Semantic Enrichment of OLAP Cubes Multidimensional Ontologies and their Representation in SQL and OWL
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1 Semantic Enrichment of OLAP Cubes Multidimensional Ontologies and their Representation in SQL and OWL Bernd Neumayr, Christoph Schütz, Michael Schrefl This work was supported by the FIT-IT research program of the Austrian Federal Ministry for Transport, Innovation, and Technology under grant FFG for the Semantic Cockpit project.
2 Motivation OLAP Cubes An OLAP cube is a multi-dimensional model representing real-world ld facts at various levels l of aggregation. Facts are quantified by measures and identified by entities from multiple dimensions. The dimensions have hierarchically organized levels which allow for the analysis of measures at different granularities. 2
3 Motivation OLAP Cubes Many data warehouse systems manage OLAP cubes in multi- dimensional i data structures t that t are optimized i for query performance. Some of these systems provide relational views as a query interface for the business analyst. 3
4 Motivation OLAP Cubes For example, medical treatments are quantified by the costs which are available by the day for a particular acting doctor and insurant. Business analysts may roll up the data in order to obtain the costs for coarser time periods and groups of acting doctors and insurants. 4
5 Motivation OLAP Cubes The fact view medtreatment stores in column costs the costs at the most granular level. Measure view costs contains the costs at every level of granularity base values and aggregated values 5
6 Motivation OLAP Cubes Measure view costsperinsurant defines the costs per insurant as a derived d measure at every level l of granularity. 6
7 Motivation OLAP Cubes Dimension views associate entities of a dimension with a particular level. l 7
8 Motivation OLAP Cubes Dimension views associate entities of a dimension with a particular level. l The measure views reference the dimension views 8
9 Motivation OLAP Cubes Roll-up views determine for each entity its superordinate entities, that t is, the transitive and reflexive closure of the immediate parent entities. 9
10 Motivation OLAP Queries Working with relational views can be cumbersome. Business analysts encode business terms directly into the SQL queries. 10
11 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
12 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time = 2010 Aggregation level 12
13 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( Big city SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
14 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( Small country SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
15 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. Acting doctor in big city SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
16 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( Acting doctor in small country SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
17 Motivation OLAP Queries Example Query: Retrieve the costs per insurant in the year 2010 by city of acting doctor where the acting doctor is in a big city of a small country. Acting doctor in big city and small country SELECT * FROM costsperinsurant WHERE actdoc IN ( SELECT Doctor FROM Doctor_rollup WHERE Doctor_sup IN ( SELECT CityE FROM CityE WHERE inhabitants > ) ) AND actdoc IN ( SELECT Doctor FROM Doctor_rolluprollup WHERE Doctor_sup IN ( SELECT e_country FROM e_country WHERE inhabitants < ) ) AND actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
