# 5.1 SKATER

Spatial C(K)luster Analysis by Tree Edge Removal (SKATER) is an optimized algorithm to prune the minimum spanning tree into several clusters that their values of selected variables are as similar as possible while retaining the contiguity structure.  For more information, please read <https://geodacenter.github.io/workbook/9c_spatial3/lab9c.html#skater>

## skater()

{% hint style="info" %}
skater() is a PostgreSQL WINDOW function. Please call it  with an OVER clause.
{% endhint %}

### Synopsis

Short version 1:

```sql
integer skater(integer k, anyarray vals,  bytea weights)
```

Short version 2:

```sql
integer skater(integer k, anyarray vals,  bytea weights, integer min_region_size)
```

Short version 3:

```sql
integer skater(integer k, anyarray vals,  bytea weights, numeric bound_vas, float min_bound)
```

Full version 1:

```sql
integer skater(integer k, anyarray vals,  bytea weights, integer min_region_size,
    character varying scale_method,
    character varying distance_type,
    integer seed,
    integer cpu_threads)

```

Full version 2:

```sql
integer skater(integer k, anyarray vals,  bytea weights, 
    numeric bound_val, float min_bound,
    character varying scale_method,
    character varying distance_type,
    integer seed,
    integer cpu_threads)

```

### Arguments

| Name             | Type              | Description                                                                                                                                                            |
| ---------------- | ----------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| k                | integer           | the number of clusters                                                                                                                                                 |
| vals             | anyarray          | an array of the numeric columns that contains the values for skater                                                                                                    |
| weights          | bytea             | a bytea column that stores the spatial weights information                                                                                                             |
| bound\_val       | numeric           | the numeric column of bound variable                                                                                                                                   |
| min\_bound       | float             | the minimum bound value that applies to all clusters                                                                                                                   |
| scale\_method    | character varying | the scaling method applies on *vals*. Options are {'*raw*', '*standardize*', '*demean*', '*mad*', '*range\_standardize*', '*range\_adjust*'}. Default: '*standardize*' |
| distance\_method | character varying | the distance metric used to measure the distance in attribute space of input *vals*. Options are {'*euclidean*', '*manhattan*'. Default: '*euclidean*'.                |
| seed             | integer           | the seed for random number generator used in LISA statistics. Default: 123456789.                                                                                      |
| cpu\_threads     | integer           | the number of cpu threads used for parallel LISA computation. Default: 6.                                                                                              |

### Return

| Type    | Description           |
| ------- | --------------------- |
| integer | the cluster indicator |

### Examples

Apply skater to create 10 spatially constrained clusters using variable \["hr60", "ue60", "dv60"] (homicide, unemployment, divorce rate 1960 in [natregimes dataset](https://geodacenter.github.io/data-and-lab/natregimes/)) and queen contiguity weights "queen\_w":

{% hint style="info" %}
Please see chapter '[Contiguity Based Weights](https://xunli.gitbook.io/postgeoda/2.-spatial-weights/2.1-contiguity-based-weights)' for how to create a Queen contiguity weights.
{% endhint %}

```sql
SELECT skater(10, ARRAY[hr60, ue60, dv60], queen_w) OVER() FROM natregimes;

 skater 
--------
      4
      1
      1
      3
      3
 ...
```

{% hint style="success" %}
Use k=0 if you don't know the number of regions. The algorithm will use the bound information (e.g. minimum size of each region, or bound variable, e.g. population, with minimum bound value) to find the best solution.
{% endhint %}

```sql
-- each region has at least 100 counties
SELECT skater(0, ARRAY[hr60, ue60, dv60], queen_w, 100) OVER() FROM natregimes;

 skater 
--------
     10
      2
     16
      2
      9
      4
      1
      1
 ...
```


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