A Methodology for Information Quality Assessment in Data Warehousing

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1 Ths full text paper was peer revewed at the drecton of IEEE ommuncatons Socety subect matter experts for publcaton n the I 008 proceedngs. A ethodology for Informaton Qualty Assessment n Data Warehousng Yng Su esource Sharng and Promotng enter Insttute of Scentfc and Techncal Informaton of hna Beng, HN suy4@sem.tsnghua.edu.cn Zhanmng Jn School of Economcs and anagement Tsnghua Unversty Beng, HN nzhm@sem.tsnghua.edu.cn Abstract Ths paper presents a methodology to determne two IQ characterstcs accuracy and comprehensveness that are of crtcal mportance to data warehousng. Ths methodology can examne how the qualty metrcs of source nformaton affect the qualty for nformaton outputs produced usng the relatonal algebra operatons selecton, proecton, and ubc product. It can be used to determne how qualty characterstcs assocated wth dverse data sources affect the qualty of the derved data. The study resulted n the development of a model of a data cube and an algebra to support IQ Assessment operatons on ths cube. Keywords- Terms Informaton Qualty, Data Warehouse, Data ube, On-ne Analytcal Processng (OAP T I. INTODUTION ODAY, nformaton s a vtal busness asset and to take advantage of that asset, companes are turnng to data warehousng, whch lets them combne large amounts of data to create a unfed, consstent vew of ther busness. The dual but related notons of data warehousng and On-ne Analytcal Processng (OAP) are, clearly, two of the most sgnfcant new technologes n the busness ntellgence arena. To develop that complete vew, however, you have to pull together data from many sources across the organzaton and n today s complex, heterogeneous IT envronments, that can be a real challenge. In many companes, data s fragmented and spread among dozens, f not hundreds, of databases and applcatons, n varous formats, and wth varous degrees of accuracy and comprehensveness. To provde the relable busness-orented nformaton that decson makers need, you must be able to manage and control nformaton qualty. However, only a few organzatons have mplemented any knd of a proect. There are two mportant factors for ths. Frst, mplementng such a proect can be qute expensve, often nvolvng mllons of dollars of software and assocated human resources. Second, frms are unable to clearly measure the qualty of data and consequently the qualty of nformaton derved from the data warehouse. Wthout ths ablty t becomes dffcult, f not mpossble, for frms to estmate the cost of poor nformaton to the organzaton. For the above reasons, the management of the nformaton qualty n data warehouse has been dentfed as a crtcal ssue for organzatons. That s the focus of our research. Specfcally, we develop a methodology to assess the qualty of nformaton based on the qualty of the source databases. The rest of ths paper s organzed as follows. After concludng related work n Secton II, we ntroduce a forma1 model proposed for data warehousng and OAP that attempts to support qualty metrcs of dfferent levels n Secton III. In secton IV, we dscuss the dfferent qualty metrcs that need to be consdered for the output of selecton operator, proecton and ubc product operators. Secton V llustrates how our analyss could be used n a varety of busness ntellgences, and concludes wth a bref dscusson of future research. II. ITEATUE EVIEW A. IQ Dmensons We assgned the four cases based on types of relatonshp of actvtes, as the second and thrd columns of TABE I.The ffth column of TABE I summarzes academc research on the multple dmensons of IQ. The frst row s Ballou and Pazer's (1985) study, whch takes an emprcal, market research approach of collectng data from nformaton consumers to determne the dmensons of mportance to them. TABE I lst the dmensons uncovered n Zmud s (1978) poneerng IQ research study, whch consders the dmensons of nformaton