Today

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

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

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 and clusters
• 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

Finding clusters of PPs

Cluster is a hard to define term

Huge literature spanning spatial analysis, statistics and computer science. Today, we’ll look at…

Density

Based

Spatial

Clustering of

Applications with

Noise

DBSCAN

(Additional) Pros:

• Not necessarily spatial
• Very fast to run so → scales relatively well → applicable to large datasets

(Additional) Cons:

• Not based on any probabilistic model (no inference)
• Hard to learn about the underlying process