标题： 国际贸易流量中潜在维度的确定 显示英文标题

标题： Determination of Latent Dimensionality in International Trade Flow

摘要： 目前，高维数据在数据科学中无处不在，这需要开发技术来分解和解释这种多维（也称为张量）数据集。 寻找数据的低维表示，即其固有结构，是理解数据中隐藏的低维潜在特征动态的一种方法。 非负RESCAL是一种这样的技术，特别适合分析自关系数据，如国际贸易流量中的动态网络。 非负RESCAL通过找到包含多种模式的潜在空间来计算低维张量表示。 估计这个潜在空间的维度对于提取有意义的潜在特征至关重要。 在这里，为了确定使用非负RESCAL的潜在空间的维度，我们提出了一种基于非负RESCAL分解的多次实现解的聚类的潜在维度确定方法。 我们在合成数据上展示了我们的模型选择方法的性能，然后将我们的方法应用于国际货币基金组织的国际贸易流量数据网络，并将结果特征与经济文献中的实证事实进行验证。 显示英文摘要

摘要： Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datasets. Finding a low dimensional representation of the data, that is, its inherent structure, is one of the approaches that can serve to understand the dynamics of low dimensional latent features hidden in the data. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Nonnegative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with nonnegative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of nonnegative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data and then we apply our method to decompose a network of international trade flows data from International Monetary Fund and validate the resulting features against empirical facts from economic literature.