A discrete morse-based approach to multivariate data analysis

作者: Federico Iuricich , Sara Scaramuccia , Claudia Landi , Leila De Floriani

DOI: 10.1145/3002151.3002166

关键词:

摘要: … The usability of common visual elements (eg, color, shape, size) deteriorates when the … Intuitively, the homology of a simplicial complex Σ detects k-dimensional cycles of Σ, ie connected …

参考文章(28)
Madjid Allili, Tomasz Kaczynski, Claudia Landi, Reducing complexes in multidimensional persistent homology theory Journal of Symbolic Computation. ,vol. 78, pp. 61- 75 ,(2017) , 10.1016/J.JSC.2015.11.020
Lars Huettenberger, Christoph Garth, A Comparison of Pareto Sets and Jacobi Sets Topological and Statistical Methods for Complex Data, Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces. pp. 125- 141 ,(2015) , 10.1007/978-3-662-44900-4_8
Leila De Floriani, Ulderico Fugacci, Federico Iuricich, Paola Magillo, Morse complexes for shape segmentation and homological analysis: discrete models and algorithms Computer Graphics Forum. ,vol. 34, pp. 761- 785 ,(2015) , 10.1111/CGF.12596
A. Gyulassy, N. Kotava, M. Kim, C. D. Hansen, H. Hagen, V. Pascucci, Direct Feature Visualization Using Morse-Smale Complexes IEEE Transactions on Visualization and Computer Graphics. ,vol. 18, pp. 1549- 1562 ,(2012) , 10.1109/TVCG.2011.272
Konstantin Mischaikow, Vidit Nanda, Morse Theory for Filtrations and Efficient Computation of Persistent Homology Discrete and Computational Geometry. ,vol. 50, pp. 330- 353 ,(2013) , 10.1007/S00454-013-9529-6
Herbert Edelsbrunner, Ernst Peter Mücke, Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms ACM Transactions on Graphics. ,vol. 9, pp. 66- 104 ,(1990) , 10.1145/77635.77639
Andrea Cerri, Barbara Di Fabio, Grzegorz Jabłoński, Filippo Medri, Comparing shapes through multi-scale approximations of the matching distance Computer Vision and Image Understanding. ,vol. 121, pp. 43- 56 ,(2014) , 10.1016/J.CVIU.2013.11.004
David Günther, Jan Reininghaus, Hubert Wagner, Ingrid Hotz, Efficient Computation of 3D Morse-Smale Complexes and Persistent Homology using Discrete Morse Theory The Visual Computer. ,vol. 28, pp. 959- 969 ,(2012) , 10.1007/S00371-012-0726-8
Hamish Carr, David Duke, Joint Contour Nets: Computation and properties ieee pacific visualization symposium. pp. 161- 168 ,(2013) , 10.1109/PACIFICVIS.2013.6596141