Find clusters of values using Postgresql - postgresql

Question

Consider the following example table:
CREATE TABLE rndtbl AS
SELECT
generate_series(1, 10) AS id,
random() AS val;
and I want to find for each id a cluster_id such that the clusters are far away from each other at least 0.1. How would I calculate such a cluster assignment?
A specific example would be:
select * from rndtbl ;
id | val
----+-------------------
1 | 0.485714662820101
2 | 0.185201027430594
3 | 0.368477711919695
4 | 0.687312887981534
5 | 0.978742253035307
6 | 0.961830694694072
7 | 0.10397826647386
8 | 0.644958863966167
9 | 0.912827260326594
10 | 0.196085536852479
(10 rows)
The result would be: ids (2,7,10) in a cluster and (5,6,9) in another cluster and (4,8) in another, and (1) and (3) as singleton clusters.

Answer 1

From
SELECT * FROM rndtbl ;
┌────┬────────────────────┐
│ id │ val │
├────┼────────────────────┤
│ 1 │ 0.153776332736015 │
│ 2 │ 0.572575284633785 │
│ 3 │ 0.998213059268892 │
│ 4 │ 0.654628816060722 │
│ 5 │ 0.692200613208115 │
│ 6 │ 0.572836415842175 │
│ 7 │ 0.0788379465229809 │
│ 8 │ 0.390280921943486 │
│ 9 │ 0.611408909317106 │
│ 10 │ 0.555164183024317 │
└────┴────────────────────┘
(10 rows)
Use the LAG window function to know whether the current row is in a new cluster or not:
SELECT *, val - LAG(val) OVER (ORDER BY val) > 0.1 AS new_cluster
FROM rndtbl ;
┌────┬────────────────────┬─────────────┐
│ id │ val │ new_cluster │
├────┼────────────────────┼─────────────┤
│ 7 │ 0.0788379465229809 │ (null) │
│ 1 │ 0.153776332736015 │ f │
│ 8 │ 0.390280921943486 │ t │
│ 10 │ 0.555164183024317 │ t │
│ 2 │ 0.572575284633785 │ f │
│ 6 │ 0.572836415842175 │ f │
│ 9 │ 0.611408909317106 │ f │
│ 4 │ 0.654628816060722 │ f │
│ 5 │ 0.692200613208115 │ f │
│ 3 │ 0.998213059268892 │ t │
└────┴────────────────────┴─────────────┘
(10 rows)
Finally you can SUM the number of true (still ordering by val) to get the cluster of the row (counting from 0):
SELECT *, SUM(COALESCE(new_cluster::int, 0)) OVER (ORDER BY val) AS nb_cluster
FROM (
SELECT *, val - LAG(val) OVER (ORDER BY val) > 0.1 AS new_cluster
FROM rndtbl
) t
;
┌────┬────────────────────┬─────────────┬────────────┐
│ id │ val │ new_cluster │ nb_cluster │
├────┼────────────────────┼─────────────┼────────────┤
│ 7 │ 0.0788379465229809 │ (null) │ 0 │
│ 1 │ 0.153776332736015 │ f │ 0 │
│ 8 │ 0.390280921943486 │ t │ 1 │
│ 10 │ 0.555164183024317 │ t │ 2 │
│ 2 │ 0.572575284633785 │ f │ 2 │
│ 6 │ 0.572836415842175 │ f │ 2 │
│ 9 │ 0.611408909317106 │ f │ 2 │
│ 4 │ 0.654628816060722 │ f │ 2 │
│ 5 │ 0.692200613208115 │ f │ 2 │
│ 3 │ 0.998213059268892 │ t │ 3 │
└────┴────────────────────┴─────────────┴────────────┘
(10 rows)