18 Motivation OLAP Queries Explicit definition of business terms in concept views allows for the reuse of business term definitions in several queries and facilitates the formulation of these queries. SELECT * FROM costsperinsurant NATURAL JOIN actdocinbigcityandsmallcountry Acting doctor in big city and small country WHERE actdoc IN ( SELECT Doctor FROM Doctor WHERE Doctor_lvl = city ) AND time =
19 Motivation Derived Measures Besides their use in the formulation of queries, concept views also facilitate the definition of derived measures. A derived measure applies some measurement instruction to the available measure values. For example, a business analyst may derive the costs per rural insurant from the costs using the concept view that defines rural patients (ruralpatient). CREATE VIEW costsperruralinsurant AS SELECT AVG(mt.costs) AS costsperruralinsurant, d.sup AS Doctor, t.sup AS Time FROM medtreatment mt NATURAL JOIN Doctor_rollup d NATURAL JOIN Time_rollup t NATURAL JOIN ruralpatient rp GROUP BY d.sup, t.sup 19
20 Motivation MDO Language Rather than defining concept views in SQL, we propose a multi-dimensional ontology (MDO) language. g The MDO language allows for an organization-wide coherent definition of business terms. In order to share definitions of business terms among business analysts there must be some sort of classification which facilitates the retrieval of concepts. Automated reasoners may organize the concepts in subsumption hierarchies. Thus, we propose a formalization in OWL of MDO concepts. 20
21 Abstract Data Model, OWL Representation and Relational Views OLAP CUBES 21
22 OLAP Cubes Entity Classes Dimensions Level-range restricted dimensions Dimension roles Dimension spaces (or multi-dimensional spaces) Measures 22
23 Entity Classes MDO OWL Relational CREATE ENTITY CityE Entity CityE(CityE, E inhabitants) t CLASS CityE (inhabitants integer) CityE_inhabitants. CityE 1CityE_inhabtiantsinhabtiants 23
24 Dimensions and Hierarchies MDO OWL Relational CREATE Doctor Node Doctor_lvl (Doctor_lvl, entityclass) DIMENSION Doctor WITH LEVELS doctor DoctorE, atlevel. doctor Doctor roleof.doctore Doctor_lvlparent (Doctor_lvl, Doctor_lvl_sup) Doctor_lvlrollup (Doctor_lvl, city CityE AND HIERARCHY doctor UNDER city; atlevel. city Doctor roleof.doctore 1rollsUpTo_doctor 1rollsUpTo_city directlyrollsupto doctor, city Doctor_lvl_sup) l Doctor(Doctor, Doctor lvl) Doctor_parent (Doctor, Doctor_sup) Doctor_rollup rollup (Doctor, Doctor_sup) insert into "Doctor_lvl" values ('doctor', 'DoctorE'); insert into "Doctor_lvl" values ('city', 'CityE'); insert into "Doctor_lvlparent lvlparent" values ('doctor',`city'); 24
25 Dimensions and Hierarchies MDO OWL Relational CREATE Doctor Node Doctor_lvl (Doctor_lvl, entityclass) DIMENSION Doctor WITH LEVELS doctor DoctorE, atlevel. doctor Doctor roleof.doctore Doctor_lvlparent (Doctor_lvl, Doctor_lvl_sup) Doctor_lvlrollup (Doctor_lvl, city CityE AND HIERARCHY doctor UNDER city; atlevel. city Doctor roleof.doctore 1rollsUpTo_doctor 1rollsUpTo_city directlyrollsupto doctor, city Doctor_lvl_sup) l Doctor(Doctor, Doctor lvl) Doctor_parent (Doctor, Doctor_sup) Doctor_rollup rollup (Doctor, Doctor_sup) insert into "Doctor_lvl" values ('doctor', 'DoctorE'); insert into "Doctor_lvl" values ('city', 'CityE'); insert into "Doctor_lvlparent lvlparent" values ('doctor',`city'); 25
26 Dimensions and Hierarchies MDO OWL Relational CREATE Doctor Node Doctor_lvl (Doctor_lvl, entityclass) DIMENSION Doctor WITH LEVELS doctor DoctorE, atlevel. doctor Doctor roleof.doctore Doctor_lvlparent (Doctor_lvl, Doctor_lvl_sup) Doctor_lvlrollup (Doctor_lvl, city CityE AND HIERARCHY doctor UNDER city; atlevel. city Doctor roleof.doctore 1rollsUpTo_doctor 1rollsUpTo_city directlyrollsupto doctor, city Doctor_lvl_sup) l Doctor(Doctor, Doctor lvl) Doctor_parent (Doctor, Doctor_sup) Doctor_rollup rollup (Doctor, Doctor_sup) insert into "Doctor_lvl" values ('doctor', 'DoctorE'); insert into "Doctor_lvl" values ('city', 'CityE'); insert into "Doctor_lvlparent lvlparent" values ('doctor',`city'); 26
