Merging Hazy Sets with m-Schemes: A Geometric Approach to Data Visualization
This provides a flexible method for data visualization researchers, though it appears incremental as it formalizes existing approaches.
The paper tackles the problem of visualizing high-dimensional metric data in 2D by introducing m-schemes, a framework for aggregating dissimilarity functions through density-aware normalization, building on methods like IsUMap. The result is a theoretically grounded approach that refines distance-based embeddings to highlight geometric and topological features.
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.