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  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  F aggr (S 1 ∪ S 2 ) = F aggr (S 1 ) op F aggr (S 2 )  S 1 ∩ S 2 = ∅  Partially consider moving objects  Others? 

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

Problems of space-driven structures Discretization problems: t t 4 4 5 4?5 5 4 5 4?5 4 4 X X

Data-driven structures Each region is the “original” rectangle t t R 1 R 2 5 5 4 4 X X

Problems with data-driven structures Intersectiong regions count twice?? t t 2 3 2 3 5 4 5 4 X X Partially overlapping query counts as a whole

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

Problems of cube model Discretization problems with trajectories : t t 1 1 1 1 X X A fast object is in 4 “places” at the same moment

Problems of cube model Discretization problems with trajectories : t t 1 ? ? 1 X X We don’t know what happens between the 2 points 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 : t t 1 1 1 1 X X A fast object is in 4 “places” at the same moment

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 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 X

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

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 S S’ 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’

Cross (1) Without ID we cannot compute: cross t t X X From aggregate data it is impossible to distinguish the two above cases (???)

Cross (2) Cross cannot be computed from cube-cross t t 1 1 1 1 S X X 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;