Files and links (1)
Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
On positive definite thresholding of correlation matrices
ArXiv.org
11 Mar 2026
Abstract
Standard thresholding techniques for correlation matrices often destroy positive semidefiniteness. We investigate the construction of positive definite functions that vanish on specific setsK β [-1,1) , ensuring that the thresholded matrix remains a valid correlation matrix. We establish existence results, define a criterion for faithfulness based on the linear coefficient of the normalized Gegenbauer expansion in analogy with Delsarte's method in coding theory, and provide bounds for thresholding at single points and pairs of points. We prove that for correlation matrices of rankn , any soft-thresholding operator that preserves positive semidefiniteness necessarily induces a geometric collapse of the feature space, as quantified by anπ(1/n)bound on the faithfulness constant. Such demonstrates that geometrically unbiased soft-thresholding limits the recoverable signal.
Metrics
1 Record Views
Details
- Title
- On positive definite thresholding of correlation matrices
- Creators
- Sujit Sakharam DamaseJames Eldred Pascoe
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022171587404721