Whirligig Charm: using soft computing methodologies to map the spatial median and the spatial percentile

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Whirligig Charm using soft computing
methodologies to map the spatial median and the
spatial percentile Robert J. Abrahart GIS
Research Group - School of GeographyFaculty of
Law Social Sciences Email bob.abrahart_at_nottin
gham.ac.uk
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• Move towards Location Based Services

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Who, What, When, Where, Why, How?

• Legacy tools
• Spatial data swamps
• Spatial data mining robust/ intelligent/
  multi-scale/ multi-dimensional/ etc. etc.
• Spatial search what are we looking for?
• Finding solutions or mapping distributions?

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Where is the spatial median?
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• What is a median/ spatial median?
• - Middle value of data placed in rank order.
• That observation above and below which there
  are an equal number of observations in a data
  set.
• What is a percentile/ spatial percentile?
• The ordered column can be divided into other
  groups
• 25th value below which 25 of the observations
  occur
• 50th value below which 50 of the observations
  occur
• 75th value below which 75 of the observations
  occur

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• Last two or three decades have seen various
  attempts to produce a robust spatial analogue to
  the univariate median
• Science behind such attempts was- based on
  complex mathematical or geometrical
  algorithms- designed to encompass one or more
  properties of the univariate median
• But was also restricted to- crisp or traditional
  logic
• - a philosophical stance that an exact solution
  or true optimal analog exists and can be
  identified

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Manhattan Median
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Euclidean Median
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Hull Peeling
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Anti-Podal Reduction
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Tukey Half Space Median
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• The reported research presents an empirical
  algorithm that challenges existing mindsets
• It will rank crisp theoretical solutions to the
  spatial median in terms of a median membership
  function
• It will construct detailed raster outputs of
  'median membership' and 'percentile membership'
  scores
• Has several similarities to the Geographical
  Analysis Machine (Openshaw et al., 1987).

Openshaw, S., Charlton, M., Wymer, C. and Craft,
A.W. 1987. "A Mark I Geographical Analysis
Machine for the Automated Analysis of Point Data
Sets", International Journal of Geographical
Information Systems, 1, 335-358.
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What is a whirligig?
Webster's 1913 Dictionary 1. A child's toy,
spun or whirled around like a wheel upon an axis,
or like a top. --Johnson. 2. Anything which
whirls around, or in which persons or things are
whirled about, as a frame with seats or wooden
horses. With a whirligig of jubilant mosquitoes
spinning about each head. --G. W. Cable. 3. A
mediaeval instrument for punishing petty
offenders, being a kind of wooden cage turning on
a pivot, in which the offender was whirled round
with great velocity. 4. Any one of numerous
species of beetles belonging to Gyrinus and
allied genera.
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Fuzzy Logic in GIS
"It is appropriate to use fuzzy sets whenever we
haveto deal with ambiguity, vagueness and
ambivalence in mathematical or conceptual models
of empirical phenomena" (Burrough 1989 479).  
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What is whirligig charm?
Percentage split on either side of all possible
linesdrawn through a point
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How is whirligig charm computed?

• Extension of the half-space median
• Uses a rotating line in which the pivotal point
  about which that line rotates can be moved to a
  specified site or series of different sites or
  locations.
• Spinning mechanism termed 'whirligig' is used
  to construct a membership value index termed
  'charm' for each pivotal point
• based on a quantification of the geographical
  points on either side of all possible lines drawn
  through that pivotal point.

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• Each spin produces a membership score 0-1 that
  has fixed limitations with respect to
• continuous scanning rotational division-
  continuous mapping spatial resolution
• The mechanism is simple to understand
• - It can be directed to build specific estimates
  at individual points
• It can be repositioned from cell to cell across
  a raster grid to build continuous 'charm'
  surfaces.
• The notion of an exact answer with a perfect
  score
• is retained as a theoretical concept that is
  not expected to be achieved.

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• The power of this computational procedure to
  distinguish between earlier theoretical
  pointbased solutions is important
• BUT so too is the production of spatial
  distributions and raster output coverages that
  can be used to
• - exclude problematic inliers or outliers- or
  combined to produce more complex output
  surfaces for subsequent multifaceted spatial
  modelling operations

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5050 grid 50 random points 5050 percentage split
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5050 grid 50 random points 2575 percentage split
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It was not a snark! It was a boojam!

• Where Next?

speed up? user interaction? parallel
processing?