27 Disjointness of Sub-Dimensions in OWL OWL 2 DL does not allow to express that a transitive property (such as rollsupto) maps to exactly one object in a given range (for example, to one node of one level). The essential characteristics of roll-up hierarchies of data warehouse dimensions are that the rollsupto-relationship relationship between nodes is transitive and each node of a level rolls up to exactly one node of each higher level (to which the former level rolls up). Without these semantics of roll-up hierarchies being captured, the subsumption hierarchy that is determined by an OWL reasoner will be sound, but incomplete. 27
28 Disjointness of Sub-Dimensions in OWL For the country level: rollsupto_country rollsupto atlevel. rollsupto. country rollsupto_country. rollsupto_country. atlevel. country l 1rollsUpTo_country For the austria node at the country level: rollsupto. austria rollsupto_country. austria 28
29 Disjointness of Sub-Dimensions in OWL For each level l, we introduce a functional roll-up property. For the country level: rollsupto_country rollsupto atlevel. rollsupto. country rollsupto_country. rollsupto_country. atlevel. country l 1rollsUpTo_country For the austria node at the country level: rollsupto. austria rollsupto_country. austria 29
30 Disjointness of Sub-Dimensions in OWL For the country level: rollsupto_country rollsupto atlevel. rollsupto. country rollsupto_country. rollsupto_country. atlevel. country l 1rollsUpTo_country For the austria node at the country level: rollsupto. austria rollsupto_country. austria We assert for every named node nd at level l that all its descendant nodes roll up to nd via this functional roll-up property 30
31 Level-Range Restricted Dimension MDO OWL Relational CREATE LEVELRANGE- Doctor_CityCountry C t create view RESTRICTED DIMENSION Doctor_CityCountry AS Doctor Doctor atlevel. rollsupto. city "Doctor_CityCountry" as select * from "Doctor" where "Doctor_lvl lvl" in ((select [city..country]; rollsupto. country "Doctor_lvl_sup" as "Doctor_lvl" from "Doctor_lvlrollup lvlrollup" where "Doctor_lvl" = 'city') intersect (select "Doctor_lvl" from "Doctor_lvlrollup" where "Doctor_lvl_sup = 'country')); 31
32 Level-Range Restricted Dimension MDO OWL Relational CREATE LEVELRANGE- Doctor_CityCountry C t create view RESTRICTED DIMENSION Doctor_CityCountry AS Doctor Doctor atlevel. rollsupto. city "Doctor_CityCountry" as select * from "Doctor" where "Doctor_lvl lvl" in ((select [city..country]; rollsupto. country "Doctor_lvl_sup" as "Doctor_lvl" from All levels that the city level rolls up to. "Doctor_lvlrollup lvlrollup" where "Doctor_lvl" = 'city') intersect (select "Doctor_lvl" from "Doctor_lvlrollup" where "Doctor_lvl_sup = 'country')); 32
33 Level-Range Restricted Dimension MDO OWL Relational CREATE LEVELRANGE- Doctor_CityCountry C t create view RESTRICTED DIMENSION Doctor_CityCountry AS Doctor Doctor atlevel. rollsupto. city "Doctor_CityCountry" as select * from "Doctor" where "Doctor_lvl lvl" in ((select [city..country]; rollsupto. country "Doctor_lvl_sup" as "Doctor_lvl" from All levels that roll up to the country level "Doctor_lvlrollup lvlrollup" where "Doctor_lvl" = 'city') intersect (select "Doctor_lvl" from "Doctor_lvlrollup" where "Doctor_lvl_sup = 'country')); 33
34 Dimension Roles MDO OWL Relational CREATE DIMENSION 1 1actDoc "actdoc" " varchar not null ROLE actdoc OF actdoc. Point references "Doctor" Doctor actdoc.doctor The nodes of the Doctor dimension may play the role of "acting doctor" within a dimension. 34
