Trajectory Data Warehouses - Mobility Data - page 74

Elevation f( )

Episode

LandUse f( )

route m( )
distance
duration
avgSpeed
riskLevel

Tempe-
rature

f( ,)

Precipi-
tation

f( ,)

Figure 4.4 Extending our running example with continuous fields.

speed of trajectories and elevation (or slope), and the latter to select trajectories
starting in a residential area and finishing on an industrial area. Further, there are
two time-dependent fields, Temperature and Precipitation . In addition,
numerical measures can be calculated from field data. An example is given
by measure riskLevel , which represents knowledge from domain experts
about the relative risk of the episodes. Such a measure (e.g., a real value) can
be computed from the measure route and the four fields. For example, an
episode with high speed in descending slopes, in residential areas, with frozen
temperatures, or with high precipitation will have high a risk level.
To be able to express OLAP queries involving fields, we define field types ,
which capture the variation in space of base types. They are obtained by applying
a constructor field ( ). Hence, a value of type field ( real ) (e.g., represent-

ing altitude) is a continuous function f : point → real . Field types have
associated operations, which are analogous to those defined for time-dependent
types in Chapter 3 . In particular, field types have lifted operations that generalize
those of the base types. Their semantics is such that the result is computed at
each point in space using the nonlifted operation. Aggregation operators are also
lifted. For instance, a lifted avg operator combines several fields, yielding a
new field where the average is computed at each point in space. In addition,
field aggregation operators compute a scalar value from all the values taken by a
field. For example, operator favg can be used to obtain the average value from
a field describing altitude.
Time-dependent fields are obtained by composing the moving and field
type constructors. For example, a value of type moving ( field ( real )), which
defines a function f : instant → ( point → real ), can be used to repre-
sent temperature, which varies on time and space. In our model the types
moving ( field ( real )) and field ( moving ( real )) are equivalent, that is, they
define a spatio-temporal cube that associates a real value to each point in the
cube. All operations defined for time-dependent types in Chapter 3 apply for

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