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Formation of groups of spatiotemporal approximate trajectories in R or PostgreSQL

I am doing some trajectory analysis using R and PostgreSQL. In order to form groups of trajectory segments where successive positions are spatio-temporal, I created the following table. What I'm still missing is a column group_id, which I am talking about.

bike_id1    datetime             bike_id2    near     group_id
      1    2016-05-28 11:00:00          2    TRUE            1
      1    2016-05-28 11:00:05          2    TRUE            1
      1    2016-05-28 11:00:10          2    FALSE          NA
[...]
      2    2016-05-28 11:00:05          3    TRUE            1
      2    2016-05-28 11:00:10          3    TRUE            1

This is the result of multiple comparisons between each trajectory with any others (all combinations without repetitions) and the internal connection on datetime(the count is always a multiple of 5 seconds). This shows that for certain positions, bikes 1 and 2 were rejected simultaneously and spatially close (some arbitrary threshold).

Now I would like to give unique identifiers for segments where two bikes are in space-time proximity ( group_id). I'm stuck here . I would like to group_idrelate to groups with several trajectories. The assignment method group_idshould understand that if bike 1 and 2 are in the group at 2016-05-28 11:00:05, then 3 belongs to the same group, if it is close to 2 in the same time stamp ( 2016-05-28 11:00:05).

Are there any tools inside R or PostgreSQL that would help me with this task? Running a loop through a table seems like the wrong way to do this.

EDIT: @wildplasser, , , , SQL. , .

CREATE TABLE nearness
        -- ( seq SERIAL NOT NULL UNIQUE -- surrogate for conveniance
        ( bike1 INTEGER NOT NULL
        , bike2 INTEGER NOT NULL
        , stamp timestamp NOT NULL
        , near boolean
        , PRIMARY KEY(bike1,bike2,stamp)
        );
INSERT INTO nearness( bike1,bike2,stamp,near) VALUES
 (1,2, '2016-05-28 11:00:00', TRUE)
,(1,2, '2016-05-28 11:00:05', TRUE)
,(1,2, '2016-05-28 11:00:10', TRUE)
,(1,2, '2016-05-28 11:00:20', TRUE) -- <<-- gap here
,(1,2, '2016-05-28 11:00:25', TRUE)
,(1,2, '2016-05-28 11:00:30', FALSE)
,(4,5, '2016-05-28 11:00:00', FALSE)
,(4,5, '2016-05-28 11:00:05', FALSE)
,(4,5, '2016-05-28 11:00:10', TRUE)
,(4,5, '2016-05-28 11:00:15', TRUE)
,(4,5, '2016-05-28 11:00:20', TRUE)
,(2,3, '2016-05-28 11:00:05', TRUE) -- <<-- bike 1, 2, 3 are in one grp @ 11:00:05
,(2,3, '2016-05-28 11:00:10', TRUE) -- <<-- no group here
,(6,7, '2016-05-28 11:00:00', FALSE)
,(6,7, '2016-05-28 11:00:05', FALSE)
        ;
+4
1

: [ ;] (set, bike_set) . (clust) , .

  • : ( , )
  • : , , .
  • bike_id, .
  • ( , uniq CTE)
  • - .

: (bike2 > bike1). , , . , . .

CREATE TABLE nearness
        ( bike1 INTEGER NOT NULL
        , bike2 INTEGER NOT NULL
        , stamp timestamp NOT NULL
        , near boolean
        , PRIMARY KEY(bike1,bike2,stamp)
        );
INSERT INTO nearness( bike1,bike2,stamp,near) VALUES
 (1,2, '2016-05-28 11:00:00', TRUE)
,(1,2, '2016-05-28 11:00:05', TRUE)
,(1,2, '2016-05-28 11:00:10', TRUE)
,(1,2, '2016-05-28 11:00:20', TRUE) -- <<-- gap here
,(1,2, '2016-05-28 11:00:25', TRUE)
,(1,2, '2016-05-28 11:00:30', FALSE)    -- <<-- these False-records serve no pupose
,(4,5, '2016-05-28 11:00:00', FALSE)    -- <<-- result would be the same without them
,(4,5, '2016-05-28 11:00:05', FALSE)
,(4,5, '2016-05-28 11:00:10', TRUE)
,(4,5, '2016-05-28 11:00:15', TRUE)
,(4,5, '2016-05-28 11:00:20', TRUE)
,(2,3, '2016-05-28 11:00:05', TRUE) -- <<-- bike 1, 2, 3 are in one grp @ 11:00:05
,(2,3, '2016-05-28 11:00:10', TRUE) -- <<-- no group here
,(6,7, '2016-05-28 11:00:00', FALSE)
,(6,7, '2016-05-28 11:00:05', FALSE)
        ;


