The Conceptual Design on Spatial Data Cube Zou Yijiang

The Faculty of Architectural Civil Engineering And Environment Ningbo University Ningbo China zyj_w@sina.com

Abstract—This paper states the purpose and significance to research spatial data cube, and explains relationship between with spatial data cube and spatial data warehouse, and introduces the concept and structure of nonspatial dimensionspatial dimension digital measure and spatial measure, and designs conceptual model for spatial data cube, i.e. extended star/sonwflake model. At last, based on mathematical tool ----algebraic system, this paper gives algebraic definition of spatial data cube.

Keywords-Spatial data cube; Dimension; Measure;

.INSTRUCTION According to statistics, 75% to 80% information has a

relation to geospatial information in world. If geospatial information can be treated as frame of carrying other information for executing multi-dimension geospatial analysis, function of spatial decision-making will become more powerful and more practicality. However, it is no high efficiency and convenient method for now GIS to execute geospatial analysis based on multi-dimension information structure. It is main restrict factor to have GIS apply in other domain.

A software technology that is called OLAP is rising in recent years. OLAP core is technology of data cube. Multi-dimension information from different domains in multi-dimension information structure is organized to spatial data cube according dimension mode. Object is described by three or more dimensions that are vertical each other. The result of object is happened on crossing of multi-dimensions. The combination body between GIS and data cube is called spatial data cube (for short SDC) that is research hot spot in GIS domain[1].

.BASIC CONCEPT A. Dimension

Dimension is a method that people observe object. For example, land department pays attention to information that land occurs change with time, they observe land information from time direction, so time is a dimension. Land department concerns information that land occurs change with region, they observe land information from region direction, so region is a dimension. Land department concerns information that land acreage occurs change with land time and region. Hence, land is called nonspatial dimension, time is called nonspatial dimension, and region

is called spatial dimension or nonspatial dimension. The size and change of land acreage is determined by land dimension time dimension and region dimension that make up of land SDC.

Dimension structure is divided into dimension hierarchy and dimension member. For more describing theirs, two methods that are called frame and tree are asked to express dimension structure[2]. 1) nonspatial dimension

Nonspatial dimension is merely a dimension that contains nonspatial data. In SDC, category of thematic data associated with DLG is regarded as nonspatial dimension such as weather condition economic structure national culture communication equipment science and educationmedical treatment and so on. Hence, it is possible for SDC to have many nonspatial dimensions. The world of nonspatial dimensions in SDC is composed of (nonspatial dimension1, nonspatial dimension2,……, nonspatial dimensionn). Thereinto, n is integer.

conceptual hierarchy of nonspatial dimension There is a lot of different hierarchical detail in

nonspatial dimension. The hierarchical detail is called conceptual hierarchy of nonspatial dimension. It describes detail information of nonspatial dimension. For example, time dimension can be described by hierarchical frame of year month day week hour minute and second. It is conceptual hierarchy of time dimension for year monthday week hour minute and second. In fact, conceptual hierarchy of nonspatial dimension is classified according to real meaning of nonspatial dimension. From tree representation of dimension, there are many hierarchies in nonspatial dimension such as year month and day.

lattice of nonspatial dimension In fact, lattice of nonspatial dimension is hierarchical

array that is assembled by all nonspatial dimensions in SDC. Suppose that there are n nonspatial dimensions in land SDC, there are n+1 hierarchies and n2 lattices. For example, there are 3 nonspatial dimensions, it is obvious that there are 4 hierarchies and 8 lattices.

The lattice hierarchy on nonspatial dimension is straight grapy that represents reliant relation among aggregation result of dimensions in SDC. Arrowhead line from top to bottom represents that an aggregation result can be educed by another aggregation result. For example, <region, time> can be educed by <region, time, land>, here land dimension is given up by aggregating. There is

This paper is supported by subject 2011BAK07B02-05 and 2011C23026 .

645978-1-4577-1415-3/12/$26.00 ©2012 IEEE

essential distinguish between conceptual hierarchy and lattice of nonspatial dimension. In general, lattice stresses on aggregation result among dimensions and reliant relation among aggregation result of dimension, conceptual hierarchy stresses on path that dimension member obtains value.

member of nonspatial dimension Member of nonspatial dimension is value sets based on

all path nodes from tree bottom to leave. The representation is expressed as follow:

Member of nonspatial dimension::(dimension.member1.member2……membern).

