# Unraveling the graph structure of tabular data through Bayesian and spectral analysis

arXiv: https://arxiv.org/abs/2110.01421 · HTML: https://mlsanity.com/paper/2110.01421/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 4 Oct 2021.

## Builds on (most cited first, 16 of 16)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [Consistent Individualized Feature Attribution for Tree Ensembles](https://mlsanity.com/paper/1802.03888/) (2018)
- [Feature relevance quantification in explainable AI: A causal problem](https://mlsanity.com/paper/1910.13413/) (2019)
- [True to the Model or True to the Data?](https://mlsanity.com/paper/2006.16234/) (2020)
- [Spectral Methods for Data Science: A Statistical Perspective](https://mlsanity.com/paper/2012.08496/) (2020)
- [MagNet: A Neural Network for Directed Graphs](https://mlsanity.com/paper/2102.11391/) (2021)
- [Hierarchical Block Structures and High-resolution Model Selection in Large Networks](https://mlsanity.com/paper/1310.4377/) (2013)
- [Magnetic Eigenmaps for the Visualization of Directed Networks](https://mlsanity.com/paper/1606.08266/) (2016)
- [A network approach to topic models](https://mlsanity.com/paper/1708.01677/) (2017)
- [Nonparametric Bayesian inference of the microcanonical stochastic block model](https://mlsanity.com/paper/1610.02703/) (2016)
- [Merge-split Markov chain Monte Carlo for community detection](https://mlsanity.com/paper/2003.07070/) (2020)
- [Characterization and comparison of large directed graphs through the spectra of the magnetic Laplacian](https://mlsanity.com/paper/2007.03466/) (2020)
- [On Spectral Analysis of Directed Signed Graphs](https://mlsanity.com/paper/1612.08102/) (2016)
- [The Atlas for the Aspiring Network Scientist](https://mlsanity.com/paper/2101.00863/) (2021)

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

- [Beyond symmetrization: effective adjacency matrices and renormalization for (un)singed directed graphs](https://mlsanity.com/paper/2406.01517/) (2024)

## Abstract (arXiv)

In the big-data age, tabular data are being generated and analyzed everywhere. As a consequence, finding and understanding the relationships between the features in these data are of great relevance. Here, to encompass these relationships, we propose a graph-based method that allows individual, group and multi-scale analyses. The method starts by mapping the tabular data into a weighted directed graph using the Shapley additive explanations technique. With this graph of relationships, we show that the inference of the hierarchical modular structure obtained by the Nested Stochastic Block Model (nSBM) as well as the study of the spectral space of the magnetic Laplacian can help us identify the classes of features and unravel non-trivial relationships. As a case study, we analyzed a socioeconomic survey conducted with students in Brazil: the PeNSE survey. The spectral embedding of the columns suggested that questions related to physical activities form a separate group. The application of the nSBM approach not only corroborated with that but allowed complementary findings about the modular structure: some groups of questions showed a high adherence with the divisions qualitatively defined by the designers of the survey. As opposed to the structure obtained by the spectrum, questions from the class Safety were partly grouped by our method in the class Drugs. Surprisingly, by inspecting these questions, we observed that they were related to both these topics, suggesting an alternative interpretation of these questions. These results show how our method can provide guidance for tabular data analysis as well as the design of future surveys.