A New Relational Spatial OLAP Approach for Multi-resolution
and Spatio-multidimensional Analysis of Incomplete Field Data
Mehdi Zaamoune
1
, Sandro Bimonte
1
, François Pinet
1
and Philippe Beaune
2
1
IRSTEA, TSCF, 24 Av. des Landais, Aubière, France
2
Agaetis, 10 allée Evariste Galois, 63 000 Clermont-Ferrand, France
Keywords: Spatial OLAP, Incomplete Continuous Field, Multi-resolution Geographic Data.
Abstract: Integrating continuous spatial data into SOLAP systems is a new research challenge. Moreover,
representation of field data at different scales or resolutions is often mandatory for an effective analysis.
Thus, in this paper, we propose a logical model to integrate spatial dimensions representing incomplete field
data at different resolutions in a classical SOLAP architecture.
1 INTRODUCTION
Spatial Data Warehouse (SDW) and Spatial OLAP
(SOLAP) systems play an important role in helping
decision-makers obtain the maximum benefits of
these large amounts of geographic data (Bédard et
al., 2001). These technologies extend Data
Warehouse (DW) and OLAP systems to integrate
spatial data with warehoused classical data to
achieve the on-line analysis of large georeferenced
data sets. SOLAP systems integrate advanced OLAP
and Geographic Information Systems (GIS) in a
unique framework usually based on the relational
storage (i.e. Oracle, etc.) of spatial data according to
the vector model, and their analysis through SOLAP
operators (Spatial Roll-Up, Spatial Slice, etc.)
implemented by the SOLAP server (e.g.
Map4Decision, etc.) and visualized by means of
tabular, graphical and cartographic displays (Gomez
et al., 2012). SDW are modeled according to the
spatio-multidimensional model that extends the
traditional multidimensional model to define spatial
dimensions (i.e. analysis axes with spatial attributes)
and spatial measures (i.e. analysis subjects) that
integrate geographic information using the vector
model (Bédard et al., 2007). SOLAP technology can
be applied in different domains (e.g. archeology,
public health, etc.).
Geographic information can be represented by
two models, depending on the nature of data:
discrete (vector) and continuous field (Mennis et al.,
2005). Continuous fields (also called continuous
spatial data) represent physical phenomena that
continuously change in space (Paolino et al., 2010),
for example the temperature, population, etc. Two
representations of field data have been proposed:
incomplete and complete (Paolino et al., 2010).
Incomplete representations store a sample of points
and need additional functions to calculate the field in
non-sampled areas (e.g. grid of points, TIN, etc.)
(e.g. Figure 2). Complete representations associate
estimated values to regions and assume that these
values are valid for each point in the regions (e.g.
raster). For those representations some ad-hoc
analysis operators have been defined that allow a
point by point analysis (i.e. map algebra (Mennis et
al., 2005)). Representation of geographic data at
different scales or resolutions (e.g. Figure 2-b) is
mandatory for an effective analysis of spatial
complex phenomena since it represents a
geovisualization method (Camossi et al., 2009).
Consequently, these resolutions or scales represent
decision-makers analysis needs that should be
explicitly represented in any data and query model.
Indeed, in the context of Geographic Information
Systems and Spatial Databases Management
Systems (SDBSM), several works addresses this
issue by proposing conceptual, logical and physical
data models and analysis techniques (Parent et al.,
2006).
Motivated by the important analysis capabilities
offered by the continuous field representation of
geographic data when integrated in SOLAP systems
(visualization, querying, etc.) recently some works
investigated the extension of the spatio-
145
Zaamoune M., Bimonte S., Pinet F. and Beaune P..
A New Relational Spatial OLAP Approach for Multi-resolution and Spatio-multidimensional Analysis of Incomplete Field Data.
DOI: 10.5220/0004434501450152
In Proceedings of the 15th International Conference on Enterprise Information Systems (ICEIS-2013), pages 145-152
ISBN: 978-989-8565-59-4
Copyright
c
2013 SCITEPRESS (Science and Technology Publications, Lda.)
multidimensional model and SOLAP operators with
complete and incomplete field data (cf. Section 6).
