r - 在 R 或 PostgreSQL 中形成时空接近轨迹组

Question

我正在使用 R 和 PostgreSQL 进行一些轨迹分析。为了形成连续位置在时空上接近的轨迹段组，我创建了下表。我仍然缺少的是 group_id 列，这就是我的问题所在。

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

这是每个轨迹与其他轨迹(所有没有重复的组合)和 datetime 上的内部连接(始终以 5 秒的倍数采样)之间的多重比较的结果。它表明，对于某些位置，自行车 1 和 2 是同时采样的，并且在空间上很接近(某个任意阈值)。

现在我想为两辆自行车在时空上接近的路段提供唯一 ID (group_id)。 这就是我卡住的地方:我希望 group_id 尊重具有多个轨迹的组。分配 group_id 的方法应该意识到，如果自行车 1 和 2 在 2016-05-28 11:00:05 属于一个组，那么 3 属于同一组如果在同一时间戳(2016-05-28 11:00:05)接近 2，则分组。

R 或 PostgreSQL 中是否有可以帮助我完成此任务的工具？在表中运行一个循环似乎是解决此问题的错误方法。

编辑:正如@wildplasser 指出的那样，这似乎是一个传统上使用 SQL 解决的差距和孤岛问题。他亲切地提供了一些示例数据，我稍微扩展了这些数据并将包含在问题中。

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)
        ;

Answer 1

更新:[理解真正的问题后 ;-] 找到自行车的等价组(set，bike_set)实际上是一个关系除法问题。在一组自行车中查找段(clust)的开始和结束与第一次尝试基本相同。

• 集群存储在数组中:(我相信集群不会变得太大)
• 该数组是通过递归查询构建的:将与当前集群有一个共同成员的每对自行车合并到其中。
• 最后，数组包含在特定时间恰好在可达范围内的所有 bike_id。
• (加上一些稍后需要被 uniq CTE 抑制的中间行)
• 剩下的就是时间序列中或多或少的标准间隙检测。

注意:代码信任 (bike2 > bike1)。这是保持数组排序并因此规范化所必需的。不能保证实际内容是规范的，因为无法保证递归查询中的添加顺序。这可能需要一些额外的工作。

---

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
        ;

---

结果:

---

 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)