mportant to users of hard-copy reports. Because of the focus on reports, nformaton accessblty dmensons, whch are crtcal wth on-lne nformaton, were not relevant. In our analyss, we consder metrcs assocated wth two well-documented nformaton qualty attrbutes: accuracy and completeness. Accuracy s defned as conformty wth the real world. ompleteness s defned as avalablty of all relevant data to satsfy the user requrement. Although many other nformaton qualty attrbutes have been ntroduced and dscussed n the exstng lterature, these two are the most wdely cted. Furthermore, accuracy and completeness can be measured n an obectve manner, somethng that s usually not Ths research was supported by Natonal Natural Scence Foundaton of hna (Proect No: , ), and hna Postdoctoral Scence Foundaton ( ) /08/$ IEEE

2 Ths full text paper was peer revewed at the drecton of IEEE ommuncatons Socety subect matter experts for publcaton n the I 008 proceedngs. Actvty Taxonomy ASE ASE Upstream Actvty Downstream Actvty TABE I ATIVITY-BASED DEFINING TO THE IQ DIENSIONS Defnton eference Dmensons of IQ for Upstream Actvty Approach onsstent representaton, Interpretablty, ase of understandng, oncse representaton, User-based Tmelness, ompleteness [1], Value-added, relevance, approprate, eanngfulness, ack of confuson []. Arrangement, eadable, easonable [3]. Intutve Precson, elablty, freedom from bas [4]. ASE User-based See also ASE ASE System Data Defcency, Desgn Defcences, Operaton Defcences [6]. Inherent IQ Accuracy, ost, Obectvty, Belevablty, eputaton, Accessblty, orrectness [8], Unambguous [10]. onsstency [11]. possble for other qualty attrbutes. B. Overvew of Data Warehousng A data warehouse can be defned as a repostory of hstorcal data used to support decson makng [5]. OAP refers to the technology that allows the user to effcently retreve nformaton from the data warehouse [7]. Fgure 1 gves an overvew of the man components of the data warehouse system, whch are to be descrbed n the paper [9].. esearch ontrbutons The contrbuton of ths research s the development of a rgorous methodology to assess the qualty characterstcs of data warehouses. Although lttle formal analyss of ths nature has been addressed n prevous research, two approaches proposed earler have nfluenced our work. Amr Parssan. (004) present a methodology to determne how the qualty metrcs of source data affect the qualty for nformaton outputs produced usng the relatonal algebra operatons selecton, proecton, and artesan product. Importantly, they show these error types to be closed under relatonal algebra operatons [1]. They do not, however, provde a methodology for dervng qualty metrcs for the OAP. sser and Batn (003) provde a multdmensonal data cube, show how requrements can be formally expressed by referrng to vews over the cube, End-User Tools Transformaton omponent Operatve Systems Data arts Data Warehouse Data Base External Data eta data anagement and thus provde a precse noton of adequacy of the suppler wth respect to ts customers' requrements, and a way for customers to rank ther supplers wth respect to the qualty profle they offer[13]. III. THE UBE ODE AND ETIS A. Basc Defntons As mentoned prevously, the data cube s almost unversally accepted as the underlyng logcal level construct to descrbe a multdmensonal database. Ths mandates that all the operators we defne (as well as ther algebra) must operate on the cube structure. The frst step, therefore, s to defne a data cube. DEFINITION 1: A data cube s the fundamental underlyng construct of the multdmensonal database and serves as the basc unt of nput and output for all operators defned on a multdmensonal database. It s defned as a 6-tuple, AfdO,,,,, where the sx components ndcate the characterstcs of the cube. These characterstcs are: s a set of m characterstcs { c1, c, cm} ; A s a set of t attrbutes A { a1, a, at} ; f s a one-to-one mappng, f : A, whch maps a set of attrbutes to each