In the same way, handling multi-resolutions of
spatial data into spatial multidimensional models has
been proposed in few works (Yvan et al., 2002)
(Gascueña and Guadalupe 2009) that propose
conceptual models to represent SDW with several
representations (scales, resolutions, etc.) of spatial
dimensions and measures.
However, to best of our knowledge existing
works concerning field data and multi-resolutions
lack of a complete implementation in a full-featured
SOLAP architecture, or in other terms they do not
propose a coupled relational and SOLAP server
model for a generic SOLAP architecture allowing (i)
the map algebra operators, (ii) the multi-resolution,
and (iii) a continuous view of the field.
In order to handle the spatio-multidimensional
analysis of incomplete regular grid field data at
different resolutions, we propose in this paper: (i) a
specific logical model, extending the well-know
relational star schema; (ii) and some new MDX-
based defined functions. We validate our proposal
using a real case study concerning the odor
monitoring, and we provide some experiments
showing the feasibility also in terms of storage and
computation performances.
2 MODELING AND ANALYSIS
REQUIREMENTS
In order to show our proposal, we present a case
study based on data issued from the monitoring of
urban odor. For each 15 minutes and type of odor
(e.g. NO2) a regular grid map (field) is produced by
means of some sample points and a simulation
model (ADMS5) . The simulation model estimates
odors for a whole urban area and produces 100*100
thematic grids. Examples of points grid are provided
in figure 2-a (odor values are represented by color:
green, yellow, red) for 10:00 19-2-2012 and 10:15
19-2-2012. Let us now suppose that the user wants
to aggregate data along a temporal dimension (year,
month, day, hour, minute) using the average to
obtain an aggregated odor map. This is an OLAP
operation of RollUp on the temporal dimension that
corresponds to a local map algebra operation (Figure
2-a
).Moreover, since space is represented in a
continuous way, decision-makers should be able to
ask for the result of any OLAP query in any point of
the spatial dimension (for example, s/he should be
interested in the odor value at 10:00 in the area
behind the building) (Figure 2-c). It is also possible
to apply a spatial slice operator on the spatial
dimension (i.e. using a spatial predicate to select a
subset of warehoused data) (Figure 2-d). In order to
answer to these last two queries spatial interpolation
methods are necessary, since in incomplete field
only the values provided by the simulation model
are stored. Spatial interpolation is the process of
prediction of almost exact values of attributes at
unsampled locations from measurements made at
control points within the same area (O'Sullivan and
Unwin, 2002). In our case the interpolation function
used is the bilinear interpolation, which is a local
deterministic method. It uses the 2 * 2 grid sample
points closest to the unknown point and calculates a
distance weighted average which determines in what
proportion the value of a neighbour impact on the
value of the point to be estimated (Figure 1).
Finally, as stated in the previous section, since
visualization of spatial data at different resolutions is
mandatory for the exploration/analysis process,
decision-makers should be able querying spatial
warehoused data at different resolutions. It is very
important to note that for each spatial phenomenon a
set of useful known resolutions exist, so they could
be predefined according to data and users needs.
Moreover, in order to calculate values at finer
resolutions spatial interpolation functions as
previously described can be used.
To summarize, spatio-multidimensional analysis
of field data implies: supporting (i) OLAP classical
operators as Map Algebra, (ii) continuous view of
spatial data, (iii) spatial slice operators using field
data, and (iv) visualizing and querying data at
different predefined resolutions.
3 SPATIO-MULTIDIMENSIONAL
MODEL FOR INCOMPLETE
FIELD DATA
In this section we describe our spatio-
multidimensional model for handling incomplete
fields at different resolutions. Our model extends the
classical spatio-multidimensional models to generate
the continuity of the phenomena over the studied
area, and represents pre-defined levels of resolution.
