Geoscience Reference

In-Depth Information

List of

id
TF

Cumulated binary

frequency (TF//tile)

Cumulated proportional frequency

(TF//tile)

id
t

T
1

[]

0

0

T
2

[TF
#6
]

1

0.21

T
3
[TF
#2
; TF
#6
]

2

1.08

T
4
[TF
#3
; TF
#6
]

2

1.98

...

Table 3.1. Example of a temporal tile-based index -

taken and then adapted from [PAL 10d]

These indexing strategies allow us to propose several indexes based on spatial and

calendar tilings: spatial indexes whose segmentations are of district, city, township,

county,region,countrylevelandaswellascalendarindexeswhosesegmentationsare

of day, week, month, season, year and century level. In a GIR context, these indexes

thenallowasearchenginetobrowsetheindexmostadaptedtothespatialandcalendar

range of the query.

3.4.1.2. Standardization by tiling: formalization of the approach

This type of standardization consists of using a tiling to describe the spatial or

temporal representations stored in the first-level indexes generated by the PIV

process flows. This approach is a form of discretization, for example it associates a

temporal object of the calendar domain with a temporal tile corresponding to a

particular segmentation of the same space.

In a more formal way (equation [3.1]), a domain T included in the space R
n

corresponds to the domain
1
O included in the space R
n
2
. The domain O is composed

of a set of objects O
1
,...,O
p
(the features of the first-level index), and the domain

T is composed of the union of m subspaces (the tiles of the standardized index). For

each subspace (T
i
) of T in intersection with one or more objects (O
j
) of O, we retain

the number of intersections (N
T
i
).

O ⊆ R
n
−→ T ⊆ R
n

O = { O
1
,O
2
,O
3
,...,O
p
}

T=
i=1
T
i

N
T
i
= Card({T
i
| T
i
∩ O
j
= ∅,∀j =1,...,p})

with Card(x)the cardinality of x

[3.1]

1 Adomainisafiniteorinfinitesetofvalues.Itisrepresentedbyalistofelementsoranecessary

andsufficientconditionofbelonging-thedomainofBooleans: {0,1},thedomainofthefingers

of the hand: {thumb, index finger, middle finger, ring finger, pinky}, the calendar domain.

2 This superset refers to spaces of dimension 1, 2 or more.

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