Reconciling Continuous Attribute Values from Multiple Data Sources

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1 Associatio for Iformatio Systems AIS Electroic Library (AISeL PACIS 2008 Proceedigs Pacific Asia Coferece o Iformatio Systems (PACIS July 2008 Recocilig Cotiuous Attribute Values from Multiple Data Sources Zhegrui Jiag Iowa State Uiversity, zr998@gmail.com Follow this ad additioal works at: Recommeded Citatio Jiag, Zhegrui, "Recocilig Cotiuous Attribute Values from Multiple Data Sources" (2008. PACIS 2008 Proceedigs This material is brought to you by the Pacific Asia Coferece o Iformatio Systems (PACIS at AIS Electroic Library (AISeL. It has bee accepted for iclusio i PACIS 2008 Proceedigs by a authorized admiistrator of AIS Electroic Library (AISeL. For more iformatio, please cotact elibrary@aiset.org.

2 RECONCILING CONTINUOUS ATTRIBUTE VALUES FROM MULTIPLE DATA SOURCES Jiag, Zhegrui, Iowa State Uiversity, 2340 Gerdi Busiess Buildig, Ames, Iowa , USA, Abstract Because of the heterogeeous ature of differet data sources, data itegratio is ofte oe of the most challegig tasks i maagig moder iformatio systems. The challeges exist at three differet levels: schema heterogeeity, etity heterogeeity, ad data heterogeeity. The existig literature has largely focused o schema heterogeeity ad etity heterogeeity; ad the very limited work o data heterogeeity either avoid attribute value coflicts or resolve them i a ad-hoc maer. The focus of this research is o data heterogeeity. We propose a decisio-theoretical framework that eables attribute value coflicts to be resolved i a cost-efficiet maer. The framework takes ito cosideratio the cosequeces of icorrect data values ad selects the value that miimizes the total expected error costs for all applicatio problems. Numerical results show that sigificat savigs ca be achieved by adoptig the proposed framework istead of simply selectig the most likely value or ad-hoc approaches. Keywords: Data itegratio, heterogeeous databases, data heterogeeity, data quality, type I, type II, ad misrepresetatio errors.

3 . INTRODUCTION Itegratig data from heterogeeous data sources is oe of the most difficult problems faced by IT/IS researchers ad practitioers. The challeges exist at three differet levels: schema heterogeeity, etity heterogeeity, ad data heterogeeity. Amog them, schema heterogeeity is caused by the use of differet structures ad/or differet ames for the same iformatio; etity heterogeeity arises whe iformatio about the same real-world etity is stored i differet data sources usig differet idetifiers; ad data heterogeeity refers to data icosistecies i the absece of schema heterogeeity. I this study, we assume that schema heterogeeity ad etity heterogeeity do ot exist or have bee completely resolved, ad focus o recocilig attribute value coflicts as a result of data heterogeeity. The mai research questio we attempt to aswer is: whe coflictig values are ecoutered i the process of data itegratio, what value should be chose ad stored i the cosolidated database, i a maer that miimizes the expected cost for a orgaizatio? Amog the three types of heterogeeities, schema heterogeeity has attracted the most attetio i the research commuity. As a result, umerous schema matchig techiques have bee proposed; a extesive review of automatic schema matchig approaches has bee provided by Rahm & Berstei (200. The body of literature o etity heterogeeity is relatively smaller, ad has focused o specific problems such etity idetificatio ad matchig (Dey et al. 998b ad data cleaig ad duplicatio removal (Heradez & Stolfo 998. Prior research o data heterogeeity, with the exceptio of the work by Jiag et al. (2007, ca be divided ito two broad categories. The first category either igores/avoids data icosistecies (Bleiholder & Nauma 2006 or attempts to store the coflictig data ad related iformatio (such as probability usig a special data structure or a exteded database model (e.g., probabilistic relatioal database by Dekhtyar et al The proposed approaches i this category do ot resolve data heterogeeity they simply fid ways to circumvet it, ad the burde of decidig how to use the icosistet data is still laid upo the users. The secod category of research proposes methods to select a value from the coflictig oes or create a value based o some give criteria, although i a rather ad-hoc maer (Bleiholder & Nauma For istace, the chose value ca be determied based o radom selectio, maority votig, or the average of the coflictig values. A maor drawback of the above metioed coflict resolutio approaches is that they do ot take ito cosideratio the future utilizatio of the data beig processed. Databases are created to help orgaizatios make iformed decisios. I the presece of data heterogeeity, the quality of their decisios will likely be affected by how the attribute value coflicts are resolved. Therefore, a soud coflict resolutio strategy should ot be developed without icorporatig the iteded usage of the data. As the oly systematic approach we have see i the literature, the attribute recociliatio framework proposed by Jiag et al. (2007 takes ito cosideratio the cosequeces associated with the differet recociliatio decisios, ad selects the values/decisios that lead to the miimum expected error cost for all applicatio problems uder cosideratio. However, that framework is oly applicable to categorical attributes. It caot be used to recocile attributes with cotiuous domais for a umber of reasos. First, for categorical attributes, a stored value is either correct or wrog; while for cotiuous attributes, it is typically iappropriate or isufficiet to state a value is correct or ot. For istace, suppose a customer s true home state is Texas while the recorded values are Louisiaa ad Mexico i two data sources, the it is safe to cosider both values icorrect. O the other had, if a customer s true icome is $76,329.25, the two recorded values of $76, ad $30,35.00 may both be cosidered wrog, but there is a sigificat differece i the magitude of the errors. The first value may ot affect ay decisio problems; while the secod oe may lead to icorrect decisios. Secod, whe measurig the reliability of a data source, the percetage of icorrect values may be sufficiet for categorical attributes; while both the frequecy ad magitude of errors are eeded for cotiuous attributes. Third, queries based o categorical attributes typically use discrete values i