In particular, a “Cube” is composed of “Facts”
and “Dimensions”. A “Dimension” is composed of
“Hierarchies”, which are composed of “Levels”. A
“Level” can be spatial or conventional. This means
that it can contain “Spatial attributes” (e.g. points,
etc.), or contain only alphanumerical attributes
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respectively. “Facts” is composed of “Spatial
Measures” or “Conventional Measures”. Moreover,
our extension defines a “Field level” as a special
type of spatial level where each member has a
geometric attribute (e.g. point), a “neighbourhood
relationship” association, and a resolution level to
which it belongs.
(a)
(b)
(c) (d)
Figure 2: a) Local map algebra aggregation over
incomplete field. b) Multiresolution representation over
incomplete field c) Querying an unsampled point d)
Querying an unsampled zone.
Indeed, as described in the previous section a
spatial interpolation function uses a set of points,
which depend on the function (e.g. bilinear function
uses a 2*2 grid), to estimate the unknown value.
Thus, in our approach values are represented by
measures, the “Neighbourhood relation” links each
detailed "Field level" to its neighbours in the less
detailed level. As soon as the value of a high
resolution "Field level" is required its neighbours are
found through the “Neighbourhood relation”.
However, this type of relationship can be
implemented in different ways, depending on the
intended purpose as shown in the next section. In
our case, we want to estimate the value of any point
(x, y) of a Field level, so neighbours are found on
the fly by the relation "Neighbourhood relation". In
the case of a change in the level of resolution, the
members of a high resolution (e.g. 200*200), are
predefined and therefore, their respective
neighbours, which belongs to the resolution
100*100, can be pre-stored as attributes.
As described in the model, a hierarchy can
contain several field levels representing the
phenomena at different resolutions. This means that
changing resolutions implies navigating into the
hierarchy and calculating values by means of the
interpolation function or an ad-hoc aggregation
function when we move from less detailed resolution
to more detailed one, or vice versa.
The odor SDW of our case study using our
spatio-multidimensional model is shown in Figure 3.
This instance describes the dimensions and facts
that constitute our cube.
In addition to the dimensions (Source, Tracer and
Time), the "Facts" class has a classical measure
“odorMeasure” and a derived measure
“EstimatedOdorMeasure”. The derived measure is
calculated according to two functions:
a) Interpolatepoint”(continuity).
b) "InterpolateBilinear" (multiresolution).
In our case, the interpolation function used is the
"bilinear interpolation". The relationship whose
cardinalities are "2, 4" represents the
“Neighbourhood relation”. A member of the
"Incomplete Field Level" can have 2 or 4
neighbours, depending on its position in the grid 2*2
that surrounds it. The “Neighbourhood relation” can
be used to retrieve neighbours of a location (x,y) to
estimate the value in that position (continuity), or to
retrieve a high resolution member’s neighbours in
the lower level of resolution to estimate its value
(multiresolution on the fly).
4 RELATIONAL AND OLAP
MODELS
In this section we present the implementation of our
spatio-multidimensional model in a typical relational
SOLAP architecture based on SQL (the Relational
DBMS standard language) and MDX, which is the
de-facto standard of OLAP Servers. This provides a
generality character to our approach, being possible
to be implemented in any architecture of this kind.
Let us suppose to have one “Field level”
representing points at the resolution 100*100, and
then the logical model of our case study is
represented as in fig. 4. It is a classical star schema.
This model is composed of a fact table containing
measures with foreign keys to dimension tables.
Each dimension table is denormalized, and has
attributes representing levels.
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Figure 3: Odor SDW multi-dimensional model.
Let us also suppose to have a classical OLAP
model based on that logical schema, where the
spatial level is called
[Field].[res100]. As we
can see, the dimensions that constitute the model
are: the temporal dimension, which consists of five
levels of granularity (Year, month, day, hour and
minute); the Source dimension that expresses the
source of the pollutant (e.g. cars); the Tracer
dimension is the type of pollutant (eg NO2), which
is also defined by its identifier and name; and the
“Field dimension” that represent a regular grid of
points and consists of one level representing the
regular grid at the 100*100 resolution, which is
composed of an identifier and a geometry
representing a point. The measure «Concentration of
odor» represents the values for all members
representing the field at a 100*100 resolution. This
representation of incomplete field data in the
multidimensional model allows making queries as
Map Algebra operators (point by point aggregation)
such as the following:
Query 1: Select average odor for each field member
during 2012.
