Determination of latent dimensionality in international trade flow

Abstract

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. Moreover, decomposition methods with non-negative constraints are shown to extract more insightful factors. Nonnegative RESCAL is one such technique, particularly well suited to analyze self-relational data, such as dynamic networks found in international trade flows. Particularly, non-negative RESCAL computes a low dimensional tensor representation by finding the latent space containing multiple modalities. Furthermore, estimating the dimensionality of this latent space is crucial for extracting meaningful latent features. Here, to determine the dimensionality of the latent space with non-negative RESCAL, we propose a latent dimension determination method which is based on clustering of the solutions of multiple realizations of non-negative RESCAL decompositions. We demonstrate the performance of our model selection method on synthetic data. We then apply our method to decompose a network of international trade flows data from International Monetary Fund and shows that with a correct latent dimension determination, the resulting features are able to capture relevant empirical facts from economic literature.

Distributed non-negative RESCAL with Automatic Model Selection for Exascale Data

“…The stability approach was recently utilized for RASCAL [26]. Here we integrated our algorithm with stability approach model selection, and for completeness, provide the main steps of this approach below:…”

“…To address the bottlenecks associated with decomposing such large tensors, we introduce a new efficient distributed algorithm for non-negative RESCAL factorization with a superior scaling and speed, capable of working on modern heterogeneous CPU/GPU architectures to factorize extralarge dense and sparse tensors. We integrated our algorithm with a model selection method based on the stability of the extracted latent communities (the columns of matrix A) [26], and call it pyDRESCALk. We evaluate pyDRESCALk on several extra-large synthetic tensors as well as on realworld data, and show that in all cases the predicted latent communities are highly correlated with the predetermined ground-truth solutions and pyDRESCALk determines accurately the latent dimension.…”

Multi-Dimensional Anomalous Entity Detection via Poisson Tensor Factorization

“…If we perfectly reconstruct the input tensor, our tensor factorization carries little information about peer groups or other shared structure; if our rank is too low, we lose vital information. Truong et al discussed this problem in [18], and introduced the Non-Negative RESCAL method. Minimal multirank in RESCAL is chosen to be the rank with low relative error and high silhouette score.…”