# Online Inference for Mixture Model of Streaming Graph Signals with Non-White Excitation

arXiv: https://arxiv.org/abs/2207.14019 · HTML: https://mlsanity.com/paper/2207.14019/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 68 references that are in the map.
- First posted on arXiv 28 Jul 2022.

## Builds on (most cited first, 30 of 34)

- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [Statistical guarantees for the EM algorithm: From population to sample-based analysis](https://mlsanity.com/paper/1408.2156/) (2014)
- [Learning graphs from data: A signal representation perspective](https://mlsanity.com/paper/1806.00848/) (2018)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Network Topology Inference from Spectral Templates](https://mlsanity.com/paper/1608.03008/) (2016)
- [Network Inference via the Time-Varying Graphical Lasso](https://mlsanity.com/paper/1703.01958/) (2017)
- [A Unified Framework for Structured Graph Learning via Spectral Constraints](https://mlsanity.com/paper/1904.09792/) (2019)
- [Non-asymptotic Analysis of Biased Stochastic Approximation Scheme](https://mlsanity.com/paper/1902.00629/) (2019)
- [Graph Spectral Image Processing](https://mlsanity.com/paper/1801.04749/) (2018)
- [Incremental Majorization-Minimization Optimization with Application to Large-Scale Machine Learning](https://mlsanity.com/paper/1402.4419/) (2014)
- [Signal Processing on Graphs: Causal Modeling of Unstructured Data](https://mlsanity.com/paper/1503.00173/) (2015)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Online Topology Inference from Streaming Stationary Graph Signals with Partial Connectivity Information](https://mlsanity.com/paper/2007.03653/) (2020)
- [Joint Inference of Multiple Graphs from Matrix Polynomials](https://mlsanity.com/paper/2010.08120/) (2020)
- [Algorithms for Learning Graphs in Financial Markets](https://mlsanity.com/paper/2012.15410/) (2020)
- [Online Discriminative Graph Learning from Multi-Class Smooth Signals](https://mlsanity.com/paper/2101.00184/) (2021)
- [Time-Varying Graph Learning with Constraints on Graph Temporal Variation](https://mlsanity.com/paper/2001.03346/) (2020)
- [Blind Community Detection from Low-rank Excitations of a Graph Filter](https://mlsanity.com/paper/1809.01485/) (2018)
- [Learning High-dimensional Gaussian Graphical Models under Total Positivity without Adjustment of Tuning Parameters](https://mlsanity.com/paper/1906.05159/) (2019)
- [State-Space Network Topology Identification from Partial Observations](https://mlsanity.com/paper/1906.10471/) (2019)
- [Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis](https://mlsanity.com/paper/2109.13573/) (2021)
- [A variational approach to stable principal component pursuit](https://mlsanity.com/paper/1406.1089/) (2014)
- [Graph Laplacian mixture model](https://mlsanity.com/paper/1810.10053/) (2018)
- [Tracking Switched Dynamic Network Topologies from Information Cascades](https://mlsanity.com/paper/1606.08882/) (2016)
- [Blind Inference of Eigenvector Centrality Rankings](https://mlsanity.com/paper/2008.11330/) (2020)
- [Detection of Core-Periphery Structure in Networks Using Spectral Methods and Geodesic Paths](https://mlsanity.com/paper/1410.6572/) (2014)
- [Blind identification of stochastic block models from dynamical observations](https://mlsanity.com/paper/1905.09107/) (2019)
- [Estimating Network Processes via Blind Identification of Multiple Graph Filters](https://mlsanity.com/paper/1909.12980/) (2019)
- [Joint inference of multiple graphs with hidden variables from stationary graph signals](https://mlsanity.com/paper/2110.03666/) (2021)

## Built on by (most cited first, 1 of 1)

- [Bayesian-based Online Label Shift Estimation with Dynamic Dirichlet Priors](https://mlsanity.com/paper/2511.18615/) (2025)

## Abstract (arXiv)

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.