Similar data belong together

Everything should be made as simple as possible, but not simpler

Albert Einstein

The need to group data

The world is complex and multidimensional

Univariate analysis focuses on only one dimension

Sometimes, world issues are best understood as multivariate

For example

Percentage of foreign-born vs What is a neighborhood?

Years of schooling vs Human development

Monthly income vs Deprivation

Grouping as simplifying

Define a given number of categories based on
many characteristics (multi-dimensional)

Find the category where each observation fits best.

Reduce complexity, keep all the relevant information

Produce easier-to-understand outputs

Types of grouping

Non-spatial clustering

Regionalisation

Non-spatial clustering

Split a dataset into groups of observations that are similar within the group
and dissimilar between groups based on a series of attributes

Machine learning

The computer learns some of the dataset’s properties without the human specifying them.

Unsupervised

There is no apriori structure imposed on the classification \(\rightarrow\) before the analysis, no observations are in a category.

K-means

Most popular clustering algorithm

Good but not perfect

partition n observations into k clusters in which each observation belongs to the cluster with the nearest mean (cluster centers or cluster centroid)

Wikipedia

Example

Palmer Penguins

The Palmer Archipelago penguins. Artwork by @allison_horst

Penguins according to their flipper length and bill length

K-Means clusters based on flipper length and bill length

distance-based

K-Means clusters based on non-standardised data

Pay attention to scales

always standardise

Many techniques

Hierarchical clustering

Agglomerative clustering

Spectral clustering

Neural networks (e.g. Self-Organizing Maps)

DBSCAN

Comparison of algorithms

Regionalization

Split a dataset into groups of observations that are similar within the group
and dissimilar between groups based on a series of attributes
with the additional constraint that observations need to be spatial neighbours

Aggregating basic spatial units (areas) into larger units (regions)

All the methods aggregate geographical areas into a predefined number of regions while optimizing a particular aggregation criterion

The areas within a region must be geographically connected (the spatial contiguity constraint)

The number of regions must be smaller than or equal to the number of areas

Each area must be assigned to one and only one region

Each region must contain at least one area

All the methods aggregate geographical areas into a predefined number of regions while optimizing a particular aggregation criterion

The areas within a region must be geographically connected (the spatial contiguity constraint)

The number of regions must be smaller than or equal to the number of areas

Each area must be assigned to one and only one region

Each region must contain at least one area

Duque et al. (2007)

Algorithms

Automated Zoning Procedure (AZP)

Arisel

Max-P

Skater

See Duque et al. (2007) for an excellent, though advanced, overview.

import sklearn