Multivariate data are becoming more and more popular in several applications, including physics, chemistry, medicine, geography, etc. A multivariate dataset is represented by a cell complex and a vector-valued function defined on the complex vertices. The major challenge arising when dealing with multivariate data is to obtain concise and effective visualizations. The usability of common visual elements (e.g., color, shape, size) deteriorates when the number of variables increases. Here, we consider Discrete Morse Theory (DMT) [Forman 1998] for computing a discrete gradient field on a multivariate dataset. We propose a new algorithm, well suited for parallel and distribute implementations. We discuss the importance of obtaining the discrete gradient as a compact representation of the original complex to be involved in the computation of multidimensional persistent homology. Moreover, the discrete gradient field that we obtain is at the basis of a visualization tool for capturing the mutual relationships among the different functions of the dataset.

A discrete Morse-based approach to multivariate data analysis / Iuricich, Federico; Scaramuccia, Sara; Landi, Claudia; De Floriani, Leila. - (2016), pp. 1-8. ((Intervento presentato al convegno SIGGRAPH ASIA 2016 Symposium on Visualization tenutosi a Macao nel December 05 - 08, 2016 [10.1145/3002151.3002166].

A discrete Morse-based approach to multivariate data analysis

LANDI, Claudia;
2016

Abstract

Multivariate data are becoming more and more popular in several applications, including physics, chemistry, medicine, geography, etc. A multivariate dataset is represented by a cell complex and a vector-valued function defined on the complex vertices. The major challenge arising when dealing with multivariate data is to obtain concise and effective visualizations. The usability of common visual elements (e.g., color, shape, size) deteriorates when the number of variables increases. Here, we consider Discrete Morse Theory (DMT) [Forman 1998] for computing a discrete gradient field on a multivariate dataset. We propose a new algorithm, well suited for parallel and distribute implementations. We discuss the importance of obtaining the discrete gradient as a compact representation of the original complex to be involved in the computation of multidimensional persistent homology. Moreover, the discrete gradient field that we obtain is at the basis of a visualization tool for capturing the mutual relationships among the different functions of the dataset.
SIGGRAPH ASIA 2016 Symposium on Visualization
Macao
December 05 - 08, 2016
1
8
Iuricich, Federico; Scaramuccia, Sara; Landi, Claudia; De Floriani, Leila
A discrete Morse-based approach to multivariate data analysis / Iuricich, Federico; Scaramuccia, Sara; Landi, Claudia; De Floriani, Leila. - (2016), pp. 1-8. ((Intervento presentato al convegno SIGGRAPH ASIA 2016 Symposium on Visualization tenutosi a Macao nel December 05 - 08, 2016 [10.1145/3002151.3002166].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1120237
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