SELECT [Field].[res100]. Members ON
ROWS, {[time].[2012]} ON COLUMNS
FROM [odorCube] WHERE
[Measures].[value]
4.1 Incomplete Field
In order to implement field levels we have defined a
GeoMDX user-defined function that represents a
spatial interpolation as:
NumericType InterpolatePoint(Geometry)
This function takes as input a geometry (point) and
returns a numerical value, which is a derived
measure in the OLAP model, representing an
estimated value calculated using the neighbourhood
values of the point given in input. Thus, let us
suppose that we want to retrieve a value of the field
in a location whose geometric property is set to the
geometric coordinates POINT(-72.1235 42.3521).
Then in order to answer to that need using the
Bilinear interpolation function, decision-makers
have to simply use a GeoMDX function in the
following way:
InterpolatePoint(POINT(-
72.1235 42.3521)).
Thus, the function will look for the neighbours of
the point given as a parameter, in the field level
([Field].[res100]), on the basis of the distance, and
then find neighbours’ respective values in the fact
table, evaluate the value of the point to estimate
using these values, and then return an estimated
derived measure. Here is an example query that uses
the "InterpolatePoint" function:
Query 2: Select a field member’s value at
coordinates (721148 3140020) for the year 2012.
With member [Measures].[value] as'
InterpolatePoint(ST_GeomFromText("
POINT (721148 3140020)"))'
SELECT [Measures].[value]ON ROWS,
[time].[2012] ON COLUMNS
FROM [odorCube]
Note that generally MDX allows defining user-
defined functions in several programming languages
(i.e. Java, .NET, etc.) depending of the OLAP Server
used. In this work we have used a Java-based
implementation in GeoMondrian (see Sec. 5). In the
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interpolation is done using an existing interpolation
Java API “javax.media.jai api” (JAI).
Figure 4: Classical star schema integrating regular grid of
points.
In this way we achieve the continuous view of
field data using incomplete fields as stated in
Section 2.
4.2 Multiresolution
Theoretically, we can measure a value of a field at
every position inside a geographic space. However,
not all resolutions are necessarily relevant. Indeed,
according to the type of analysis performed by the
user, a more or less detailed resolution can be
requested. The multiresolution is an approach that
consists in defining resolution levels likely to
improve the rendering of the requests made by the
user. To model an incomplete field at several
resolutions in a multi-dimensional model, we
propose two Approaches based on the “Classical
Star Schema”: The “field aggregation star-schema”
approach and the “field interpolation star schema”
approach.
4.2.1 Field Aggregation Star-schema
Approach
Based on the star schema model previously
described, we propose a logical schema where the
spatial dimension presents different field levels at
different resolutions (fig. 5-a). This model extends
the spatial dimension of figure 4
with 2 other levels
each representing a different level of resolution
(
[Field].[res200] and [Field].[res400]).
Each level of the field dimension is composed of an
identifier and a geometry representing a point.
The
fact table is associated, classically, to the most
detailed level of the field dimension.
In this way, decision-maker can explore
warehoused field data at different resolutions during
the same analysis MDX-based session. Only need to
change the level of resolution in the query to change
the level of details of the result. Using this approach,
we use in an MDX query, the appropriate level of
resolution of the field dimension as in the following
where the Query 1 becomes:
Query 3: Select average odor for each field member
at the 400*400 resolution during 2012.
SELECT [Field].[res400]. Members ON
ROWS, {[time].[2012]} ON COLUMNSFROM
[odorCube]
WHERE [Measures].[value]
4.2.2 Field Interpolation Star-schema
Approach
As stated in Section 2, in order to provide field data
at finer resolutions, spatial interpolation methods can
be used. Then, here we propose a variation of the
previously proposed schema for handling multiple
field resolution levels, by associating the fact table
to the field at less detailed resolution as shown on
figure 5-b. In our approach moving from fact table
values to finer spatial members’ values implies
applying spatial interpolation functions. Note that
this approach is possible only when dealing with
spatial data, because according to the Tobler law
geographical position of data can be used for
estimating missing values.