35 Dimension Roles MDO OWL Relational CREATE DIMENSION 1 1actDoc "actdoc" " varchar not null ROLE actdoc OF actdoc. Point references "Doctor" Doctor actdoc.doctor Acting doctors are doctors, that is, nodes from the Doctor dimension. 35
36 Dimension Roles MDO OWL Relational CREATE DIMENSION 1 1actDoc "actdoc" " varchar not null ROLE actdoc OF actdoc. Point references "Doctor" Doctor actdoc.doctor Point in a dimension space (or multi-dimensional space). 36
37 Dimension Spaces MDO OWL Relational CREATE DIMENSION d1 ds1 Point Pi t actdoc. create view "ds1" as select * SPACE ds1 AS (actdoc Doctor_CityCountry, time Time_MonthYear) Doctor_CityCountry time.time_monthyear from (select "Doctor" as "actdoc" from "Doctor_CityCountry CityCountry") natural join (select "Time" as "time" from "Time_MonthYear MonthYear"); 37
38 Measures MDO OWL Relational CREATE MEASURE costs. d ds1 costs(actdoc, t( td time, costs) t) costs FOR ds1 38
39 Entity Concepts, Dimensional and Multi-Dimensional Concepts DEFINING MDO CONCEPTS OVER OLAP CUBES 39
40 MDO Concepts Entity concepts Dimensional concepts Multi-dimensional concepts 40
41 Entity Concepts (1) MDO OWL Relational CREATE ENTITY bigcity CityE create view "bigcity" as select CONCEPT bigcity FOR CityE bigcity "CityE from "CityE" where "inhabitants" > AS inhabitants > CiteE_inhabitants.integer ;
42 Entity Concepts (1) MDO OWL Relational CREATE ENTITY bigcity CityE create view "bigcity" as select CONCEPT bigcity FOR CityE bigcity "CityE from "CityE" where "inhabitants" > AS inhabitants > CiteE_inhabitants.integer ; An entity concept is defined over an entity For example, bigcity is defined over the entity CityE 42
43 Entity Concepts (1) MDO OWL Relational CREATE ENTITY bigcity CityE create view "bigcity" as select CONCEPT bigcity FOR CityE bigcity "CityE from "CityE" where "inhabitants" > AS inhabitants > CiteE_inhabitants.integer ; Entity concepts may be defined using attribute-value restrictions. For example, a bigcity has more than inhabitants. 43
44 Entity Concepts (2) MDO OWL Relational CREATE ENTITY bigorsmallcity CityE create view "bigorsmallcity" as CONCEPT bigorsmallcity FOR CityE AS bigorsmallcity bigcity smallcity (select "CityE" from "bigcity") union (select "CityE" from "smallcity"); UNION OF ( bigcity, smallcity ); Entity concepts may also be defined as unions, intersections, complements of existing entity concepts. For example, bigorsmallcity is the union of big and small cities. 44
45 Dimensional Concepts (1) MDO OWL Relational CREATE DIMENSIONAL CONCEPT doc_bigcity FOR Doctor_city AS Doctor:bigCity; doc_bigcity Doctor_city doc_bigcity Doctor roleof.bigcity Ofbi All nodes of the Doctor dimension create view "doc_bigcity" as select "Doctor" from "Doctor" where "Doctor" in (select * from "bigcity") ") 45
46 Dimensional Concepts (1) MDO OWL Relational CREATE DIMENSIONAL CONCEPT doc_bigcity FOR Doctor_city AS Doctor:bigCity; doc_bigcity Doctor_city doc_bigcity Doctor roleof.bigcity Ofbi create view "doc_bigcity" as select "Doctor" from "Doctor" where "Doctor" in (select * from "bigcity") ") All nodes of the Doctor dimension that satisfy the bigcity concept 46
47 Dimensional Concepts (1) MDO OWL Relational CREATE DIMENSIONAL CONCEPT doc_bigcity FOR Doctor_city AS Doctor:bigCity; doc_bigcity Doctor_city doc_bigcity Doctor roleof.bigcity Ofbi create view "doc_bigcity" as select "Doctor" from "Doctor" where "Doctor" in (select * from "bigcity") ") Dimension concepts are defined over (level-range restricted) dimensions. For example, doc_bigcity is defined for Doctor_city, that is, all nodes of the Doctor dimension at the city level. The members of a dimension concept are nodes of the dimension 47
