```
import geopandas as gpd
import seaborn as sns
from libpysal import graph
from sklearn import cluster
```

# Clustering and regionalisation

This session is all about finding groups of similar observations in data using clustering techniques.

Many questions and topics are complex phenomena that involve several dimensions and are hard to summarise into a single variable. In statistical terms, you call this family of problems *multivariate*, as opposed to *univariate* cases where only a single variable is considered in the analysis. Clustering tackles this kind of questions by reducing their dimensionality -the number of relevant variables the analyst needs to look at - and converting it into a more intuitive set of classes that even non-technical audiences can look at and make sense of. For this reason, it is widely used in applied contexts such as policymaking or marketing. In addition, since these methods do not require many preliminary assumptions about the structure of the data, it is a commonly used exploratory tool, as it can quickly give clues about the shape, form and content of a dataset.

The basic idea of statistical clustering is to summarise the information contained in several variables by creating a relatively small number of categories. Each observation in the dataset is then assigned to one, and only one, category depending on its values for the variables originally considered in the classification. If done correctly, the exercise reduces the complexity of a multi-dimensional problem while retaining all the meaningful information contained in the original dataset. This is because once classified, the analyst only needs to look at in which category every observation falls into, instead of considering the multiple values associated with each of the variables and trying to figure out how to put them together in a coherent sense. When the clustering is performed on observations that represent areas, the technique is often called geodemographic analysis.

Although there exist many techniques to statistically group observations in a dataset, all of them are based on the premise of using a set of attributes to define classes or categories of observations that are similar *within* each of them, but differ *between* groups. How similarity within groups and dissimilarity between them is defined and how the classification algorithm is operationalised is what makes techniques differ and also what makes each of them particularly well suited for specific problems or types of data.

In the case of analysing spatial data, there is a subset of methods that are of particular interest for many common cases in Spatial Data Science. These are the so-called *regionalisation* techniques. Regionalisation methods can also take many forms and faces but, at their core, they all involve statistical clustering of observations with the additional constraint that observations need to be geographical neighbours to be in the same category. Because of this, rather than category, you will use the term *area* for each observation and *region* for each category, hence regionalisation, the construction of regions from smaller areas.

The Python package you will use for clustering today is called `scikit-learn`

and can be imported as `sklearn`

.

## Attribute-based clustering

In this session, you will be working with another dataset you should already be familiar with - the Scottish Index of Multiple Deprivation. This time, you will focus only on the area of Glasgow City prepared for this course.

### Scottish Index of Multiple Deprivation

As always, the table can be read from the site:

```
= gpd.read_file(
simd "https://martinfleischmann.net/sds/clustering/data/glasgow_simd_2020.gpkg"
)
```

Instead of reading the file directly off the web, it is possible to download it manually, store it on your computer, and read it locally. To do that, you can follow these steps:

- Download the file by right-clicking on this link and saving the file
- Place the file in the same folder as the notebook where you intend to read it
- Replace the code in the cell above with:

```
= gpd.read_file(
simd "glasgow_simd_2020.gpkg",
)
```

Inspect the structure of the table:

` simd.info()`

```
<class 'geopandas.geodataframe.GeoDataFrame'>
RangeIndex: 746 entries, 0 to 745
Data columns (total 52 columns):
# Column Non-Null Count Dtype
--- ------ -------------- -----
0 DataZone 746 non-null object
1 DZName 746 non-null object
2 LAName 746 non-null object
3 SAPE2017 746 non-null int64
4 WAPE2017 746 non-null int64
5 Rankv2 746 non-null int64
6 Quintilev2 746 non-null int64
7 Decilev2 746 non-null int64
8 Vigintilv2 746 non-null int64
9 Percentv2 746 non-null int64
10 IncRate 746 non-null object
11 IncNumDep 746 non-null int64
12 IncRankv2 746 non-null float64
13 EmpRate 746 non-null object
14 EmpNumDep 746 non-null int64
15 EmpRank 746 non-null float64
16 HlthCIF 746 non-null int64
17 HlthAlcSR 746 non-null int64
18 HlthDrugSR 746 non-null int64
19 HlthSMR 746 non-null int64
20 HlthDprsPc 746 non-null object
21 HlthLBWTPc 746 non-null object
22 HlthEmergS 746 non-null int64
23 HlthRank 746 non-null int64
24 EduAttend 746 non-null object
25 EduAttain 746 non-null float64
26 EduNoQuals 746 non-null int64
27 EduPartici 746 non-null object
28 EduUniver 746 non-null object
29 EduRank 746 non-null int64
30 GAccPetrol 746 non-null float64
31 GAccDTGP 746 non-null float64
32 GAccDTPost 746 non-null float64
33 GAccDTPsch 746 non-null float64
34 GAccDTSsch 746 non-null float64
35 GAccDTRet 746 non-null float64
36 GAccPTGP 746 non-null float64
37 GAccPTPost 746 non-null float64
38 GAccPTRet 746 non-null float64
39 GAccBrdbnd 746 non-null object
40 GAccRank 746 non-null int64
41 CrimeCount 746 non-null int64
42 CrimeRate 746 non-null int64
43 CrimeRank 746 non-null float64
44 HouseNumOC 746 non-null int64
45 HouseNumNC 746 non-null int64
46 HouseOCrat 746 non-null object
47 HouseNCrat 746 non-null object
48 HouseRank 746 non-null float64
49 Shape_Leng 746 non-null float64
50 Shape_Area 746 non-null float64
51 geometry 746 non-null geometry
dtypes: float64(16), geometry(1), int64(22), object(13)
memory usage: 303.2+ KB
```

Before you jump into exploring the data, one additional step that will come in handy down the line. Not every variable in the table is an attribute that you will want for the clustering. In particular, you are interested in sub-ranks based on individual SIMD domains, so you will only consider those. Hence, first manually write them so they are easier to subset:

```
= [
subranks "IncRankv2",
"EmpRank",
"HlthRank",
"EduRank",
"GAccRank",
"CrimeRank",
"HouseRank"
]
```

You can quickly familiarise yourself with those variables by plotting a few maps like the one below to build your intuition about what is going to happen.

`"IncRankv2", "geometry"]].explore("IncRankv2", tiles="CartoDB Positron", tooltip=False) simd[[`