This paper treats a blind detection problem to identify the central nodes in a graph from filtered graph signals. Unlike prior works which impose strong restrictions on the data model, we only require the underlying graph filter to satisfy a low pass property with a generic low-rank excitation model. We treat two cases depending on the low pass graph filter's strength. When the graph filter is strong low pass, i.e., it has a frequency response that drops sharply at the high frequencies, we show that the principal component analysis (PCA) method detects central nodes with high accuracy. For general low pass graph filter, we show that the graph signals can be described by a structured factor model featuring the product between a low-rank plus sparse factor and an unstructured factor. We propose a two-stage decomposition algorithm to learn the structured factor model via a judicious combination of the non-negative matrix factorization and robust PCA algorithms. We analyze the identifiability conditions for the model which lead to accurate central nodes detection. Numerical experiments on synthetic and real data are provided to support our findings. We demonstrate significant performance gains over prior works.

Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis

/pdf/egc2-enhanced-graph-classification-with-easy-graph-v75w3qq4.pdf

EGC2: Enhanced graph classification with easy graph compression

This paper proposes a mixture model of low pass filtered graph signals. Our aim is to jointly estimate the eigen-centrality vectors for the underlying graphs and identify the graph signal samples with their corresponding graphs, without knowing the graph topology a-priori. The problem is challenging as the observed graph signals lack any obvious identity with their associated graphs. We leverage a low-rank plus sparse structure of the unknown parameters to de-rive a customized expectation-maximization (EM) algorithm for the joint problem. Our algorithm assumes general excitation and does not require prior knowledge of the graph topology. Numerical experiments show the efficacy of our customized EM algorithm.

Joint Centrality Estimation and Graph Identification from Mixture of Low Pass Graph Signals

This paper treats a blind detection problem to identify the central nodes in a graph from filtered graph signals. Unlike prior works which impose strong restrictions on the data model, we only require the underlying graph filter to satisfy a low pass property with a generic low-rank excitation model. We treat two cases depending on the low pass graph filter's strength. When the graph filter is strong low pass, i.e., it has a frequency response that drops sharply at the high frequencies, we show that the principal component analysis (PCA) method detects central nodes with high accuracy. For general low pass graph filter, we show that the graph signals can be described by a structured factor model featuring the product between a low-rank plus sparse factor and an unstructured factor. We propose a two-stage decomposition algorithm to learn the structured factor model via a judicious combination of the non-negative matrix factorization and robust PCA algorithms. We analyze the identifiability conditions for the model which lead to accurate central nodes detection. Numerical experiments on synthetic and real data are provided to support our findings. We demonstrate significant performance gains over prior works. 

/pdf/detecting-central-nodes-from-low-rank-excited-graph-signals-244ryfiy.pdf

Detecting Central Nodes From Low-Rank Excited Graph Signals via Structured Factor Analysis

This paper considers learning a product graph from multi-attribute graph signals. Our work is motivated by the widespread presence of multilayer networks that feature interactions within and across graph layers. Focusing on a product graph setting with homogeneous layers, we propose a bivariate polynomial graph filter model. We then consider the topology inference problems thru adapting existing spectral methods. We propose two solutions for the required spectral estimation step: a simplified solution via unfolding the multi-attribute data into matrices, and an exact solution via nearest Kronecker product decomposition (NKD). Interestingly, we show that strong inter-layer coupling can degrade the performance of the unfolding solution while the NKD solution is robust to inter-layer coupling effects. Numerical experiments show efficacy of our methods.

pdf/product-graph-learning-from-multi-attribute-graph-signals-1xsega7p.pdf

Product Graph Learning From Multi-Attribute Graph Signals with Inter-Layer Coupling

We consider the problem of estimating a network's eigenvector centrality only from data on the nodes, with no information about network topology. Leveraging the versatility of graph filters to model network processes, data supported on the nodes is modeled as a graph signal obtained via the output of a graph filter applied to white noise. We seek to simplify the downstream task of centrality ranking by bypassing network topology inference methods and, instead, inferring the centrality structure of the graph directly from the graph signals. To this end, we propose two simple algorithms for ranking a set of nodes connected by an unobserved set of edges. We derive asymptotic and non-asymptotic guarantees for these algorithms, revealing key features that determine the complexity of the task at hand. Finally, we illustrate the behavior of the proposed algorithms on synthetic and real-world datasets.

Blind Inference of Eigenvector Centrality Rankings

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Blind Inference of Eigenvector Centrality Rankings