entirely different methodology. This system groups products by the relative amount of capital, labor, land, or skills needed to export each product.
In the final Product Space visualization, it is clear that the network exhibits heterogeneity and a core-periphery structure: the core of the network consists of metal products, machinery, and chemicals, whereas the periphery is formed by fishing, tropical, and cereal agriculture. On the left side of the network, there is a strong outlying cluster formed by garments and another belonging to textiles. At the bottom of the network, there exists a large electronics cluster, and at its right mining, forest, and paper products. The clusters of products in this space bear a striking resemblance to Leamer's product classification system, which employed an entirely different methodology. This system groups products by the relative amount of capital, labor, land, or skills needed to export each product.
在最终的产品空间可视化中，网络表现出异质性和一个有核心的外围结构：网络的核心由金属产品、机械产品和化学品组成，而外围则由渔业、热带和谷物农业组成。在网络的左侧，有一个由服装产品形成的强大的外围簇，另一边属于纺织产业。在网络的底部，有一个大型的电子集群，在它的右边是采矿、森林和纸张产品。这一领域的产品集群与利默的产品分类方案有着惊人的相似之处，后者采用了一种完全不同的方法。该系统根据出口每种产品所需的资本、劳动力、土地或技能的相对数量对产品进行分组。
The Product Space also reveals a more explicit structure within product classes. Machinery, for example, appears to be naturally split into two clusters: heavy machinery in one, and vehicles and electronics in the other. Although the machinery cluster is connected to some capital-intensive metal products, it is not interwoven with similarly classified products such as textiles. In this way, the Product Space presents a new perspective on product classification.
The Product Space also reveals a more explicit structure within product classes. Machinery, for example, appears to be naturally split into two clusters: heavy machinery in one, and vehicles and electronics in the other. Although the machinery cluster is connected to some capital-intensive metal products, it is not interwoven with similarly classified products such as textiles. In this way, the Product Space presents a new perspective on product classification.
产品空间还更明确揭示了产品的类别结构。例如，机械很自然地分为两类: 一类是重型机械，另一类是车辆和电子设备。虽然机械集群与一些资本密集型金属产品相关联，但它并未与类似分类的产品(如纺织品)交织在一起。这样，产品空间为产品分类提供了一个新的视角。
==Dynamics of the Product Space==
==Dynamics of the Product Space==
The impact of Product Space's structure can be evaluated through simulations in which a country repeatedly moves to new products with proximities above a given threshold. At a threshold of proximity equal to 0.55, countries are able to diffuse through the core of the Product Space but the speed at which they do so is determined by the set of initial products. By raising the threshold to 0.65, some countries, whose initial products occupy periphery industries, become trapped and cannot find any near-enough products. This implies that a country's orientation within the space can in fact dictate whether the country achieves economic growth.
The impact of Product Space's structure can be evaluated through simulations in which a country repeatedly moves to new products with proximities above a given threshold. At a threshold of proximity equal to 0.55, countries are able to diffuse through the core of the Product Space but the speed at which they do so is determined by the set of initial products. By raising the threshold to 0.65, some countries, whose initial products occupy periphery industries, become trapped and cannot find any near-enough products. This implies that a country's orientation within the space can in fact dictate whether the country achieves economic growth.
产品空间结构的影响可以通过一个国家中某产品的邻近程度在阈值周围的波动来模拟评估。在邻近度为0.55的临界值时，各国能够扩散经过产品空间的核心，但扩散的速度取决于初始产品集。通过将门槛提高到0.65，一些最初的产品占据周边产业的国家陷入困境，找不到任何接近足够的产品。这意味着一个国家在产品空间范围内的定位事实上可以决定该国是否实现经济增长。
==Future work==
==Future work==