A Multidimensional Model for Correct Aggregation of Geographic Measures - Evolving Application Domains of Data Warehousing and Mining - page 170

Figure 4. Vertical aggregation of trees using average

Table 1. Roll-up on the time dimension

These two examples show that:

Year Phenomenon Aggregated Zone

1. aggregation process has to take into account

overlapping geometries and

1978 Fire Zone E

… … …

2. alphanumeric aggregation functions applied

to the descriptive attributes of geographic
measures depend on their semantics (∑:
measures that can be summed, ω : measures
that can be averaged, c: measures that can be
only counted), on used dimensions (as for
classical OLAP measures), and on spatial
function (as in geostatistic models). In other
words, additive measures cannot be added if
a spatial disaggregation function is used.

of Zone V1, Zone V2 and Zone V3. The number
of trees is the sum of the number of trees of Zone
V1, Zone V2 and Zone V3 (24= 10+8+6). Without
this approach, damaged trees for the Zone E will
be erroneously 32 as it is the union of Zone A and
Zone B and as the associated sum operation does
not consider that the damaged trees of the Zone 2
of A, Zone 1 of B are counted twice when aggre-
gating on the time dimension. Finally, the result
of the Roll-Up operator is shown in table 1.
Let us use another spatial function: intersec-
tion . In the OLAP context, intersection (Shekar
et al., 2001) is a spatial aggregation function, but
it should be better to considered it as a spatial
disaggregation function following the geostatis-
tic approach (c.f. Sec. “Geographic Data” and
“Geostatistic Models”).
In this case, the multidimensional query is:
“ Where and how many trees have been damaged
by all fires during 1978 ?” (Query 2). The number
of trees cannot be calculated using the sum of the
averages because it is not representative of the
number of trees in the intersected zone. Therefore,
instead of applying sum, we apply a weighted
average on the area (Figure 6). Consequently,
the number of trees of Zone E is the same than
the one of Zone V2 (8). Damages trees are not
counted twice.

Finally, the aggregation process of geographic
measures can be seen as a three-step process using
two alphanumeric aggregation functions (noted
φ and κ) for each alphanumeric attribute and a
spatial function (spatial aggregation or spatial
disaggregation) for the spatial attribute.
The three steps are:

Figure 5. Aggregation of park's zones on the time
dimension.