We have implemented a GeoMDX function in
the same way of the function defined in Section 4.1:
Numeric-type InterpolateBilinear (Field
Member)
However, this function, named "InterpolateBilinear"
is prepared to receive as input a field level member
instead of geometry and return an interpolated value
of this member. We can also see that in this case, the
neighbors of each member of a higher resolution
than the original one are also stored in the “Field”
(Neighbours2, Neighbours3), since members of each
resolution are pre-defined in advance, but their
values are not since they depend on other
dimensions.
Calling this function as follows:
InterpolateBilinear
([Field].[res400].CurrentMember) in the
formula of a derived measure, allows to find the
values of all the members of the level “res400”
(incomplete field at a 400*400 resolution) using
their neighbors “Neighbors3” . Thus, the query 3 can
be performed as follows:
SELECT
{[Field].[res400].Members} ON ROWS,
{[time].[2012]} ON COLUMNS
FROM [odorCube]
Where [Measures].[EstimatedValue]
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(a) (b)
Figure 5: (a) Field Aggregation Star Schema (FASS), (b) Field Interpolation Star Schema (FISS).
While in the multidimensional SOLAP schema,
the "InterpolateBilinear" function is called in the
“EstimatedValue” calculated measure formula as:
formula="InterpolateBilinear([Field].
[res400].CurrentMember)"
As we can see in the previous query, the call of the
calculated measure enables to find the values at a
given scale transparently to the decision maker as a
classical aggregation (SQL). This approach is
motivated by performance issues as described in the
next section.
5 EXPERIMENTATIONS
In this section we detail the performances of the two
approaches proposed in Section 4.2 (FASS and
FISS) in terms of storage and time computation.
The computer used for the following tests has the
following configuration: processor Intel® core ™ i3
2,20 GHz, RAM 4 Go, Operating system Windows 7
professional, System OS 64 bits.
In particular, spatial data is stored in PostGIS
Spatial DBMS. PostGIS is an open source software
that adds support for geographic objects to
the PostgreSQL object-relational database. PostGIS
follows the Simple Features for SQL specification
from the Open Geospatial Consortium (OGC); we
use GeoMondrian as a SOLAP server; and JPivot as
a client. GeoMondrian is an Open Source Spatial
Online Analytical Processing Server.
In order to test our proposal we define different
cases where the spatial dimension presents: one field
level at the 100*100 resolution; two levels at the
resolutions 100*100 and 200*200; and finally three
levels at the resolutions 100*100, 200*200 and
400*400. We also vary the size of the temporal
dimension in order to understand impact of the
spatial and non spatial dimension on performances.
Figure 6-a shows the size of the fact table
measured in function of the number of spatial and
temporal members (spatial finest resolution /
temporal finest granularity) using the two
approaches. We can easily see two important
differences: i) the field aggregation approach is
expensive in terms of storage than the field
interpolation one since the latter stores only facts
values at a less detailed spatial granularity, ii) in the
field interpolation approach the size of the fact table
only varies depending on the size of the non spatial
dimensions. Thus, even increasing the size of the
spatial dimension, the fact table does not change
since it contains only measures related to the first
level of resolution.
In order to evaluate computation performance we
execute the queries previously cited, where we
combine roll-up operation on non spatial
dimensions, and spatial slice operators over different
field resolutions.
Figure 6-b represents the execution time of the
query 3, which consists in generating values of the
members at different resolutions taking into account
different sizes of the time dimension. This figure
shows a certain degree of approximation in
execution time between the two approaches to a
certain level. Beyond this level, we note that the gap
widens considerably. Thus, minimizing storage and
relations has allowed the field interpolation
approach we propose to have better execution time
than the field aggregation approach at all resolution
levels (100*100, 200*200 and 400*400). Figure 9
shows that the execution time in the “field
approach” increases depending on the number of
spatial and temporal members, whereas in the “field
interpolation approach”, it increases mainly
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(a) (b)
Figure 6: a) Fact table size with the field aggregation and the field interpolation approaches b) Execution time for Query 3
for the Field aggregation Star Schema and the Field Interpolation Star Schema approaches.
of temporal members. Indeed the size of the spatial
dimension does not influence much on performance, since
there is no relationship between the fact table and the
members who belong to high resolutions.
