I am working with a dataset and I would like to analyze the interrelationships between variables using a statistic based on the eigenvectors of its correlation matrix.
Specifically, I am looking for a single scalar metric that summarizes the strength or structure of the relationship based on the eigenvectors, while remaining independent of the number of variables (i.e., the dimensionality of the dataset).
The motivation is to detect or compare the overall structure of association in different datasets or subsets, without the metric being biased simply due to differing variable counts.
Do you know of any established approaches, transformation techniques, or metrics that can help achieve this? Are there any papers or references that explore this kind of analysis?
I would appreciate any guidance, even if it’s from multivariate statistics, spectral graph theory, or dimensionality reduction literature
Hey Mustafa,
Really thoughtful question — summarizing variable relationships from eigenvectors in a dimension-independent way is definitely a challenge!
One scalar metric that might help is Spectral Entropy. It gives you a single number that reflects the distribution of variance across eigenvectors of the correlation (or covariance) matrix — and it's fairly independent of dimensionality. It's been used in areas like signal processing and network analysis, but works great in multivariate data too.
Here’s the general idea:
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