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Basics:

Explore the fundamentals of spatial data analysis including notation, parameters, means, spectral distance, covariance, classification rules, statistics, and spatial continuity.

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Basics:

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  1. Basics: Notation: Sum:

  2. PARAMETERS * the statistical average * the central tendency * the spread of the values about the mean MEAN: Sample Variance: Standard Deviation:

  3. 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.

  4. Dimensionality N = the number of bands = dimensions …. an (n) dimensional data (feature) space Measurement Vector Mean Vector Feature Space - 2dimensions 190 85 Band B Band A

  5. Spectral Distance * a number that allows two measurement vectors to be compared

  6. 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

  7. ISODATA I - iterative S - self O - organizing D - data A - analysis T - technique A - (application)? ClusteringMinimum Spectral Distance - unsupervised Band B Band A Band B Band A 1st iteration cluster mean 2nd iteration cluster mean

  8. 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

  9. cluster mean Candidate pixel Parallelepiped • Maximum likelihood • (bayesian) • probability • Bayesian, a prior (weights) Band B Band A Minimum Distance Band B Band A

  10. GeoStatistics • Univariate • Bivariate • Spatial Description

  11. 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)

  12. 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

  13. Bivariate Scatterplots Correlation Linear Regression slope constant

  14. * Xj,Yj tj hij=tj-ti * Xi,Yi * ti (0,0) Spatial Description - Data Postings = symbol maps (if only 2 classes = indicator map - Contour Maps - Moving Windows => “heteroscedasticity” (values in some region are more variable than in others) - Spatial Continuity (h-scatterplots Spatial lag = h = (0,1) = same x, y+1 h=(0,0) h=(0,3) h=(0,5) correlation coefficient (i.e the correlogram, relationship of p with h

  15. moment of inertia = • 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 x=y OR: as |h| points drift away from x=y

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