Depth functions as a quality measure and for steering multidimensional projections

Douglas Cedrim, Viktor Vad, Afonso Paiva, Meister Eduard Gröller, Luis Gustavo Nonato, Antonio Castelo
Depth functions as a quality measure and for steering multidimensional projections
Computers & Graphics (Special Section on SIBGRAPI 2016), 60:93-106, November 2016. [image] [Paper]

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Abstract

The analysis of multidimensional data has been a topic of continuous research for many years.This type of data can be found inseveral different areas ofscience. The analysis of multidimensional data has been a topic of continuous research for many years. This type of data can be found in several different areas of science. A common task while analyzing such data is to investigate patterns by interacting with spatializations of the data in a visual domain. Understanding the relation between the underlying dataset characteristics and the technique used to provide its visual representation is of fundamental importance since it can provide a better intuition on what to expect from the spatialization. In this paper, we propose the usage of concepts from non-parametric statistics, namely depth functions, as a quality measure for spatializations. We evaluate the action of multi-dimensional projection techniques on such estimates. We apply both qualitative and quantitative ana-lyses on four different multidimensional techniques selected according to the properties they aim to preserve. We evaluate them with datasets of different characteristics: synthetic, real world, high dimensional; and contaminated with outliers. As a straightforward application, we propose to use depth information to guide multidimensional projection techniques which rely on interaction through control point selection and positioning. Even for techniques which do not intend to preserve any centrality measure, interesting results can be achieved by separating regions possibly contaminated with outliers.

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BibTeX

@article{Groeller_2016_P7,
  title =      "Depth functions as a quality measure and for steering
               multidimensional projections",
  author =     "Douglas Cedrim and Viktor Vad and Afonso Paiva and Meister
               Eduard Gr{"o}ller and Luis Gustavo Nonato and Antonio
               Castelo",
  year =       "2016",
  abstract =   "The analysis of multidimensional data has been a topic of
               continuous research for many years.This type of data can be
               found inseveral different areas ofscience.  The analysis of
               multidimensional data has been a topic of continuous
               research for many years. This type of data can be found in
               several different areas of science. A common task while
               analyzing such data is to investigate patterns by
               interacting with spatializations of the data in a visual
               domain. Understanding the relation between the underlying
               dataset characteristics and the technique used to provide
               its visual representation is of fundamental importance since
               it can provide a better intuition on what to expect from the
               spatialization. In this paper, we propose the usage of
               concepts from non-parametric statistics, namely depth
               functions, as a quality measure for spatializations. We
               evaluate the action of multi-dimensional projection
               techniques on such estimates. We apply both qualitative and
               quantitative ana-lyses on four different multidimensional
               techniques selected according to the properties they aim to
               preserve. We evaluate them with datasets of different
               characteristics: synthetic, real world, high dimensional;
               and contaminated with outliers. As a straightforward
               application, we propose to use depth information to guide
               multidimensional projection techniques which rely on
               interaction through control point selection and positioning.
               Even for techniques which do not intend to preserve any
               centrality measure, interesting results can be achieved by
               separating regions possibly contaminated with outliers. ",
  month =      nov,
  issn =       "doi: 10.1016/j.cag.2016.08.008",
  journal =    "Computers & Graphics (Special Section on SIBGRAPI 2016)",
  volume =     "60",
  pages =      "93--106",
  URL =        "https://www.cg.tuwien.ac.at/research/publications/2016/Groeller_2016_P7/",
}