4 their selectio coditio; while queries based o cotiuous attributes ofte make selectios based o value itervals. Because of these key differeces, it is ecessary to develop a separate framework for hadlig the recociliatio of cotiuous attributes. The attribute value recociliatio framework we propose i this study is decisio-theoretic the optimal value to be chose is the oe that miimizes the total expected error cost for a orgaizatio. To fid out the cost-miimizig value, our proposed framework explicitly takes ito cosideratio the future applicatios of the data uder cosideratio ad the probability distributio of the true values of the relevat attribute. Due to space limitatio, we oly cosider the recociliatio of a sigle attribute with cotiuous domai i this research. The rest of the paper is orgaized as follows. I sectio 2, we derive the probability distributio of the true values of a attribute. I Sectio 3, we discuss differet types of data applicatio problems, supportig queries, ad the associated error costs. I sectio 4, we demostrate how certai value itervals ca be used to geerate cadidate values ad simply the estimatio of probabilities. I Sectio 5, we select the best attribute value based o the estimated probabilities ad the cost parameters. I the last sectio, we coclude with discussio ad future research directios. 2. PROBABILITY DERIVATION Suppose a cotiuous attribute A appears i data sources S, S 2,, S. For a particular etity istace, the stored value of A i data source S k is deoted by A S k. For a variety of reasos, these stored values for the same etity istace may be differet i the multiple data sources. We assume that these data sources are separately maitaied ad hece the errors are idepedet across data sources. Give the stored values i these data sources, we would like to estimate the probability desity fuctio of the true values of A: f a A,..., A, a D, ( ( S S A where D A is the domai of A. Alteratively, we ca estimate the probability distributio of A if the rouded discrete values are cosidered: P( A= a A,..., A, i {, 2, K, m}, (2 i S S where m represets the umber of discrete values i the domai of A. I geeral, the derivatio of the desity fuctio show i ( is feasible oly if the patter of errors i each data source follows a well-defied distributio, such as the ormal distributio. Sice most data errors i the real-world are ulikely to exhibit a well-defied patter, we focus our derivatio of probabilities as show i (2. Based o Bayes theorem ad the assumptio that errors are idepedet across data sources, we have: P( A a A,..., A = i S S m P( AS,..., AS A = ai P( A = ai = = P( A = = S,..., AS A a P( A a Because a database ca oly store a limited umber of decimal places, eve values of attributes with cotiuous domais i the real world are stored i the database i a discrete form. For attributes with a large rage of possible values, such as Icome, the stored values may eve be rouded to the earest iteger. The framework we propose i this research is ot affected by such roudig so log as the same level of graularity is used i queries ad i decidig cadidate values or cadidate value itervals.