6 RELATED WORK
In order to integrate fields data in a SOLAP model,
(Ahmed and Miquel, 2005) propose a
multidimensional model for handling continuous
discrete fields, storing a sample of points as spatial
members, to create a discrete cube which is
interpolated in the client-side to simulate a
continuity. (McHugh, 2008) defines new types of
dimensions handling fields as a regular grid of
squares (raster): “hybrid dimension”, “mixed hybrid
dimension”, “mixed matrix dimension” and
“geometric matrix dimension”. She also defines the
“matrix cube” where facts are cells of the matrix
grid. The “field aggregation approach” presented in
section 4.2.1 is based on this work. However, the
“field interpolation approach” we propose, although
it gives the same result, it is more efficient in terms
of storage and execution time. (Gomez et al., 2012)
presents a discrete data model for representing
continuous fields and an algebra that makes use of
OLAP operators (e.g. Dice, Slice, Roll-up, Drill-
down …). However, the discrete model the authors
propose does not support the continuous aspect of
the field, which consists to retrieve a value for each
point with coordinates x and y in the map. In
(Gomez et al., 2010), the authors propose a
multidimensional model handling fields. They
define two types of fields, “field” and “tempfield”
(spatial field and temporal field), and semantics for
the operators associated to these data types. They
include the notion of field dimensions and field
measures. They define the “field dimension” as a
dimension containing at least one level that is a field
(temperature, precipitation…), the “field measure”
as a measure represented by a field and the “field
hierarchy” as a set of related field levels, which
allows a field to be seen at different levels of
granularity. They also propose a physical model for
data warehouses with continuous fields. However,
no implementation has been proposed and the
hierarchical relationship between field levels has not
been brought to light. (Bimonte and Myoung, 2011)
provide a multidimensional model that integrates
field data independently from their implementation,
as measures and dimensions. They also present a
formal representation of the spatio-multidimensional
model schema where they define the concepts of
field dimensions, field measures, and field views. To
our knowledge, no implementation including the
continuous appearance of incomplete field or the
multiresolution over incomplete fields has been
proposed.
Representation of multidimensional data under
different resolution levels or scales may be
considered as multirepresentation. (Bernier et al.,
2005) proposes an approach to provide on-Demand
multi-scale maps. Although this approach models
maps features at different scales by using spatial
hierarchies, but it does not contain measures. (Yvan
et al., 2002) defines a UML-based conceptual model
that integrates multiple geometric and semantic
representations properties of spatial levels. However,
this work does not present a complete
multidimensional model with facts and hierarchies.
Moreover, (Bédard et al., 2002) suggests
(without providing details) using a different spatial
data warehouse for each representation. Therefore,
changing the representation corresponds to move to
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another spatial data warehouse. (Gascueña and
Guadalupe 2009) propose a conceptual model with a
multi-representation of spatial members. They also
propose a physical schema, but any implementation
into a classical ROLAP architecture is presented.
Finally, (McGuire et al., 2008)define a snowflake
schema for an environmental application where
three dimensions represent the same spatial
members at different resolutions.
7 CONCLUSIONS AND FUTURE
WORK
In this paper we present a multidimensional model
for incomplete fields at several resolutions and its
implementation in a SOLAP architecture based on
standards (e.g. SQL and MDX). We are working on
using spatial data mining to speed-up map algebra
operations and implement a SOLAP visualization
client. We also work in integrating other
interpolation functions to generalize the proposed
approach.
ACKNOWLEDGEMENTS
The authors wish to thank the FEDER and the region
for funding this project and project partners who
provide us the data.
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