# Adjacency Spectral Embeddings of Correlation Networks

arXiv: https://arxiv.org/abs/2602.21055 · HTML: https://mlsanity.com/paper/2602.21055/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 31 of its 77 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 30 of 31)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Community Detection and Stochastic Block Models](https://mlsanity.com/paper/1703.10146/) (2017)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [A statistical interpretation of spectral embedding: the generalised random dot product graph](https://mlsanity.com/paper/1709.05506/) (2017)
- [Rate-Optimal Perturbation Bounds for Singular Subspaces with Applications to High-Dimensional Statistics](https://mlsanity.com/paper/1605.00353/) (2016)
- [Community Detection in Degree-Corrected Block Models](https://mlsanity.com/paper/1607.06993/) (2016)
- [Heteroskedastic PCA: Algorithm, Optimality, and Applications](https://mlsanity.com/paper/1810.08316/) (2018)
- [Network cross-validation by edge sampling](https://mlsanity.com/paper/1612.04717/) (2016)
- [On a 'Two Truths' Phenomenon in Spectral Graph Clustering](https://mlsanity.com/paper/1808.07801/) (2018)
- [Perfect Clustering for Stochastic Blockmodel Graphs via Adjacency Spectral Embedding](https://mlsanity.com/paper/1310.0532/) (2013)
- [Community Detection and Classification in Hierarchical Stochastic Blockmodels](https://mlsanity.com/paper/1503.02115/) (2015)
- [Detecting Overlapping Communities in Networks Using Spectral Methods](https://mlsanity.com/paper/1412.3432/) (2014)
- [Network Cross-Validation for Determining the Number of Communities in Network Data](https://mlsanity.com/paper/1411.1715/) (2014)
- [Mixed Membership Estimation for Social Networks](https://mlsanity.com/paper/1708.07852/) (2017)
- [Inference for Heteroskedastic PCA with Missing Data](https://mlsanity.com/paper/2107.12365/) (2021)
- [Limit theorems for eigenvectors of the normalized Laplacian for random graphs](https://mlsanity.com/paper/1607.08601/) (2016)
- [One-Hot Graph Encoder Embedding](https://mlsanity.com/paper/2109.13098/) (2021)
- [Network Representation Using Graph Root Distributions](https://mlsanity.com/paper/1802.09684/) (2018)
- [Entrywise Estimation of Singular Vectors of Low-Rank Matrices with Heteroskedasticity and Dependence](https://mlsanity.com/paper/2105.13346/) (2021)
- [Spectral embedding of weighted graphs](https://mlsanity.com/paper/1910.05534/) (2019)
- [Recovering shared structure from multiple networks with unknown edge distributions](https://mlsanity.com/paper/1906.07265/) (2019)
- [Estimating a network from multiple noisy realizations](https://mlsanity.com/paper/1710.04765/) (2017)
- [Spectral clustering under degree heterogeneity: a case for the random walk Laplacian](https://mlsanity.com/paper/2105.00987/) (2021)
- [Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCA](https://mlsanity.com/paper/2303.06198/) (2023)
- [Limit theorems for out-of-sample extensions of the adjacency and Laplacian spectral embeddings](https://mlsanity.com/paper/1910.00423/) (2019)
- [Davis-Kahan Theorem in the two-to-infinity norm and its application to perfect clustering](https://mlsanity.com/paper/2411.11728/) (2024)
- [Introduction to correlation networks: Interdisciplinary approaches beyond thresholding](https://mlsanity.com/paper/2311.09536/) (2023)
- [A central limit theorem for an omnibus embedding of multiple random graphs and implications for multiscale network inference](https://mlsanity.com/paper/1705.09355/) (2017)
- [Ergodic Limits, Relaxations, and Geometric Properties of Random Walk Node Embeddings](https://mlsanity.com/paper/2109.04526/) (2021)

## Abstract (arXiv)

In many applications, weighted networks are constructed based on time series data: each time series is associated to a vertex and edge weights are given by pairwise correlations. The result is a network whose edge dependency structure violates the assumptions of most common network models. Nonetheless, it is common to analyze these "correlation networks" using embedding methods derived from edge-independent network models, based on a belief that the edges are approximately independent. In this work, we put this modeling choice on firm theoretical ground. We show that when the time series are expressible in terms of a small number of Fourier basis elements (or in some other suitably-chosen basis), correlation networks correspond to latent space networks with dependent edge noise in which the vertex-level latent variables encode the basis coefficients. Further, we show that when time series are observed subject to noise, spectral embedding of the resulting noisy correlation network still recovers these true vertex-level latent representations under suitable assumptions. This characterization of embeddings as learning Fourier coefficients appears to be folklore in the signal processing community in the context of principal component analysis, but is, to the best of our knowledge, new to the statistical network analysis literature.