# Interpretable Network Representation Learning with Principal Component Analysis

arXiv: https://arxiv.org/abs/2106.14238 · HTML: https://mlsanity.com/paper/2106.14238/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 64 references that are in the map.
- First posted on arXiv 27 Jun 2021.

## Builds on (most cited first, 17 of 17)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [DeepWalk: Online Learning of Social Representations](https://mlsanity.com/paper/1403.6652/) (2014)
- [LINE: Large-scale Information Network Embedding](https://mlsanity.com/paper/1503.03578/) (2015)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Graph Embedding Techniques, Applications, and Performance: A Survey](https://mlsanity.com/paper/1705.02801/) (2017)
- [A Tutorial on Principal Component Analysis](https://mlsanity.com/paper/1404.1100/) (2014)
- [Statistical inference on random dot product graphs: a survey](https://mlsanity.com/paper/1709.05454/) (2017)
- [The impossibility of low rank representations for triangle-rich complex networks](https://mlsanity.com/paper/2003.12635/) (2020)
- [Principled Multilayer Network Embedding](https://mlsanity.com/paper/1709.03551/) (2017)
- [Multi-scale brain networks](https://mlsanity.com/paper/1608.08828/) (2016)
- [Network classification with applications to brain connectomics](https://mlsanity.com/paper/1701.08140/) (2017)
- [Statistical inference for network samples using subgraph counts](https://mlsanity.com/paper/1701.00505/) (2017)
- [Varying-coefficient models for dynamic networks](https://mlsanity.com/paper/1702.03632/) (2017)
- [Stochastic Weighted Graphs: Flexible Model Specification and Simulation](https://mlsanity.com/paper/1505.04015/) (2015)
- [Multiplex networks in metropolitan areas: generic features and local effects](https://mlsanity.com/paper/1508.07265/) (2015)
- [An overview and perspective on social network monitoring](https://mlsanity.com/paper/1603.09453/) (2016)
- [Monitoring communication outbreaks among an unknown team of actors in dynamic networks](https://mlsanity.com/paper/1606.09308/) (2016)

## Abstract (arXiv)

We consider the problem of interpretable network representation learning for samples of network-valued data. We propose the Principal Component Analysis for Networks (PCAN) algorithm to identify statistically meaningful low-dimensional representations of a network sample via subgraph count statistics. The PCAN procedure provides an interpretable framework for which one can readily visualize, explore, and formulate predictive models for network samples. We furthermore introduce a fast sampling-based algorithm, sPCAN, which is significantly more computationally efficient than its counterpart, but still enjoys advantages of interpretability. We investigate the relationship between these two methods and analyze their large-sample properties under the common regime where the sample of networks is a collection of kernel-based random graphs. We show that under this regime, the embeddings of the sPCAN method enjoy a central limit theorem and moreover that the population level embeddings of PCAN and sPCAN are equivalent. We assess PCAN's ability to visualize, cluster, and classify observations in network samples arising in nature, including functional connectivity network samples and dynamic networks describing the political co-voting habits of the U.S. Senate. Our analyses reveal that our proposed algorithm provides informative and discriminatory features describing the networks in each sample. The PCAN and sPCAN methods build on the current literature of network representation learning and set the stage for a new line of research in interpretable learning on network-valued data. Publicly available software for the PCAN and sPCAN methods are available at https://www.github.com/jihuilee/.