Clustering and Geography

Jon Reades

Space Adds Complexity

We now have to consider two more types of clustering:

1. With respect to polygons: regions are built from adjacent zones that are more similar to one another than to other adjacent zones.
2. With respect to points: points are distributed in a way that indicates ‘clumping’ at particular scales.

Type 1 is probably what you were thinking of in terms of clustering.

Type 2 is point pattern analysis and should be considered a substantially different area of research and type of analysis.

Trade-offs (Again)…

Consider:

• Clustering algorithms are inherently spatial.
• Clustering algorithms do not take space geography into account.

Does this matter?

All clustering algorithms are about inter-observation and intra-cluster distances so they have some conceptualisation of ‘space’.

Spatially-aware clustering algorithms exist but are generally much more computationally-intensive than ‘regular ones’.

Different Approaches

Algorithm	Pros	Cons	Geographically Aware?
k-Means	Fast. Deterministic.	Every observation to a cluster.	N.
DBSCAN	Allows for clusters and outliers.	Slower. Choice of \(\epsilon\) critical. Can end up with all outliers.	N, but implicit in \(\epsilon\).
OPTICS	Fewer parameters than DBSCAN.	Even slower.	N, but implicit in \(\epsilon\).
Hierarchical/ HDBSCAN	Can cut at any number of clusters.	No ‘ideal’ solution.	Y, with connectivity parameter.
ADBSCAN	Scales. Confidence levels.	May need large data set to be useful. Choice of \(\epsilon\) critical.	Y.
Max-p	Coherent regions returned.	Very slow if model poorly specified.	Y.

Setting the Relevant Distance

Many clustering algorithms rely on a distance specification (usually \(\epsilon\)). So to set this threshold:

• In high-dimensional spaces this threshold will need to be large.
• In high-dimensional spaces the scale will be meaningless (i.e. not have a real-world meaning, only an abstract one).
• In 2- or 3-dimensional (geographical) space this threshold could be meaningful (i.e. a value in metres could work).

Choosing a Distance Metric

n Dimensions	How to Set	Examples
2 or 3	Theory/Empirical Data	Walking speed; Commute distance
2 or 3	K/L Measures	Plot with Simulation for CIs to identify significant ‘knees’.
3	Marked Point Pattern?
> 3	kNN	Calculate average kNN distance based on some expectation of connectivity.

Remember: inter-observation distance increases with dimensionality!

> There is no ‘best’ clustering algorithm, it’s all about judgement.

Geodemographics as a Business

Experian

Specialist in consumer segmentation and geodemographics (bit.ly/2jMRhAW).

• Market cap: £14.3 billion.
• Mosaic: “synthesises of 850 million pieces of information… to create a segmentation that allocates 49 million individuals and 26 million households into one of 15 Groups and 66 detailed Types.””
• More than 450 variables used.

Most retail companies will have their own segmentation scheme. Competitors: CACI, Nielsen, etc.

Experian Groups

Experian Mapping

Output Area Classification

OAC set up as ‘open source’ alternative to Mosaic:

• Well documented (UCL Geography a major contributor)
• Doesn’t require a license or payment
• Can be tweaked/extended/reweighted by users as needed