@Article{NMTMA-3-195,
author = {M. Emelianenko},
title = {Fast Multilevel CVT-Based Adaptive Data Visualization Algorithm},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2010},
volume = {3},
number = {2},
pages = {195--211},
abstract = {<p style="text-align: justify;">Efficient data visualization techniques are critical for many scientific applications.
Centroidal Voronoi tessellation (CVT) based algorithms offer a convenient vehicle
for performing image analysis, segmentation and compression while allowing to optimize
retained image quality with respect to a given metric. In experimental science
with data counts following Poisson distributions, several CVT-based data tessellation
algorithms have been recently developed. Although they surpass their predecessors
in robustness and quality of reconstructed data, time consumption remains to be an
issue due to heavy utilization of the slowly converging Lloyd iteration. This paper discusses
one possible approach to accelerating data visualization algorithms. It relies on
a multidimensional generalization of the optimization based multilevel algorithm for
the numerical computation of the CVTs introduced in [1], where a rigorous proof of
its uniform convergence has been presented in 1-dimensional setting. The multidimensional
implementation employs barycentric coordinate based interpolation and maximal
independent set coarsening procedures. It is shown that when coupled with bin
accretion algorithm accounting for the discrete nature of the data, the algorithm outperforms
Lloyd-based schemes and preserves uniform convergence with respect to the
problem size. Although numerical demonstrations provided are limited to spectroscopy
data analysis, the method has a context-independent setup and can potentially deliver
significant speedup to other scientific and engineering applications.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2010.32s.5},
url = {http://global-sci.org/intro/article_detail/nmtma/5996.html}
}