Thereinto, 1,2,……n represents nonspatial dimension hierarchies. For example, value of member in time dimension is equal to “time dimension.1995 year.2 month.18day”. 2) spatial dimension

Spatial dimension is merely a dimension that contains geospatial data. Spatial information and attributive information of geo-feature is defined as spatial dimension in SDC. It plays different role for spatial information and attributive information in spatial dimension:

Attributive information makes up of geo-nonspatial dimension on geographic concept in SDC. Object to be described is determined by geo-nonspatial dimension and other nonspatial dimensions.

Spatial information is not a dimension, and is regarded as GIS graph background to display object result. No matter what is happen to, when spatial information is treated as GIS graph background, its graphic shape spatial position and spatial relation is never changed.

conceptual hierarchy of spatial dimension Conceptual hierarchy of spatial dimension is similar to conceptual hierarchy of nonspatial dimension. Also, conceptual hierarchy of spatial dimension is classified according to real meaning of spatial dimension too. There are many conceptual hierarchies in spatial dimension. The conceptual hierarchy of spatial information and attributive information are discussed in this paper. The conceptual hierarchy of spatial information is classified according to geometrical character of geo-feature.

The conceptual hierarchy of attributive information is classified according to attributive character of geo-feature. The attributive character is divided into main codeidentification code descriptive code qualitative codequantitative code and place name.

lattice of spatial dimension

There is no lattice for spatial dimension in SDC. There is only lattice for nonspatial dimension. If there is no spatial dimension in hierarchical array that is assembled by all dimensions in SDC, SDC cann’t be made.

member of spatial dimension

Member of spatial dimension is similar to nonspatial dimension. Member of spatial dimension is value sets based on all path nodes from tree bottom to leave. The representation is expressed as follow:

Member of spatial dimension::(dimension.member1.member2……membern).

Thereinto, 1,2,……n represents spatial dimension hierarchies. The general representation is expressed as follow:

Member of spatial dimension:: (spatial dimension.mian code.ideniification code.descriptive code.qualitative code.quantitative code.place name).

For example, value in member of traffic road dimension is equal to “spatial dimension.traffic road.national road.highway.pavement.width.place name”.

B. Measure

Measure is attributive value of object determined by all dimensions or some dimensions. The value of measure occurs to cross of all dimensions or some dimensions. SDC is different form data cube. There are two category measures, i.e. digital measure and spatial measure. There are many digital measures and spatial measures in SDC. The world of measures in SDC is composed of (measure1, measure2,……, measuren)[3].

1)digital measure

In SDC, the object determined by dimensions is often nonspatial entity. The aggregation value of nonspatial entity for the object is called digital measure. The digital measure is a measure contained digital value and is divided into distributive algebraic and holistic measure. Suppose value of digital measure can be aggregated from all sub-cuboids by distributive aggregation function acted on all sub-cuboids such as count() and sum(), digital measure is distributive measure. Suppose value of digital measure can be aggregated from all sub-cuboids by algebraic aggregation function acted on all sub-cuboids such as avg() that is equal to sum()/count(), digital measure is algebraic measure. Except for distributive and algebraic measure, other digital measure is holistic measure.

2) spatial measure

In SDC, the object determined by dimensions is often geospatial entity. The aggregation value of geospatial entity for the object is spatial measure. For example, there are different scope values in two adjacent polygons. When user asks to carry out general operation, a scope value in polygon may be equal to another polygon. The two adjacent polygons that have same scope value can be jointed into large polygon. The large polygon is an aggregation result of two adjacent polygons. Hence, spatial measure is pointer collection of spatial object that is an aggregation result of geospatial entity, and can execute spatial operation of

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geospatial entity such as polygon overlapping and polygon jointing.