characterstc; d s a Boolean-valued functon that parttons nto a set of dmensons D and a set of measures. Thus, D where D. O s a set of partal orders such that each O s a partal order defned on o f ( c ) and O ; s a set of cube cells. A cube cell s represented as an address, content par. The address n ths par s an n-tuple, α1, α, αn, where n s the number of dmensonal attrbutes n the cube. The content of a cube cell s defned smlarly. It s a k-tuple, χ1, χ, χk, where k s the number of metrc attrbutes n the cube;.e., k Am, where A m represents the set of all metrc attrbutes. Fg. 1. Data Warehouse System (Helfert and aur, 001)

3 Ths full text paper was peer revewed at the drecton of IEEE ommuncatons Socety subect matter experts for publcaton n the I 008 proceedngs. B. ube-evel etrcs Based on the above defntons, we defne the followng qualty metrcs for a cube., A, I, and denote the cardnaltes of the sets, A, I,, and, respectvely. Accuracy of, measured asα A, s the probablty that a tuple n accurately represents an entty n the real world. Inaccuracy of, measured as β I, s the probablty that a tuple n s naccurate. smembershp of, measured as, s the probablty that a tuple n s a msmember. Incompleteness of, measured as χ ( + ), s the probablty that an nformaton resource n the real world s not captured n. Because A, I, and consttute, we have 0 α, β, 1 and α + β + 1. Wth T + and T, we have0 1. χ When a cube s empty, we defne α 1, β 0 and 0. When the correspondng conceptual cube s empty, χ 0 otherwse χ 1. The data cube s a data model for representng busness nformaton usng multdmensonal database (DDB) technology. The followng example about a cube Sale llustrates these metrcs. TABE III shows the data stored n the feature class, and TABE IV shows the ncomplete nformaton for. The attrbute set {year, product_name,cty} forms the address for. The Tuple Status column n TABE II ndcates whether a tuple s accurate (A), naccurate (I), or a msmember () ells n that are set n bold type contan naccurate values, and the row set n bold type s a msmember. TABE IV TABE II FEATUE ASS UBE ID Year Product Tuple ty Amount Quant. name Status herry t. 10, A ot os 7,34 00 A Walnut Hll 9, I Park Blvd. 8, A Valley Vew 8,77 10 I herry t. 9, A ot d. 8, Beverly Hll 1, I oyal ane 8, I ID Year Product name TABE III INOPETE UBE ty Amount Quant Tuple Status herry t. 11, descrbes errors n, and TABE V provdes the qualty measures. IV. UBE-EVE ETIS FO POPOSED OPEATIONS A. Selecton Operaton The selecton operator restrcts the values on one or more attrbutes based on specfed condtons, where a gven condton s n the form of a predcate. Thus, a set of predcates s evaluated on selected attrbutes, and cube cells are retreved only f they satsfy a gven predcate. If there are no cube cells that satsfy P, the result s an empty cube. The algebra of the selecton operator s then defned as follows: Input: A cube I,A, f,d,o, and a compound predcate P. Output: A cube O,A,f,d,O, O where 0 and 0 { l ( l ) ( lsatsfes P)} athematcal Notaton: σ PI O (1) U T We defne a conceptual cube (denoted by U) that s obtaned by applyng the predcate condton to the conceptual cube T. U denotes nstances n T that satsfy the predcate condton for A, I, and. Fg. shows the mappng between the subsets of the conceptual and stored and cubes. We make two assumptons that are wdely applcable. After query executon, all accurate tuples satsfyng the predcate condton reman accurate n. Smlarly, all selected naccurate and msmember tuples contnue to be naccurate and msmember n, respectvely. Tuples belongng to the ncomplete dataset that would have satsfed the predcate condton now become part of, the ncomplete set for. Therefore, there s no change n the tuple status for the selected tuples. The expected value of A s A. Smlarly, we have UA UI U TA TI T I I,, and. Usng these denttes n the defntons of a, β, and χ, t s easly seen that α α, β β, and χ χ. We show the algebra for χ here: A I Fg.. appng elatons between the oncept and Physcal A I

