exploratory spatial data analysis (esda) analysis through visualization

Exploratory Spatial Data Analysis (ESDA)

Analysis through Visualization

Data Normalization

• Values (attributes) by themselves are sometimes misleading.

• Normalization refers to the division of multiple sets of data by a common variable in order to negate that variable's effect on the data.

• Normalization can help to compare samples.• Example: The number of people in a county does not

tell us about the relative density of the people. What we may want is the # of people per area.

Density = (# of people in county / county area)

Data NormalizatoinApproaches

• Density – divide count by area

• Divide an area –based count variable by another area based count variableX = Area on wheat / Total area in crops X = higher ratio indicates that wheat is more important

• Compute ratio of two count variablesX = $ of Wheat Sold / $ of all Crops SoldX = higher ratio indicates that wheat contributed more income to

area

• Compute summary numerical measures for each unit (sum, mean, SD, etc.)

Data Normalization

Raw - # of Hispanics per Tract

Normalized - #Hispanic/Total#

MappingCommon ESDA Methods• Quantile - Each class contains an equal number of features. • Percentile - Sort values in numerical order, compute % of

total observations. Note that the Median = 50% quartile• Standard Deviation – good for normal distribution• Box Map – Shows outliers as the function of quartiles.

IQR = Q75 – Q25Lower Outlier = Q25 – Hinge * IQRUpper Outlier = Q75 + Hinge * IQR

Mapping (%Hispanic)

Exploration of Data

• Histogram - examine distribution

• Scatter Plot - examine correlation between variables

• Box Plot - compare distribution between variables

• Parallel Coordinate Plot - examine relation between variables

Box Plots and Quantile

Spatial Autocorrelation• First law of geography: “everything is related to

everything else, but near things are more related than distant things” – Waldo Tobler

• Spatial Autocorrelation – correlation of a variable with itself through space.– If there is any systematic pattern in the spatial distribution of a

variable, it is said to be spatially autocorrelated.– If nearby or neighboring areas are more alike, this is positive spatial

autocorrelation.– Negative autocorrelation describes patterns in which neighboring areas

are unlike.– Random patterns exhibit no spatial autocorrelation.

Why spatial autocorrelation is important

• Most statistics are based on the assumption that the values of observations in each sample are independent of one another

• Positive spatial autocorrelation may violate this, if the samples were taken from nearby areas

• Goals of spatial autocorrelation– Measure the strength of spatial autocorrelation in a map – test the assumption of independence or randomness

Moran’s I• One of the oldest indicators of spatial

autocorrelation (Moran, 1950). Still a defacto standard for determining spatial autocorrelation.

• Applied to zones or points with continuous variables associated with them.

• Compares the value of the variable at any one location with the value at all other locations.

Moran’s I

Where N is the number of casesXi is the variable value at a particular locationXj is the variable value at another locationX-bar is the mean of the variableWij is a weight applied to the comparison between location i and location j. Weights are based either on distance or adjacency.

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