How to group timestamps into islands (based on arbitrary gap)? - sql

Question

Consider this list of dates as timestamptz:
I grouped the dates by hand using colors: every group is separated from the next by a gap of at least 2 minutes.
I'm trying to measure how much a given user studied, by looking at when they performed an action (the data is when they finished studying a sentence.) e.g.: on the yellow block, I'd consider the user studied in one sitting, from 14:24 till 14:27, or roughly 3 minutes in a row.
I see how I could group these dates with a programming language by going through all of the dates and looking for the gap between two rows.
My question is: how would go about grouping dates in this way with Postgres?
(Looking for 'gaps' on Google or SO brings too many irrelevant results; I think I'm missing the vocabulary for what I'm trying to do here.)

Answer 1

SELECT done, count(*) FILTER (WHERE step) OVER (ORDER BY done) AS grp
FROM (
SELECT done
, lag(done) OVER (ORDER BY done) <= done - interval '2 min' AS step
FROM tbl
) sub
ORDER BY done;
The subquery sub returns step = true if the previous row is at least 2 min away - sorted by the timestamp column done itself in this case.
The outer query adds a rolling count of steps, effectively the group number (grp) - combining the aggregate FILTER clause with another window function.
fiddle
Related:
Query to find all timestamps more than a certain interval apart
How to label groups in postgresql when group belonging depends on the preceding line?
Select longest continuous sequence
Grouping or Window
About the aggregate FILTER clause:
Aggregate columns with additional (distinct) filters
Conditional lead/lag function PostgreSQL?

Answer 2

Building up on Erwin's answer, here is the full query for tallying up the amount of time people spent on those sessions/islands:
My data only shows when people finished reviewing something, not when they started, which means we don't know when a session truly started; and some islands only have one timestamp in them (leading to a 0-duration estimate.) I'm accounting for both by calculating the average review time and adding it to the total duration of islands.
This is likely very idiosyncratic to my use case, but I learned a thing or two in the process, so maybe this will help someone down the line.
-- Returns estimated total study time and average time per review, both in seconds
SELECT (EXTRACT( EPOCH FROM logged) + countofislands * avgreviewtime) as totalstudytime, avgreviewtime -- add total logged time to estimate for first-review-in-island and 1-review islands
FROM
(
SELECT -- get the three key values that will let us calculate total time spent
sum(duration) as logged
, count(island) as countofislands
, EXTRACT( EPOCH FROM sum(duration) FILTER (WHERE duration != '00:00:00'::interval) )/( sum(reviews) FILTER (WHERE duration != '00:00:00'::interval) - count(reviews) FILTER (WHERE duration != '00:00:00'::interval)) as avgreviewtime
FROM
(
SELECT island, age( max(done), min(done) ) as duration, count(island) as reviews -- calculate the duration of islands
FROM
(
SELECT done, count(*) FILTER (WHERE step) OVER (ORDER BY done) AS island -- give a unique number to each island
FROM (
SELECT -- detect the beginning of islands
done,
(
lag(done) OVER (ORDER BY done) <= done - interval '2 min'
) AS step
FROM review
WHERE clicker_id = 71 AND "done" > '2015-05-13' AND "done" < '2015-05-13 15:00:00' -- keep the queries small and fast for now
) sub
ORDER BY done
) grouped
GROUP BY island
) sessions
) summary