4 Ths full text paper was peer revewed at the drecton of IEEE ommuncatons Socety subect matter experts for publcaton n the I 008 proceedngs. χ ( + ) ( ) ( ) ( ) B. Proecton Operaton The metrc proecton operator restrcts the output of a cube to nclude only a subset of the orgnal set of measures. et S be a set of proecton attrbutes such that S Am. Then the output of the resultng cube ncludes only those measures n S. The algebra of metrc proecton s defned as follows: Input: A cube I,A, f,d,o, and a set of proecton attrbutes S. Output: A cube O,A O,f O,d,O,O where AO S Ad, : AO fo, such that f O (c) f(c) AO, and O { lo l, lo. A l. A, lo. l. [ s1], l. [ s],, l. [ sn] }, where{ s1, s,, sn} S. athematcal Notaton: Π SI O (3) Fg. 3 llustrates the mappng between tuples n and. The notaton IA, II, and IN refer to those naccurate tuples n that become accurate, reman naccurate, and become msmembers, respectvely, n. Each tuple n IN contrbutes a correspondng tuple to the ncomplete dataset ; we denote ths contrbuton by I. We denote by kp and q p the number of address and content attrbutes of that are proected nto. The probablty that a tuple s accurate n s therefore gven by 1 k kp K 1 kp Q S qp K k S qp Q α ( α + β) ( α + β) ( ) ( ) kp K + kp Q ks qp K + qp Q α + β kp K ks p K kp Q ks qp Q α β α β kp K ks q p K µ 1 α + β q β ( + ) 1 ( + ) ( ) TABE IV EOS UBE IN A A ID ows Status Error Descrpton IA 3 Inaccurate Amount should be 9,031 I 5 Inaccurate ty II should be 6 Valley Vew I 7 smember Should not belong to cube 8 Inaccurate Quantty I should be Inaccurate Product name should be ks qs I TABE V kp qp EOS UBE IN UBE SIZE α β Fg. 3. Tuple Transformatons for the Proecton Operaton χ () ( )( ) ( ) χ [ χ µ + 1α β 1 χ ] 1 µ 1χ 1χ k k q 1 ( α β) 1 ( α + β) 1µ 1µ p K S p K. ubc Product Operaton The ubc Product operator s a bnary operator that can be used to relate any two cubes. Often t s useful to combne the nformaton n two cubes to answer certan queres (whch we wll llustrate wth an example). The algebra of the ubc Product operator s defned as follows: Input: A cube 1 1, A1,f 1,d 1, O1, 1 and a cube, A,f,d, O, Output: A cube O 0, A0,f 0,d 0, O0, 0, where 0 Λ 1( 1) Λ( ) ; A0 Λ1( A1) Λ( A) ; O { lo l1, l, l, l, l. A l. Al. A, l. l. l. w here l1. Al. A denotes the concatenaton of l 1. A and l. A. In addton: f1whenappled toc 1c c ( 1 ) fo fwhenappled toc c ( ) c d O ( ( ) ( )) a f f d1whenappled toc 1c dwhenappled toc c O1whenappled toa f ( 1) OO Owhenappled toa f ( ) athematcal Notaton: 1 O (4) Formally, let 1 and be two relatons on whch the ubc product operaton s performed, and let be the result of the operaton. Furthermore, let t 1 be a tuple n 1 (or 1 ), t be a tuple n (or ), and t be a tuple n (or ). summarzes how tuples should be categorzed n. Note that the concatenaton of t 1 1N and t, and t 1 1 and t N, are not meanngful to our analyss because they appear nether n the true world of nor n the observed verson of. The cardnalty of the accurate, naccurate, and msmember tuples n, and the ncomplete tuples n, are as shown below. A 1A A TABE VI TUPE FO THE UBI PODUT OPEATION 1 t A t I t N t t 1 1A t A t I t N t t 1 1I t I t I t N t t 1 1N t N t N t N t 1 1 t t t }

5 Ths full text paper was peer revewed at the drecton of IEEE ommuncatons Socety subect matter experts for publcaton n the I 008 proceedngs. + + I 1A I 1I A 1I I + N 1A N 1I N N A 1N I 1N N + 1A 1I A I et a, β, and χ ndcate the qualty profles of S 1,. a, β, and χ ndcate the qualty profles of the ubc product. Usng 1 and the defntons n Secton ube-evel etrcs, we have 1A A α α1 α (5) S S β + + 1A I 1I A 1I I α β + α β + β β A N 1I N 1N A + ( 1 ) ( 1 ) 1N I 1N N (7) From equalty(6), we have χ1+ χ χ1χ χ 1χ ( ) ( ) ( ) ( ) Therefore, we have χ1+ χ χ1χ χ ( 11) ( 1) 1 + ( 1χ1 ) ( 1χ ) (6) 1 χ1+ χ χ1χ ( ) ( ) ( ) ( ) ( ) χ1 1χ χ1+ χ χ1 χ (8) From Equalty(5), we can see that the accuracy of the output of