# LogSpecT: Feasible Graph Learning Model from Stationary Signals with Recovery Guarantees

arXiv: https://arxiv.org/abs/2305.01379 · HTML: https://mlsanity.com/paper/2305.01379/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 49 references that are in the map.
- First posted on arXiv 2 May 2023.

## Builds on (most cited first, 20 of 20)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [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)
- [Generalized Spectral Clustering via Gromov-Wasserstein Learning](https://mlsanity.com/paper/2006.04163/) (2020)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Multi-modal Graph Learning for Disease Prediction](https://mlsanity.com/paper/2203.05880/) (2022)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [A User Guide to Low-Pass Graph Signal Processing and its Applications](https://mlsanity.com/paper/2008.01305/) (2020)
- [Learning Graphs from Smooth and Graph-Stationary Signals with Hidden Variables](https://mlsanity.com/paper/2111.05588/) (2021)
- [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)
- [Semi-supervised Learning in Network-Structured Data via Total Variation Minimization](https://mlsanity.com/paper/1901.09838/) (2019)
- [Detecting Central Nodes from Low-rank Excited Graph Signals via Structured Factor Analysis](https://mlsanity.com/paper/2109.13573/) (2021)
- [Graph Laplacian mixture model](https://mlsanity.com/paper/1810.10053/) (2018)
- [Localized Linear Regression in Networked Data](https://mlsanity.com/paper/1903.11178/) (2019)
- [Generalized Sampling on Graphs With Subspace and Smoothness Priors](https://mlsanity.com/paper/1905.04441/) (2019)
- [Joint inference of multiple graphs with hidden variables from stationary graph signals](https://mlsanity.com/paper/2110.03666/) (2021)
- [One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations](https://mlsanity.com/paper/1304.5038/) (2013)
- [Product Graph Learning from Multi-attribute Graph Signals with Inter-layer Coupling](https://mlsanity.com/paper/2211.00909/) (2022)

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

- [Directed Graph Topology Inference via Graph Filter Identification](https://mlsanity.com/paper/2606.27455/) (2026)

## Abstract (arXiv)

Graph learning from signals is a core task in Graph Signal Processing (GSP). One of the most commonly used models to learn graphs from stationary signals is SpecT. However, its practical formulation rSpecT is known to be sensitive to hyperparameter selection and, even worse, to suffer from infeasibility. In this paper, we give the first condition that guarantees the infeasibility of rSpecT and design a novel model (LogSpecT) and its practical formulation (rLogSpecT) to overcome this issue. Contrary to rSpecT, the novel practical model rLogSpecT is always feasible. Furthermore, we provide recovery guarantees of rLogSpecT, which are derived from modern optimization tools related to epi-convergence. These tools could be of independent interest and significant for various learning problems. To demonstrate the advantages of rLogSpecT in practice, a highly efficient algorithm based on the linearized alternating direction method of multipliers (L-ADMM) is proposed. The subproblems of L-ADMM admit closed-form solutions and the convergence is guaranteed. Extensive numerical results on both synthetic and real networks corroborate the stability and superiority of our proposed methods, underscoring their potential for various graph learning applications.