Core Concepts
The nonnegative Tucker decomposition (NNTuck) is a tensor factorization model that can identify latent structure and interdependence between layers in a multilayer network.
Abstract
The content presents a tensor factorization model called the nonnegative Tucker decomposition (NNTuck) for analyzing multilayer networks. The key points are:
The NNTuck generalizes existing stochastic block models (SBMs) to the multilayer setting by allowing for distinct latent structure in both the nodes and layers of the network.
The third factor matrix Y in the NNTuck decomposition captures the interdependence between layers. The authors propose three ways to interpret Y to quantify layer independence, dependence, and redundancy.
The authors show the equivalence between maximizing the log-likelihood under a Poisson model and minimizing the KL-divergence in the NNTuck, allowing for efficient estimation using multiplicative updates.
The authors propose definitions of layer interdependence based on likelihood ratio tests between nested NNTuck models that differ in the structure of the Y matrix.
The NNTuck is evaluated on both synthetic and real-world multilayer networks, including biological, cognitive, and social support networks. The analysis identifies layer independence, dependence, and redundancy in these empirical examples.
Stats
The content does not contain any explicit numerical data or statistics. It focuses on the conceptual development and interpretation of the NNTuck model.
Quotes
"Quantifying interdependencies between layers can identify redundancies in the structure of a network, indicate relationships between disparate layers, and potentially inform survey instruments for collecting social network data."
"We build upon these motivations from previous work and develop the NNTuck as a natural way to identify a latent space in the dimension of the layers."
"Analyzing the third factor matrix is a significant focus of our work, and we propose three methods for interpreting it to quantify layer interdependence based on the structure of that factor matrix."