the ubc product operator s less than the accuracy of ether of the nput relatons, and that the accuracy can become very low f the partcpatng tables are not of hgh qualty. smembershp and ncompleteness also ncrease for the output. V. ONUSIONS In ths paper, we have addressed an mportant ssue wthn the realm of decson support databases: the lack of a precse, commonly agreed upon conceptual model for assurng the qualty of nformaton. To address ths problem, we have made two sgnfcant contrbutons. Frst, we have presented a detaled data model for the data cube. Secondly, we have presented a detaled operatons model for the data cube to determne how source data cube of dfferent qualty could mpact those OAP derved usng Selecton, Proecton, and ubc product operatons. Our models can be used n several ways. For example, consder selectng prospectve customers for a promoton usng n-house customer transacton data along wth geographcal data purchased from an external vendor. Data from the two tables would need to be oned and then the approprate selecton condton appled to the result of the on. The on requres a artesan product operaton that would typcally lead to an ncrease n the msmembershp of the resultng table as compared to ether of the partcpatng relatons. The selecton operaton would further ncrease the msmembershp n the target address tag. The estmates for ncompleteness provded by our models would help determne whether addtonal data should be purchased from vendors. Because data mnng could support multple such applcatons, our analyss would be useful n dentfyng whch data sets wll have acceptable qualty, and whch ones wll not. Fnally, our results can be mplemented on top of data warehouses engne that can assst end users to obtan qualty profles of the nformaton they receve. The qualty nformaton wll allow users to account for the relablty of the nformaton receved thereby leadng to decsons wth better outcomes. EFEENES [1] D. P. Ballou and H.. Pazer, "odelng Data and Process Qualty n ult-input, ult-output Informaton Systems," anagement Scence, vol. 31, p. 150, Feb [] D.. Goodhue, "Understandng user evaluatons of nformaton systems," anagement Scence, vol. 41, p. 187, [3]. W. Zmud, "AN EPIIA INVESTIGATION OF THE DIENSIONAITY OF THE ONEPT OF INFOATION," Decson Scences, vol. 9, pp , [4] W. H. Deone and E.. cean, "The Deone and cean model of nformaton systems success: a ten-year update," Journal of anagement Informaton Systems, vol. 19, pp. 9-30, Spr 003. [5] A. Sen and A. P. Snha, "Toward Developng Data Warehousng Process Standards: An Ontology-Based evew of Exstng ethodologes," IEEE Transactons on Systems, an & ybernetcs: Part - Applcatons & evews, vol. 37, pp , [6] K.-T. Huang, Y. W. ee, and. Y. Wang, Qualty nformaton and knowledge. Upper Saddle ver, N.J. : Prentce Hall PT, [7] B. H. Hunter and D. E. Smth, "Surveyng moble populatons: essons from recent longtudnal surveys of ndgenous Australans," The Australan Economc evew, vol. 35, pp , Sep 00. [8]. Y. Wang and D.. Strong, "Beyond accuracy: What data qualty means to data consumers," Journal of anagement Informaton Systems, vol. 1, p. 5, Sprng [9]. Helfert and E. v. aur, "A Strategy for anagng Data Qualty n Data Warehouse Systems," n Internatonal onference on Informaton Qualty (IT IQ onference), IT, 001, p. 10. [10] Y. Wand and. Y. Wang, "Anchorng data qualty dmensons n ontologcal foundatons," Assocaton for omputng achnery. ommuncatons of the A, vol. 39, pp , Nov [11]. P. Englsh, Improvng data warehouse and busness nformaton qualty methods for reducng costs and ncreasng profts New York: Wley, [1] A. Parssan, S. Sarkar, and V. S. Jacob, "Assessng Data Qualty for Informaton Products: Impact of Selecton, Proecton, and artesan Product," anagement Scence, vol. 50, pp , Jul 004. [13] P. sser and. Batn, "A ultdmensonal odel for Informaton Qualty n ooperatve Informaton Systems," n Internatonal onference on Informaton Qualty (IT IQ onference), IT, 003, p. 16.