        -- Recursive union-find to glue together sets of bike_ids
        -- ,occuring at the same moment.
        -- Sets are represented as {ordered,unique} arrays here
WITH RECURSIVE wood AS (
        WITH omg AS (
                SELECT bike1 ,bike2,stamp
                , row_number() OVER(ORDER BY bike1,bike2,stamp) AS seq
                , ARRAY[bike1,bike2]::integer[] AS arr
                FROM nearness n WHERE near = True
                )
        -- Find all existing combinations of bikes
        SELECT o1.stamp, o1.seq
                , ARRAY[o1.bike1,o1.bike2]::integer[] AS arr
        FROM omg o1
        UNION ALL
        SELECT o2.stamp, o2.seq -- avoid duplicates inside the array
                , CASE when o2.bike1 = ANY(w.arr) THEN w.arr || o2.bike2
                ELSE  w.arr || o2.bike1 END AS arr
        FROM omg o2
        JOIN wood w
                ON o2.stamp = w.stamp AND o2.seq > w.seq
                AND (o2.bike1 = ANY(w.arr) OR o2.bike2 = ANY(w.arr))
                AND NOT (o2.bike1 = ANY(w.arr) AND o2.bike2 = ANY(w.arr))
        )
, uniq  AS (    -- suppress partial sets caused by the recursive union-find buildup
        SELECT * FROM wood w
        WHERE NOT EXISTS (SELECT * FROM wood nx
                WHERE nx.stamp = w.stamp
                AND nx.arr @> w.arr AND nx.arr <> w.arr -- contains but not equal 
                )
        )
, xsets AS (    -- make unique sets of bikes
        SELECT DISTINCT arr
        -- , MIN(seq) AS grp
        FROM uniq
        GROUP BY arr
        )
, sets AS (     -- enumerate the sets of bikes
        SELECT arr
        , row_number() OVER () AS setnum
        FROM xsets
        )
, drag AS (             -- Detect beginning and end of segments of consecutive observations
        SELECT u.*      -- within a constant set of bike_ids
        -- Edge-detection begin of group
        , NOT EXISTS (SELECT * FROM uniq nx
                WHERE nx.arr = u.arr
                AND nx.stamp < u.stamp
                AND nx.stamp >= u.stamp - '5 sec'::interval
                ) AS is_first
        -- Edge-detection end of group
        , NOT EXISTS (SELECT * FROM uniq nx
                WHERE nx.arr = u.arr
                AND nx.stamp > u.stamp
                AND nx.stamp <= u.stamp + '5 sec'::interval
                ) AS is_last
        , row_number() OVER(ORDER BY arr,stamp) AS nseq
        FROM uniq u
        )
, top AS ( -- id and groupnum for the start of a group
        SELECT nseq
        , row_number() OVER () AS clust
        FROM drag
        WHERE is_first
        )
, bot AS ( -- id and groupnum for the end of a group
        SELECT nseq
        , row_number() OVER () AS clust
        FROM drag
        WHERE is_last
        )
SELECT w.seq as orgseq  -- results, please ...
        , w.stamp
        , g0.clust AS clust
        , row_number() OVER(www) AS rn
        , s.setnum, s.arr AS bike_set
        FROM drag w
        JOIN sets s ON s.arr = w.arr
        JOIN top g0 ON g0.nseq <= w.seq
        JOIN bot g1 ON g1.nseq >= w.seq AND g1.clust = g0.clust
        WINDOW www AS (PARTITION BY g1.clust ORDER BY w.stamp)
        ORDER BY g1.clust, w.stamp
        ;

:

 orgseq |        stamp        | clust | rn | setnum | bike_set 
--------+---------------------+-------+----+--------+----------
      1 | 2016-05-28 11:00:00 |     1 |  1 |      1 | {1,2}
      4 | 2016-05-28 11:00:20 |     3 |  1 |      1 | {1,2}
      5 | 2016-05-28 11:00:25 |     3 |  2 |      1 | {1,2}
      6 | 2016-05-28 11:00:05 |     4 |  1 |      3 | {1,2,3}
      7 | 2016-05-28 11:00:10 |     4 |  2 |      3 | {1,2,3}
      8 | 2016-05-28 11:00:10 |     4 |  3 |      2 | {4,5}
(6 rows)
+1

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