Union-Free Generic Depth for Non-Standard Data
Hannah Blocher, Georg Schollmeyer

TL;DR
The paper introduces ufg-depth, a novel framework extending data depth concepts to non-standard data types, enabling structure-preserving statistical analysis beyond classical spaces.
Contribution
It proposes the ufg-depth framework that respects the true structure of non-standard data, bridging the gap between data integrity and statistical analysis capabilities.
Findings
Theoretical analysis of ufg-depth properties.
Application to mixed categorical-numerical-spatial data.
Demonstration of structure-preserving analysis.
Abstract
Non-standard data, which fall outside classical statistical data formats, challenge state-of-the-art analysis. Examples of non-standard data include partial orders and mixed categorical-numeric-spatial data. Most statistical methods required to represent them by classical statistical spaces. However, this representation can distort their inherent structure and thus the results and interpretation. For applicants, this creates a dilemma: using standard statistical methods can risk misrepresenting the data, while preserving their true structure often lead these methods to be inapplicable. To address this dilemma, we introduce the union-free generic depth (ufg-depth) which is a novel framework that respects the true structure of non-standard data while enabling robust statistical analysis. The ufg-depth extends the concept of simplicial depth from normed vector spaces to a much broader…
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Taxonomy
TopicsAlgorithms and Data Compression · Handwritten Text Recognition Techniques · Image Processing and 3D Reconstruction
