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

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.

@article{barth2025_2503.01664,
  title={ Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization },
  author={ Lukas Silvester Barth and Hannaneh Fahimi and Parvaneh Joharinad and Jürgen Jost and Janis Keck },
  journal={arXiv preprint arXiv:2503.01664},
  year={ 2025 }
}