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ST_lcsDistance

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Calculates the dissimilarity between two trajectories using the Longest Common Subsequence (LCSS) algorithm. A lower return value indicates greater similarity between the two trajectories.

Syntax

float8 ST_lcsDistance(trajectory traj1, trajectory traj2, float8 dist, distanceUnit unit default 'M');
float8 ST_lcsDistance(trajectory traj1, trajectory traj2, float8 dist, interval lag, distanceUnit unit default 'M');

Parameters

ParameterTypeDescription
traj1trajectoryThe first trajectory.
traj2trajectoryThe second trajectory.
distfloat8The distance tolerance for matching a pair of trajectory points. Unit: meters.
lagintervalThe time tolerance for matching a pair of trajectory points. If omitted, only distance is used as the matching condition.
unitdistanceUnitThe unit for measuring distance. Default: 'M'. Valid values: 'M' (meters), 'KM' (kilometers), 'D' (degrees, valid only when the WGS84 (4326) spatial reference is used).

How it works

The function applies the LCSS algorithm to find the longest common subsequence between two trajectories. Two trajectory points are considered a match when both of the following conditions are met:

  • The spatial distance between the points is within the dist tolerance.

  • The time difference between the points is within the lag tolerance (when lag is specified).

The return value is calculated using the following formula:

1 - LCSS / min(leafcount(traj1), leafcount(traj2))

In the example above, three trajectory point pairs (1, 3, and 6) meet the matching conditions, so the LCSS value is 3. With min(leafcount(traj1), leafcount(traj2)) = 5, the return value is 1 - 3/5 = 0.4.

If a trajectory has no spatial reference identifier (SRID), the function uses WGS84 (SRID 4326) as the default.

Examples

All examples construct two trajectories using ST_makeTrajectory and compute their LCSS-based distance.

Example 1: Distance tolerance only

WITH traj AS (
    SELECT ST_makeTrajectory('STPOINT', 'LINESTRINGZ(114.000528 33.588163 54.87, 114.000535 33.588235 54.85, 114.000447 33.588272 54.69, 114.000348 33.588287 54.73, 114.000245 33.588305 55.26, 114.000153 33.588305 55.3)'::geometry,
                             ARRAY['2010-01-01 11:30'::timestamp, '2010-01-01 11:31', '2010-01-01 11:32', '2010-01-01 11:33', '2010-01-01 11:34', '2010-01-01 11:35'], NULL) a,
           ST_makeTrajectory('STPOINT', 'LINESTRINGZ(114.000529 33.588163 54.87, 114.000535 33.578235 54.85, 114.000447 33.578272 54.69, 114.000348 33.578287 54.73, 114.000245 33.578305 55.26, 114.000163 33.588305 55.3)'::geometry,
                             ARRAY['2010-01-01 11:29:58'::timestamp, '2010-01-01 11:31:02', '2010-01-01 11:33', '2010-01-01 11:33:09', '2010-01-01 11:34', '2010-01-01 11:34:30'], NULL) b)
SELECT ST_lcsDistance(a, b, 100) FROM traj;
--  st_lcsdistance
-- -------------------
--  0.666666666666667
--  (1 row)

Example 2: Distance and time tolerance

WITH traj AS (
    SELECT ST_makeTrajectory('STPOINT', 'LINESTRINGZ(114.000528 33.588163 54.87, 114.000535 33.588235 54.85, 114.000447 33.588272 54.69, 114.000348 33.588287 54.73, 114.000245 33.588305 55.26, 114.000153 33.588305 55.3)'::geometry,
                             ARRAY['2010-01-01 11:30'::timestamp, '2010-01-01 11:31', '2010-01-01 11:32', '2010-01-01 11:33', '2010-01-01 11:34', '2010-01-01 11:35'], NULL) a,
           ST_makeTrajectory('STPOINT', 'LINESTRINGZ(114.000529 33.588163 54.87, 114.000535 33.578235 54.85, 114.000447 33.578272 54.69, 114.000348 33.578287 54.73, 114.000245 33.578305 55.26, 114.000163 33.588305 55.3)'::geometry,
                             ARRAY['2010-01-01 11:29:58'::timestamp, '2010-01-01 11:31:02', '2010-01-01 11:33', '2010-01-01 11:34:15', '2010-01-01 11:34:50', '2010-01-01 11:34:30'], NULL) b)
SELECT ST_lcsDistance(a, b, 100, interval '30 seconds') FROM traj;
--  st_lcsdistance
-- -------------------
--  0.666666666666667
--  (1 row)

Example 3: Distance tolerance, time tolerance, and explicit unit

WITH traj AS (
    SELECT ST_makeTrajectory('STPOINT', 'LINESTRINGZ(114.000528 33.588163 54.87, 114.000535 33.588235 54.85, 114.000447 33.588272 54.69, 114.000348 33.588287 54.73, 114.000245 33.588305 55.26, 114.000153 33.588305 55.3)'::geometry,
                             ARRAY['2010-01-01 11:30'::timestamp, '2010-01-01 11:31', '2010-01-01 11:32', '2010-01-01 11:33', '2010-01-01 11:34', '2010-01-01 11:35'], NULL) a,
           ST_makeTrajectory('STPOINT', 'LINESTRINGZ(114.000529 33.588163 54.87, 114.000535 33.578235 54.85, 114.000447 33.578272 54.69, 114.000348 33.578287 54.73, 114.000245 33.578305 55.26, 114.000163 33.588305 55.3)'::geometry,
                             ARRAY['2010-01-01 11:29:58'::timestamp, '2010-01-01 11:31:02', '2010-01-01 11:33', '2010-01-01 11:34:15', '2010-01-01 11:34:50', '2010-01-01 11:34:30'], NULL) b)
SELECT ST_lcsDistance(a, b, 100, interval '30 seconds', 'M') FROM traj;
--  st_lcsdistance
-- -------------------
--  0.666666666666667
--  (1 row)

What's next

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