548 research outputs found
Spectral partitioning of time-varying networks with unobserved edges
We discuss a variant of `blind' community detection, in which we aim to
partition an unobserved network from the observation of a (dynamical) graph
signal defined on the network. We consider a scenario where our observed graph
signals are obtained by filtering white noise input, and the underlying network
is different for every observation. In this fashion, the filtered graph signals
can be interpreted as defined on a time-varying network. We model each of the
underlying network realizations as generated by an independent draw from a
latent stochastic blockmodel (SBM). To infer the partition of the latent SBM,
we propose a simple spectral algorithm for which we provide a theoretical
analysis and establish consistency guarantees for the recovery. We illustrate
our results using numerical experiments on synthetic and real data,
highlighting the efficacy of our approach.Comment: 5 pages, 2 figure
Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis
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
Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation
This paper considers a joint multi-graph inference and clustering problem for
simultaneous inference of node centrality and association of graph signals with
their graphs. We study a mixture model of filtered low pass graph signals with
possibly non-white and low-rank excitation. While the mixture model is
motivated from practical scenarios, it presents significant challenges to prior
graph learning methods. As a remedy, we consider an inference problem focusing
on the node centrality of graphs. We design an expectation-maximization (EM)
algorithm with a unique low-rank plus sparse prior derived from low pass signal
property. We propose a novel online EM algorithm for inference from streaming
data. As an example, we extend the online algorithm to detect if the signals
are generated from an abnormal graph. We show that the proposed algorithms
converge to a stationary point of the maximum-a-posterior (MAP) problem.
Numerical experiments support our analysis
Graph Filters for Signal Processing and Machine Learning on Graphs
Filters are fundamental in extracting information from data. For time series
and image data that reside on Euclidean domains, filters are the crux of many
signal processing and machine learning techniques, including convolutional
neural networks. Increasingly, modern data also reside on networks and other
irregular domains whose structure is better captured by a graph. To process and
learn from such data, graph filters account for the structure of the underlying
data domain. In this article, we provide a comprehensive overview of graph
filters, including the different filtering categories, design strategies for
each type, and trade-offs between different types of graph filters. We discuss
how to extend graph filters into filter banks and graph neural networks to
enhance the representational power; that is, to model a broader variety of
signal classes, data patterns, and relationships. We also showcase the
fundamental role of graph filters in signal processing and machine learning
applications. Our aim is that this article provides a unifying framework for
both beginner and experienced researchers, as well as a common understanding
that promotes collaborations at the intersections of signal processing, machine
learning, and application domains
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