Today

• The point of points
• Point patterns
• Visualization of point patterns

The point of points

Points like polygons

Points can represent "fixed" entities

In this case, points are qualitatively similar to polygons/lines

The goal here is, taking location fixed, to model other aspects of the data

Points like polygons

Examples:

• Cities (in most cases)
• Buildings
• Polygons represented as their centroid
• ...

When points are not polygons

Point data are not only a different geometry than polygons or lines...

... Points can also represent a fundamentally different way to approach spatial analysis

Points unlike polygons

• Rather than exhausting the entire space, points can be events subject to occur anywhere
• The location of the event is part of what we are trying to understand/model
• The interest focuses on characterizing the pattern that the points follow over space

Points unlike polygons

• Rather than exhausting the entire space, points can be events subject to occur anywhere
• The location of the event is part of what we are trying to understand/model
• The interest focuses on characterizing the pattern that the points follow over space

A few examples...

[Source]

[Source]

UFO Sightings (1933-)

Geo-tagged tweets

Point patterns

Point patterns

Distribution of points over a portion of space

Assumption is a point can happen anywhere on that space, but only happens in specific locations

Point Pattern Analysis

Describe, characterize, and explain point patterns, focusing on their generating process

• Visual exploration
• Clustering properties
• Statistical modeling of the underlying processes

Visualization of PPs

Visualization of PPs

Two routes (today):

• Aggregate  ↔  "Histogram"
• Smooth  ↔  KDE

Aggregation

Use polygon boundaries and count points per area

[Insert your skills for choropleth mapping here!!!]

But, the polygons need to "make sense" (their delineation needs to relate to the point generating process)

Hex-binning

If no polygon boundary seems like a good candidate for aggregation...

...draw a hexagonal (or squared) tesselation!!!

But...

Kernel Density Estimation

Kernel Density Estimation

Estimate the (continuous) observed distribution of a variable

[Source]

Bivariate (spatial) KDE

Probability of finding observations at a given point in space

• Bivariate version: distribution of pairs of values
• In space: values are coordinates (XY), locations
• Continuous "version" of a choropleth

Recapitulation

• Points can be understood as a fixed or random process over space
• If seen as a random, where points are located is part of the interest in the (point pattern) analysis
• Visualization of point patterns can be done through aggregation or smoothing (but issues relating to the MAUP and underlying populations need to be kept in mind!)