5 P( AS A= ai... P( AS A= ai P( A= ai. (3 = P( A = = = S A a... P( AS A a P( A a = m I the above equatio, P( A= a, {, 2, K, m} represets the prior distributio of attribute A; ad P( A A= a, k {, 2, K, }, {, 2, K, m} represets the patter of errors i each S k data source. The values of these terms ca be estimated usig statistical samplig techiques. However, to cover all possible combiatios of true values ad observed values i all data sources, users of this procedure have to estimate km 2 probabilities. This could be practically ifeasible if the value of m is large. There are two possible solutios to this problem: (i roud the values to the earest tes, hudreds, etc., util the umber of possible values becomes maageable; ad (ii divide the domai ito a reasoable umber of value itervals. I Sectio 4, we will show how such value itervals ca be derived based o characteristics of queries. 3. QUERIES AND ERROR COSTS Orgaizatios collect ad merge data from differet sources to support operatioal ad maagerial activities. These activities typically ivolve retrievig data for all or a subset of the etity istaces from a database, followed by certai actios o the selected etity istaces. We call this type of activities applicatio problems. For istace, a firm may create a master record of curret ad potetial customers to support applicatio problems such as direct marketig, customer survey, aftersale services, ad maagemet of product recalls. To retrieve the ecessary data from the master record, each applicatio problem eeds a correspodig query. I costructig such a query, the attributes that are used as the criteria to select the etity istaces should appear i the selectio coditio of the query, ad those that are eeded i the subsequet actios should appear i the proectio list of the query. For istace, if a firm plas to directly market a product to potetial customers i a certai icome bracket, the the Icome attribute should appear i the selectio coditio of the correspodig query. If Icome is used oly i selectig the target customers but ot i the subsequet direct marketig actios, the Icome eeds ot appear i the proectio list of the query. For istace, the followig query may be used for this direct marketig applicatio problem: Q: Display Name, Occupatio, ad Address of those customers whose Icome is i the rage of $00,000 $49,999. If Icome is also eeded i the direct marketig actios to further tailor the product offerigs to targeted customers, the Icome should also appear i the proectio list of the query. The followig is a example query for this sceario: Q2: Display Name, Icome, Geder, ad Address of those customers whose Icome is i the rage of $80,000 $9,999. I yet aother sceario, if Icome is ot used i selectig the etity istaces but are eeded i the subsequet actios of a applicatio problem, the Icome should oly appear i the proectio list of the correspodig query. Q3 represets such a sceario: Q3: Display Name, Icome, Occupatio, ad Address of those customers who have previously made at least $,000 i TotalPurchases from the compay. 2 The proper costructio of queries eables us to use queries, istead of the applicatio problems they support, i our subsequet aalyses. 2 To avoid further complicatig the problem, we assume that the values of attribute TotalPurchase are always correct i this research.

