Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization

• URL: http://arxiv.org/abs/2503.01664v1
• Date: Mon, 03 Mar 2025 15:40:08 GMT
• Title: Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization
• Authors: Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck,
• Abstract summary: We introduce a framework for aggregating dissimilarity functions that arise from locally adjusting a metric through density-aware normalization.<n>We formalize these approaches as m-schemes, a class of methods closely related to t-norms and t-conorms in probabilistic metrics.
• Score: 0.09320657506524149
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Many machine learning algorithms try to visualize high dimensional metric data in 2D in such a way that the essential geometric and topological features of the data are highlighted. In this paper, we introduce a framework for aggregating dissimilarity functions that arise from locally adjusting a metric through density-aware normalization, as employed in the IsUMap method. We formalize these approaches as m-schemes, a class of methods closely related to t-norms and t-conorms in probabilistic metrics, as well as to composition laws in information theory. These m-schemes provide a flexible and theoretically grounded approach to refining distance-based embeddings.

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