Basics: Notation: Sum:

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

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

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

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

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

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

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

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)

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 Summary of a histogram

Bivariate Scatterplots Correlation Linear Regression slope constant

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 * X j,Y j t j h ij =t j -t i * X i,Y i * t i (0,0) 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

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 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