ST Data-warehousefor 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 on 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

44t

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

44

4?5

4?5

5

5

X

Data-driven structures

Each region is the “original” rectangle

X

t

54

t

54

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

XWe 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 inLeave: before in; now outStay within: before and now inCross: before out; now out; region touchedBypass: 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 outward), 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 Sright-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;