Data cube

Data Warehousing and Data mining

1. Data Cube:
A Multidimensional
Data Model

2. Example
•Althoughweusuallythinkofcubesas3-Dgeometricstructures,indata
warehousingthedatacubeisn-dimensional.
•Togainabetterunderstandingofdatacubesandthemultidimensional
datamodel,let’sstartbylookingatasimple2-Ddatacubethatis,infact,a
tableorspreadsheetforsalesdatafromAllElectronics.
•Inparticular,wewilllookattheAllElectronicssalesdataforitemssoldper
quarterinthecityofVancouver.
•ThesedataareshowninTable4.2.Inthis2-Drepresentation,thesalesfor
Vancouverareshownwithrespecttothetimedimension(organizedin
quarters)andtheitemdimension(organizedaccordingtothetypesof
itemssold).
•Thefactormeasuredisplayedisdollarssold(inthousands).

3. 2-D

4. Example
•Now, suppose that we would like to view the sales data with a third
dimension.
•For instance, suppose we would like to view the data according to
time and item, as well as location, for the cities Chicago, New York,
Toronto, and Vancouver.
•These 3-D data are shown in Table 4.3. The 3-D data in the table are
represented as a series of 2-D tables.
•Conceptually, we may also represent the same data in the form of a 3-
D data cube, as in Figure 4.3.

5. 3-D
Inthisway,wemaydisplayanyn-dimensionaldataasaseriesof(n-1)-dimensional“cubes.”Thedata
cubeisametaphorformultidimensionaldatastorage.Theactualphysicalstorageofsuchdatamay
differfromitslogicalrepresentation.Theimportantthingtorememberisthatdatacubesaren-
dimensionalanddonotconfinedatato3-D.

6. 3-D data cube representation

7. 4.4 is often referred to as a cuboid

8. Lattice

9. Stars, Snowflakes, and Fact Constellations:
Schemas for Multidimensional Data Models
Themostpopulardatamodelforadatawarehouseisamultidimensional
model,whichcanexistintheformofastarschema,asnowflakeschema,or
afactconstellationschema.Let’slookateachofthese.
•Starschema:Themostcommonmodelingparadigmisthestarschema,in
whichthedatawarehousecontains(1)alargecentraltable(facttable)
containingthebulkofthedata,withnoredundancy,and(2)asetof
smallerattendanttables(dimensiontables),oneforeachdimension.The
schemagraphresemblesastarburst,withthedimensiontablesdisplayed
inaradialpatternaroundthecentralfacttable.

10. Star schema of sales data warehouse

11. Snowflakeschema:Thesnowflakeschemaisavariantofthestar
schemamodel,wheresomedimensiontablesarenormalized,thereby
furthersplittingthedataintoadditionaltables.Theresultingschema
graphformsashapesimilartoasnowflake.

12. Snowflake schema of a sales data warehouse

13. •Factconstellation:Sophisticatedapplicationsmayrequiremultiple
facttablestosharedimensiontables.Thiskindofschemacanbe
viewedasacollectionofstars,andhenceiscalledagalaxyschemaor
afactconstellation.

14. Fact constellation schema of a sales and shipping
data warehouse

15. Dimensions: The Role of Concept Hierarchies
•Aconcepthierarchydefinesasequenceofmappingsfromasetof
low-levelconceptstohigher-level,moregeneralconcepts.
•Consideraconcepthierarchyforthedimensionlocation.Cityvalues
forlocationincludeVancouver,Toronto,NewYork,andChicago.
•Eachcity,however,canbemappedtotheprovinceorstatetowhichit
belongs.
•Forexample,VancouvercanbemappedtoBritishColumbia,and
ChicagotoIllinois.

16. Example

17. Hierarchical and lattice structures

18. A concept hierarchy for price.

19. Examples of typical OLAP operations on
multidimensional data

20. A StarnetQuery Model for Querying
Multidimensional Databases

21. Source