1. Spatial Outlier Detection

2. Spatial Outlier Detection: An Example
Osama bin Laden's compound
“the main buildings in the compound lay on a 38,000- square-foot (3,500 m2) plot of land, much larger than those of nearby houses”
” The house itself did not stand out architecturally from others in the neighbourhood, except for its size and exaggerated security measures;”

3. What is Spatial Outlier?
Global outlier (anomaly)
Data samples different from other samples in population
Defined based on global distribution
Spatial outlier (anomaly)
Locations where samples different from their neighbors
Defined based on neighborhood context
Global outlier
Spatial outlier

4. What is Spatial Outlier?
Spatial attribute
Attribute related to object location and footprint
Coordinates (latitude, longitude), extent
Spatial neighborhood relationship
Determined based on spatial attribute
Distance threshold, touch, network topology
Non-spatial attributes
House age, color, income
Spatial outlier
Object whose non-spatial attributes differ significantly from their neighbors’

5. How to Detection Spatial Outliers
Visualization approach
Variogram cloud
Moran scatterplot
Neighborhood approach
Distance-based neighbors
Graph-based neighbors

6. Spatial Outlier Detection: Variogram Cloud

7. Spatial Outlier Detection: Moran Scatterplot

8. Spatial Outlier Detection: Neighborhood Approach
𝑍 𝑆(𝑥) = 𝑆 𝑥 − 𝜇 𝑠 𝛿 𝑠
where 𝑆 𝑥 is difference of one observation from its neighborhood average, 𝜇 𝑠 is expectation of 𝑆 𝑥 , 𝛿s is standard deviation of 𝑆 𝑥
Assuming Gaussian distribution
Spatial outliers

9. Question 1: Is Spatial Scale Important for Spatial Outlier Detection?
Is the house circled a spatial outlier?

10. Question 2: How to Find Object with Anomalous Shape?
distance to center
distance to center
angle
angle