Unraveling the graph structure of tabular datasets through Bayesian and spectral analysis

• URL: http://arxiv.org/abs/2110.01421v1
• Date: Mon, 4 Oct 2021 12:51:55 GMT
• Title: Unraveling the graph structure of tabular datasets through Bayesian and spectral analysis
• Authors: Bruno Messias F. de Resende, Eric K. Tokuda, Luciano da Fontoura Costa
• Abstract summary: We show that the inference of the hierarchical modular structure obtained by the nested block model (nSBM) can help us identify the classes of features and unravel non-trivial relationships. We analyzed a socioeconomic survey conducted with students in Brazil: the PeNSE survey.
• Score: 3.128267020893596
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In the big-data age tabular datasets are being generated and analyzed everywhere. As a consequence, finding and understanding the relationships between the features of these datasets are of great relevance. Here, to encompass these relationships we propose a methodology that maps an entire tabular dataset or just an observation 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, corroborated with that and 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. However, questions from the class \textit{Safety} were partly grouped by our method in the class \textit{Drugs}. Surprisingly, by inspecting these questions, we observed that they were related to both these topics, suggesting an alternative interpretation of these questions. Our method can provide guidance for tabular data analysis as well as the design of future surveys.

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