. THE DESIGN AND DEFITION CONCEPTUAL MODEL

A. Basic concept

Above-mentioned, SDC is composed of nonspatial dimension spatial dimension digital measure and spatial measure. The general representation of SDC is expressed as follow[4]:

SDC::(nonspatial dimension1, nonspatial dimension2,……, nonspatial dimensionn, spatial dimension1, spatial dimension2,……, spatial dimensionm, digital measure1,digital measure2,……,digital measurei, spatial measure1,spatial measure2,……,spatial measurej), thereinto, n m i and j are positive integer.

Two SDC that are respectively spatial dimension data cube (SDDC) and spatial measure data cube (SMDC) are discussed in this paper. The general representations of SDDC and SMDC are expressed as follow:

SDDC::( nonspatial dimension1, nonspatial dimension2,……, nonspatial dimensionn, spatial dimension, digital measure1,digital measure2,……,digital measurei), thereinto, n and i are positive integer.

SMDC:: (nonspatial dimension1, nonspatial dimension2,……, nonspatial dimensionn, digital measure1,digital measure2,……,digital measurei, spatial measure) , thereinto, n and i are positive integer.

B. Conceptual model

1) conceptual model of SDDC

The difference between SDDC and data cube is spatial dimension. The conceptual model difference between SDDC and data cube is that there is spatial dimension table in SDDC. In SDDC, digital measure in fact table is together aggregated by members of spatial dimension table and members of nonspatial dimension table. Result of digital measure is displayed on screen by geo-feature in spatial dimension. Here, no change of spatial position spatial shape and spatial relationship happens to geo-feature in spatial dimension, geo-feature is treated as graphic background to express aggregation result of digital measure.

Thereinto, D-Table and SD-Table respectively represent nonspatial dimension table and spatial dimension table, D-measure and D-member respectively represent digital measure and dimension member.

2) conceptual model of SMDC

The difference between SMDC and data cube is spatial

measure. The conceptual model difference between SMDC and data cube is that there is spatial measure in fact table in which spatial measure is pointer collection to point to geo-feature polygon such as hydrography traffic roadinhabited place vegetation boundary and land quality and so on. In SMDC, digital measure and spatial measure in fact table are together aggregated by member of nonspatial dimensions. Change of spatial position spatial shape and spatial relationship happens to geo-feature polygon in spatial measure, geo-feature polygon is treated as graphic background to express aggregation result of digital measure.

Thereinto, D-Table represents nonspatial dimension table, D-member represents dimension member, D-measure and S-measure respectively represent digital measure and spatial measure.

C. Algebraic definition

SDC definition: n dimension SDC is expressed as DstrMDR ,, thereinto

ndddD ,,, 21 is called dimension sets id is called dimension ni , there is a spatial dimension in D

kMMMM ,,, 21 is called measure sets jM is called measure kj , there is a spatial measure in M

nnaaaDstr ,,,,,,,,, 2211 is called sets of dimension structure iia ,, defines conceptual hierarchy structure and aggregation restriction of dimension id every set in ia is called hierarchy attribute of dimension id

M depends on D in function there is a function between D and M such as

kn MDOMMDOMdDOMdDOMF 11:thereinto, idDOM is value domain of dimension id

jMDOM is value domain of measure jM .

. CONCLUSION

So far, SDC research on theory and technology is beginning. Its aim is to meet development demand of spatial decision-making. It is such a good chance for us to make SDC deep-seated research in order to support spatial decision-making. This paper has discussed technology frame of SDC in a certain extent. It is sure that there are some misgivings in paper. I hope that this paper plays a role of introduction on SDC.

ACKNOWLEDGEMENY

This research is supported by subject2011BAK07B02-05 and 2011C23026 . This support

is gratefully acknowledged.Thank to all.

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1 Nebojsa Stefanovic Jiawei Han.Object-Based Selective Materialization for Efficient Implementation of Spatial Data Cubes.IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING VOL.12 NO.6 2000.12.

2 Xiaofang Zhou Jiawei Han.Efficient Polygon Amalgamation Methods for Spatial OLAP and Spatial Data Mining.Sixth SSD1999.

3 Dimitris Papadias Efficient OLAP Operations in Spatial Data Warehouses. Technical Report HKUST-CS01-01 january 2001.

4 Xiaofang Zhou Jiawei Han.Efficient Polygon Amalgamation Methods for Spatial OLAP and Spatial Data Mining.Sixth SSD1999.

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