Map Comparison

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Map Comparison

• Evaluation of spatial models
• 24 January 2006

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Map Comparison

• Methods
• Cell-by-cell based method
• Introducing tolerance by aggregation
• Fuzzy set approach
• Structure based comparison
• Interpretation
• Validity
• Significance
• Sensitivity

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Many reasons for map comparison

• Understanding spatial changes
• Trends
• Outliers, Hot-spots, errors
• Calibration and validation of spatial models
• Intercomparison of model runs
• Investigating consistency of cartographic methods
• Unequal resolution
• Unequal legends
• And what the cat drags in
• Vande Walle et al. 2005 Comparison of mental
  maps of Brussels accorsing to French and Flemish
  speaking students.
• Bifurcation Seeker

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Cell-by-cell

• All cells on the map are either equal or not

Percentage Correct 79
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Separating location and quantity

• Also composition / configuration

Differences in location and in quantity 5
differences
Only differences in location 8 differences
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Kappa statistic

• Resolve a bias considering uneven distributions
  more alike
• Controversial amongst remote sensers (Turk 2002,
  Stehman 2002)
• Variations define component of Kappa related to
  location and quantity (histogram). (Pontius
  2000, Hagen 2002)
• PA Percentage of agreement
• E(PA) Expected PA, subject to histograms
• Max Maximal PA, subject to histograms

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Contingency table

• Also confusion table/matrix and transition
  table/matrix

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Per category

• Temporarily reclassify map for Kappa statistics
  per category (Monserud Leemans)
• Most useful when prioritizing calibration efforts

Open
Park
River
City
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The limits of cell-by-cell methods
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Aggregation based methods

• Compare at coarser scales by means of aggregation
• Costanza 1987, Pontius 2004, Remmel et al 2005

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Aggregation versus moving window
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Fuzzy Set Map Comparison

• Tolerarance for confounding similar categories
• Fuzziness of category
• Tolerance for small spatial differences
• Fuzziness of location
• Overall map similarity
• Fuzzy Kappa

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Fuzziness of categories
Original map
Categorical Fuzzy map
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Fuzziness of location
Neighbour influence set by distance decay function
Original map
Categorical Fuzzy Map
Full Fuzzy Map
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Two way comparison step 1
Original Map B
Fuzzified map A is compared to crisp (original)
map B. And vice versa Similarity(A, B)
Intersection (A, B)
Original Map A
Full Fuzzy Map A
Partial comparison
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Two way comparison step 2
Originals
Comparison
Partial comparison
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Complete process
Map A
Map B
Original
Full Fuzzy
Comparison
Categorical Fuzzy
Partial Comparison
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Fuzzy Set Map Comparison applied
Fuzzy Kappa 0.49 Fraction Correct 0.91
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Fuzzy Kappa per category
Open
Park
City
River
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Impact of differences on structure

• Contiguous areas -gt Mean patch size
• Composition -gt Diversity

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Balancing structure and overlap
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Distance weighted moving window
Moving porthole with a fish-eye perspective
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Smoothly from overlap to structure
Similarity
Landscape
Neighbourhood
Local
Halving distance
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Mean patch size
Difference
Patch size
Map
Porthole
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Shannon Diversity
Difference
Porthole
Diversity
Map
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Validation

• Kappa and Fuzzy Kappa similarity relative to
  expected similarity
• Purpose to remove bias
• In practice expected similarity is as a benchmark
  model
• Better benchmarks can be thought of

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Random Constraint Match
Open -32 City -15 River 18 Park 29
Before
After
RCM
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Other neutral models

• Landscape ecology
• RULE and others
• Do not start from initial situation

Fractal
Source McGarical 2001
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Sensitivity and multi-scale analysis

• Parameters in Fuzzy Kappa, Aggregation and Moving
  window approaches express scale of the analysis
• Sensivity analysis Multi-scale analysis
• Generally, as scale increases, so does similarity

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Significance

• Apply reference model in Monte Carlo approach

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That was all !