ST Data-warehouse for trajectories Some preliminary ideas S. - - PowerPoint PPT Presentation

ST Data-warehouse for trajectories

Some preliminary ideas

• S. Orlando, R. Orsini, A. Raffaetà, A. Roncato

Requirements and Starting points

 Trajectories arrive in streams, as triples

 (ID, SpatialPos, TemporalPos)  to insert information associated with them in our data warehouse, spatial and temporal dimensions must be discretized to fit our cube model  For example, we can think of considering two Spatial and one Temporal dimensions

 What are the main approaches present in the literature to deal with ST aggregates?  Which are the aggregates that we would like to compute

• n trajectories?

 Can ST aggregates in literature be applied to our case?

Main approaches in the literature

 I.F. Vega Lopez, R.T. Snodgrass, B. Moon. ST Aggregation Computation: A Survey. IEEE TKDE, 17:2, 2005

 Aggregates computed on partitions, obtained by grouping on attributes  Simple or sliding window aggregates  No moving objects



• Y. Tao, D. Papadias. Historical ST Aggregation, ACM TOIS,

23:1, 2005

 Main focus is on index data structures  Typical aggregates are distributive

 Faggr(S1 ∪ S2) = Faggr(S1) op Faggr(S2)  S1 ∩ S2 = ∅

 Partially consider moving objects

 Others?

The cube model: an example

The pollution density data: X t 5 4 3 X 5 4 3 5 3 4 4 4 t Dx Dt + in this ST area the pollution is 5; + in this ST area the pollution is 4; + in this ST area the pollution is 3;

Problems of space-driven structures

Discretization problems:

X t 5 4 t 4 4 4 4 4?5 4?5 5 5 X

Data-driven structures

Each region is the “original” rectangle

X t 5 4 t 5 4 X

R1

R2

Problems with data-driven structures

Intersectiong regions count twice??

X t 5 4 t 5 4 X 2 3 2 3

Partially overlapping query counts as a whole

The cube model for trajectories

The number of objects: X t X t Dx Dt 2 2 1 1 + a steady object (constant x); + a forward moving object (increasing x); + a backward moving object (decreasing x);

Problems of cube model

Discretization problems with trajectories :

X t t X A fast object is in 4 “places” at the same moment 1 1 1 1

Problems of cube model

Discretization problems with trajectories :

X t t X We don’t know what happens between the 2 points 1 1 ? ? Should we interpolate and how?

Different kinds of queries

 Queries computed by using only the given attributes  Queries computed by a pre-calculation which can involve more than one “close” subcubes (ST properties not explicitly given but computed)  Queries computed by considering the whole trajectory hence by using not only close subcubes  Not distributive queries

First kind of queries

 ST density of objects

 Number of objects in a fixed area and in a given time interval  Area and temporal intervals depend on the granularity of our cube

• To compute such aggregates
• We need only info related to the

presence/absence of objects in the given ST element

• Thus, we forget IDs and other spatio-temporal

information (speed, distance etc.)

Problems of cube model

Discretization problems with trajectories :

X t t X A fast object is in 4 “places” at the same moment 1 1 1 1

Second kind of queries

 Total distance or average distance  Number of objects moving towards East  Number of objects which change direction

Third kind of queries

 Number of objects which have covered a certain distance  Number of objects which are back to the starting point  Difference between the going and back

• The aggregation used to solve such a

kind of queries should be recomputed changing the parameter

Fourth kind of queries

 Shape of the average trajectory  Compute the median

Topological queries

With ID: enter, leave, cross, stay within, bypass X t Enter: before out; now in Leave: before in; now out Stay within: before and now in Cross: before out; now out; region touched Bypass: not touched

Left-in and Right-in

Without ID we can compute the following queries: left-in (passing the left borderline inward), right-in (passing the right borderline inward); left-out (passing the left borderline

• utward), right-out (passing the right borderline outward)

X t left-in = enter from left + cross from left left-in+right-in ≠ enter

How to compute left-in, right-in

Problems on computing in: 1) The aggregate is on left-in and right-in not directly on in; 2) The associative function to compute left-in (right-in) is a left projection (right projection) function: does the commercial products provide these functions? Let S and S’ be left-in S ∪ S’ = left(left-in S, left-in S’) = left-in S right-in S ∪ S’ = right(right-in S, rigth-in S’) = right-in S’ S S’

Cross (1)

Without ID we cannot compute: cross X t X t From aggregate data it is impossible to distinguish the two above cases (???)

Cross (2)

Cross cannot be computed from cube-cross X t X t 1 1 1 1 S cube-cross = 2 on shaded area, while cross = 0

Navigational queries

Considering derived information: speed (max, avg, min), heading, traveled distance, covered area. Are these computable from aggregates? Speed is of type 2; Heading is of type 3; Traveled distance is of type 2; Covered area is of type 3;