GeoStatistics

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GeoStatistics

• Univariate
• Bivariate
• Spatial Description

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Univariate

• One Variable
• Frequency (table)
• Histogram (graph)
• Do the same thing (i.e count of observations in
  intervals or classes
• Cumulative Frequency (total below cutoffs)

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Summary of a histogram

• Measurements of location (center of distribution
• mean (m µ x )
• median
• mode
• Measurements of spread (variability)
• variance
• standard deviation
• interquartile range
• Measurements of shape (symmetry length
• coefficient of skewness
• coefficient of variation

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Bivariate
Scatterplots
Correlation
Linear Regression
slope constant
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Basics for Spatial data
A data layer, grid, raster, or single band of an
image spatial dataset
Rows of b
Columns of b
Total number of bands or layers, the count of
bdimensions
Total number of rows, the count of i
Total number of columns, the count of j
, the total size of b
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Basics for Spatial Data
And
A cell (pixel or place) having an assigned value
And
Any given i, j pair
Such that
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Basics for Spatial Data
Therefore the Sum for a single band (grid,
coverage) across all cells (space) is
and the Sum for a single cell (space) across all
bands (grids, coverages) is
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terms

• Parametric based upon statistical parameters
  (mean standard deviation)
• Non-Parametric based upon objects (polygons) in
  feature space
• Decision Rules rules for sorting pixels into
  classes

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Spatial Parameters
the statistical average the central
tendency the spread of the values about the
mean
MEAN Sample Variance Standard Deviation
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Covariance
measures the tendencies of data file values for
the same pixel, but in different bands, to vary
with each other in relation to the means of their
respective bands.
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Dimensionality
B the number of bands dimensions . A
multi-dimensional data (feature) space
Measurement Vector
Mean Vector
Feature Space - 2dimensions
190 85
Band B
Band A
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Spectral Distance
a number that allows two measurement vectors to
be compared
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ClusteringMinimum Spectral Distance -
unsupervised
Band B
Band A
Band B
Band A
1st iteration cluster mean
2nd iteration cluster mean
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Classification Decision Rules

• Non-Parametric
• parallelepiped
• feature space
• Unclassified Options
• parametric rule
• unclassified
• Overlap Options
• parametric rule
• by order
• unclassified
• Parametric
• minimum distance
• Mahalanobis distance
• maximum likelihood

• If the non-parametric test results in one unique
  class, the pixel will be assigned to that class.
• if the non-parametric test results in zero
  classes (outside the decision boundaries) the the
  unclassified rule applies either left
  unclassified or classified by the parametric rule
• if the pixel falls into more than one class the
  overlap rule applies left unclassified, use the
  parametric rule, or processing order

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Parallelepiped

• Maximum likelihood
• (bayesian)
• probability
• Bayesian, a prior (weights)

Band B
Band A
Minimum Distance
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Spatial Description
- Data Postings symbol maps (if only 2 classes
indicator map - Contour Maps - Moving Windows
gt heteroscedasticity (values in some region
are more variable than in others) - Spatial
Continuity (h-scatterplots
Spatial lag h (0,1) same x, y1
h(0,0) h(0,3) h(0,5)
correlation coefficient (i.e the correlogram,
relationship of p with h
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• Correlogram p(h) the relationship of the
  correlation coefficient of an h-scatterplot and h
  (the spatial lag)
• Covariance C(h) the relationship of
  thecoefficient of variation of an h-scatterplot
  and h
• Semivariogram variogram moment of
  inertia

OR half the average sum difference between the x
and y pair of the h-scatterplot OR for a h(0,0)
all points fall on a line xy OR as h
points drift away from xy