48 Dimensional Concepts (2) MDO OWL Relational CREATE DIMENSIONAL CONCEPT DocInBigCity FOR Doctor_doctorCity AS doc_bigcity*; DocInBigCity Doctor_doctorCity DocInBigCity rollsupto_city.doc_bigcity create view "DocInBigCity" as select "Doctor" from "Doctor_rollup" where "Doctor_sup" "in (select * from "bigcity") 48
49 Dimensional Concepts (3) MDO OWL Relational CREATE DIMENSIONAL CONCEPT DocInBgCtySmCntry C t FOR Doctor doctorcity AS INTERSECTION OF( DocInBigCity, DocInSmallCountry ); DocInBgCtySmCntry Doctor_doctorCity DocInBgCtySmCntry C DocInBigCity DocInSmallCountry create view "DocInBgCtySmCntry" as (select "Doctor" from "DocInBigCity") intersect (select "Doctor" " from "DocInSmallCountry") 49
50 Multi-Dimensional Concepts (1) MDO OWL Relational CREATE MULTI- DIMENSIONAL CONCEPT leaddocinbgctysm- Cntry FOR ds_leaddoc AS leaddoc: DocInBgCtySmCntry; leaddocinbgctysmcntry ds_leaddoc leaddocinbgctysmcntry C ds_leaddoc.docinbgctysmcntry Defined over some dimension space create view "leaddocinbgctysmcntry" as select * from leaddoc where leaddoc in ( select * from "DocInBgCtySmCntry") 50
51 Multi-Dimensional Concepts (1) MDO OWL Relational CREATE MULTI- DIMENSIONAL CONCEPT leaddocinbgctysm- Cntry FOR ds_leaddoc AS leaddoc: DocInBgCtySmCntry; leaddocinbgctysmcntry ds_leaddoc leaddocinbgctysmcntry C ds_leaddoc.docinbgctysmcntry The elements are points in the dimension space create view "leaddocinbgctysmcntry" as select * from leaddoc where leaddoc in ( select * from "DocInBgCtySmCntry") 51
52 Multi-Dimensional Concepts (1) MDO OWL Relational CREATE MULTI- DIMENSIONAL CONCEPT leaddocinbgctysm- Cntry FOR ds_leaddoc AS leaddoc: DocInBgCtySmCntry; leaddocinbgctysmcntry ds_leaddoc leaddocinbgctysmcntry C leaddoc.docinbgctysmcntry create view "leaddocinbgctysmcntry" as select * from leaddoc where leaddoc in ( select * from "DocInBgCtySmCntry") The elements are points in the dimension space where the points satisfy the dimensional i concepts in the indicated d dimension i roles. For example, where in the leaddoc role a doctor in a big city of a small country is referenced. 52
53 Multi-Dimensional Concepts (2) MDO OWL Relational CREATE MULTIDIMENSIONAL CONCEPT leaddocinbgctysm- CntryIn2010 FOR ds_leaddoc_time AS INTERSECTION OF ( leaddocinbgctysmcntry, timein2010) ) ; leaddocinbgctysm CntryIn2010 ds_leaddoc_time create view "leaddocinbgstysm- CntryIn2010" as select * from "leaddocinbgctysmcntry" natural join "timein2010" leaddocinbgctysm CntryIn2010 leaddocinbgctysmctry timein
54 Multi-Dimensional Concepts (3) MDO OWL Relational CREATE MULTI- DIMENSIONAL CONCEPT expensivedoctorcombos FOR leaddoc_actdoc_year AS mediancostsperins > 1000 expensivedoctorcombos leaddoc_actdoc_year expensivedoctorcombos mediancostsperins. double 1000:0 create view "expensivedoctorcombos" as select * from "leaddoc_actdoc_year" " natural join "mediancostsperins" where "mediancostsperins" > 1000; 54
55 Conclusion A multi-dimensional ontology (MDO) is a formal representation of a conceptualization ti of a data analysis domain. This formal representation facilitates the unambiguous interpretation of query results and allows business analysts to share their knowledge in data analysis projects. By providing translations of MDO concepts to relational views, semantically-enriched cubes may be queried using SQL. By providing a representation of MDO in OWL, off-the-shelf reasoners may be used for the classification of business terms which is vital for the management of large vocabularies. 55
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