IEEE VIS 2024 Content: 2D Embeddings of Multi-dimensional Partitionings

2D Embeddings of Multi-dimensional Partitionings

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Marina Evers - University of Münster, Münster, Germany

 Lars Linsen - University of Münster, Münster, Germany

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2024-10-16T14:51:00ZGMT-0600Change your timezone on the schedule page
2024-10-16T14:51:00Z

Exemplar figure, described by caption below — We present an approach for visualizing a multi-dimensional partitioning in a 2D embedding. Each segment in the embedding corresponds to a multi-dimensional segment of the given partitioning. A multi-dimensional partitioning is modeled as a graph that is embedded into a 2D plane. The graph embedding is used as a starting point for a cellular automaton approach to compute a 2D embedding of the multi-dimensional embedding preserving topology, area, and boundary length. To its outcome, we apply a rendering that highlights relevant features.

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Keywords

Multi-dimensional partitionings, segmentations, dimensionality reduction, parameter space visualization.

Abstract

Partitionings (or segmentations) divide a given domain into disjoint connected regions whose union forms again the entire domain. Multi-dimensional partitionings occur, for example, when analyzing parameter spaces of simulation models, where each segment of the partitioning represents a region of similar model behavior. Having computed a partitioning, one is commonly interested in understanding how large the segments are and which segments lie next to each other. While visual representations of 2D domain partitionings that reveal sizes and neighborhoods are straightforward, this is no longer the case when considering multi-dimensional domains of three or more dimensions. We propose an algorithm for computing 2D embeddings of multi-dimensional partitionings. The embedding shall have the following properties: It shall maintain the topology of the partitioning and optimize the area sizes and joint boundary lengths of the embedded segments to match the respective sizes and lengths in the multi-dimensional domain. We demonstrate the effectiveness of our approach by applying it to different use cases, including the visual exploration of 3D spatial domain segmentations and multi-dimensional parameter space partitionings of simulation ensembles. We numerically evaluate our algorithm with respect to how well sizes and lengths are preserved depending on the dimensionality of the domain and the number of segments.