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GeoStatistics

- Univariate
- Bivariate
- Spatial Description

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)

Summary of a histogram

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

Bivariate

Scatterplots

Correlation

Linear Regression

slope constant

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

Basics for Spatial Data

And

A cell (pixel or place) having an assigned value

And

Any given i, j pair

Such that

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

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

Spatial Parameters

the statistical average the central

tendency the spread of the values about the

mean

MEAN Sample Variance Standard Deviation

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.

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

Spectral Distance

a number that allows two measurement vectors to

be compared

ClusteringMinimum Spectral Distance -

unsupervised

Band B

Band A

Band B

Band A

1st iteration cluster mean

2nd iteration cluster mean

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

Parallelepiped

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

Band B

Band A

Minimum Distance

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

- 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