The latent structure of diversification from relatedness and network embeddings
4 affiliations
- 1Nova IMS, Universidade Nova de Lisboa, Lisbon, Portugal.
- 2Computational Research in Social Science Laboratory, School of Engineering and School of Government, Universidad del Desarrollo, Santiago, Chile.
- 3Facultad de Ingeniería, Instituto de Data Science, Universidad del Desarrollo, Santiago, Chile.
- 4Northwestern Institute on Complex Systems, Kellogg School of Management, Northwestern University, Evanston, United States of America.
Abstract
Economic diversification is commonly modeled using co-occurrence-based measures of relatedness that quantify pairwise overlap among activities in a capability network. Although such measures are derived from network structure, they operate at the level of first-order neighborhood relations and summarize proximity through local co-occurrence. They do not explicitly encode higher-order structural context, such as indirect connectivity patterns or global positional similarity, into a continuous representation of entities and activities. We develop an embedding-based framework that learns such representations from network topology, enabling the construction of interpretable geometric features, including capability alignment, displacement, and portfolio entropy, that extend standard measures used in economic complexity. We apply this framework to two systems: international trade (1998–2023) and public procurement firms (2009–2024). The resulting representations reveal different structural organization across scales: firms exhibit modular clustering patterns, whereas countries occupy broader, nested capability configurations. In predictive tasks for product and activity specialization, embedding-derived features provide additional explanatory power beyond relatedness in several settings, particularly when forecasting variation in the magnitude of comparative advantage. For country-level entry events, however, persistence remains the strongest predictor. Our results show that relatedness remains the dominant predictor of entry events. In contrast, embedding-derived features become more informative in specific settings, particularly for modeling variation in specialization magnitude and in low-relatedness regimes. More broadly, the findings indicate that diversification depends on structural signals that are both prediction-target-dependent and scale-dependent, with relatedness and embedding-derived features capturing different aspects of the capability space (local overlap vs. structural position).
Related
- Recovering Collective Structure in Congressional Voting: A Fused Latent Factor and Network Approach
- SPLICE: Latent Diffusion over JEPA Embeddings for Conformal Time-Series Inpainting
- Integrating Network Psychometrics and LLMs: The Ising-Embeddings-Model applied to Reliability Auditing
- Spectral Dynamics of DeepWalk Embeddings for Dynamic Network Change-Point Detection
- Dynamic Latent Space Modeling of Inhomogeneous Poisson Network Processes with Applications to International Relations
BibTeX
@article{sturm2026latent,
title = {{The latent structure of diversification from relatedness and network embeddings}},
author = {Niclas Frederic Sturm and Cristian Candia and Bruno Damásio and Flávio L Pinheiro},
journal = {PLOS One},
year = {2026},
month = oct,
doi = {10.1371/journal.pone.0344958},
url = {https://doi.org/10.1371/journal.pone.0344958},
note = {CC BY},
}
RIS
TY - JOUR
TI - The latent structure of diversification from relatedness and network embeddings
AU - Niclas Frederic Sturm
AU - Cristian Candia
AU - Bruno Damásio
AU - Flávio L Pinheiro
PY - 2026
DA - 2026/10/22
JO - PLOS One
DO - 10.1371/journal.pone.0344958
UR - https://doi.org/10.1371/journal.pone.0344958
AB - Economic diversification is commonly modeled using co-occurrence-based measures of relatedness that quantify pairwise overlap among activities in a capability network. Although such measures are derived from network structure, they operate at the level of first-order neighborhood relations and summarize proximity through local co-occurrence. They do not explicitly encode higher-order structural context, such as indirect connectivity patterns or global positional similarity, into a continuous representation of entities and activities. We develop an embedding-based framework that learns such representations from network topology, enabling the construction of interpretable geometric features, including capability alignment, displacement, and portfolio entropy, that extend standard measures used in economic complexity. We apply this framework to two systems: international trade (1998–2023) and public procurement firms (2009–2024). The resulting representations reveal different structural organization across scales: firms exhibit modular clustering patterns, whereas countries occupy broader, nested capability configurations. In predictive tasks for product and activity specialization, embedding-derived features provide additional explanatory power beyond relatedness in several settings, particularly when forecasting variation in the magnitude of comparative advantage. For country-level entry events, however, persistence remains the strongest predictor. Our results show that relatedness remains the dominant predictor of entry events. In contrast, embedding-derived features become more informative in specific settings, particularly for modeling variation in specialization magnitude and in low-relatedness regimes. More broadly, the findings indicate that diversification depends on structural signals that are both prediction-target-dependent and scale-dependent, with relatedness and embedding-derived features capturing different aspects of the capability space (local overlap vs. structural position).
SN - 1932-6203
ER -