6 Whe a query is executed, a icorrect value stored i a database ca cause three types of errors: Type I, Type II, ad misrepresetatio errors. A type I error occurs whe a etity istace that should have bee selected based o the true value of a attribute is ot selected. A type II error occurs whe a etity istace that should ot have bee selected based o the true attribute value is selected. A misrepresetatio error occurs whe the value of a attribute used i the actio o a selected etity istace is icorrectly represeted. The defiitios of these three types of errors are cosistet with those give by Medelso ad Saharia (986 ad Dey et al. (998a. A icorrect value of a attribute ca cause Type I or Type II errors to a query oly if the attribute appears i the selectio coditio of the query. A misrepresetatio error ca occur oly if the attribute appears i the proectio list of the query. Based o these two rules, a icorrect Icome value ca cause oly Type I or Type II errors to Q, while it may lead to Type I, Type II, as well as misrepresetatio errors to Q2. The costs of Type I, Type II errors, deoted by γ I ( q ad γ II ( q, are uique to a query q. The coefficiet of misrepresetatio error cost, deoted by γ m ( q, A, is uique to the query q ad a give attribute A. The values of these cost parameters ca be estimated based o the uderlyig applicatio problem. For istace, γ I (Q equals the expected et profit per correctly targeted customer i the direct marketig campaig, ad γ II (Q equals the expected loss per icorrectly targeted customer i the same campaig. Assume Q Q3 represet all queries that iclude Icome i its selectio coditio ad/or proectio list. We ow use them to demostrate how the expected error cost associated with a chose value ca be derived. Suppose that i the process of data itegratio, the Icome value chose ad stored i the cosolidated database is $95,000 for a customer amed Richard Smith. Subsequetly, whe Q is executed, Richard Smith will ot be selected. Give that he is ot selected, if his true icome is ideed withi the rage of [00,000, 49,999], a Type I error occurs. The cost of this error equals the product of the cost of Type I error for Q ad the probability that his true icome is withi that rage, i.e., γ I(Q P( Icome [00,000,49,999]. O the other had, whe Q2 is executed, Richard Smith will be selected if his stored Icome value is $95,000. Give that Richard Smith is selected, if his true icome is outside of the rage of [80,000, 9,999], a Type II error occurs. The expected cost of this error equals the product of the cost of Type II error for Q2 ad the probability that his true icome is ot withi the rage show i Q2, i.e., γ II(Q2 P( Icome [80,000,9,999]. I additio, sice Icome is i the proectio list of Q2, if Richard Smith s true Icome value is ot $95,000, a misrepresetatio error occurs. The fuctioal form for the cost of misrepresetatio error is specific to a applicatio problem. Here, we use the quadratic cost fuctio, i which the cost is proportioal to the square of the magitude of error, to demostrate the effect of misrepresetatio cost o attribute value recociliatio. The expected cost of this misrepresetatio error for Q2 takes the form 2 γ m (Q2, Icome P( Icome= icome ( 95,000, i i icomei where icome i represets a true Icome value, ad i is the idex over all cosidered values withi the domai of Icome. We ext examie Q3. Sice Icome does ot appear i the selectio coditio of Q3, a icorrect Icome value does ot cause ay Type I or Type II error. Furthermore, uless a particular etity istace is selected, misrepresetatio error will ever occur. Therefore, we ca igore Q3 if Richardso Smith s TotalPurchses is less tha $,000. If Richard Smith s TotalPurchses is greater tha $,000, the he will be selected by Q3, ad the expected misrepresetatio cost equals 2 γ (Q3, Icome P( Icome= icome i ( icome 95,000. i m i By addig the idividual costs derived for Q Q3, we obtai the total expected error cost associated with the chose Icome value of $95,000 for Richard Smith. The expected cost associated with ay other cadidate value ca be obtaied i a similar maer. Apparetly, if we have to calculate the expected cost for all possible values, the computatioal cost could be prohibitively high. I additio, as we explai i Sectio 2, with a large umber of attribute values uder cosideratio, the plottig of

7 error patters for each data source could be too complex to be feasible. I the ext sectio, we show how these two challeges ca be overcome by cosiderig the characteristics of the queries. 4. RETRIEVAL INTERVALS FOR CANDIDATE VALUE SELECTION AND PROBABILITY ESTIMATION From the cost derivatio show i the previous sectio, we observe that so log as the chose Icome value for Richard Smith is from the iterval of [80,000, 99,999], the resultig Type I ad Type II errors ad the associated error costs remai the same for Q ad Q2. Upo further examiatio, we fid that the same coclusio holds for the itervals of [mivalue, 79,999], [00,000, 9,999], [20,000, 49,999], ad [50,000, maxvalue]. We ame this type of itervals retrieval itervals. As show i Figure, the retrieval itervals for a attribute ca be obtaied by first idetifyig the ed values of all itervals appearig i the selectio coditios of all queries, ad the isertig these values ito the domai of the attribute. I I 2 I 3 I 4 I 5 mivalue $80K $00K $20K 50K Figure. Retrieval Itervals for Icome maxvalue Withi a give retrieval iterval, sice the costs of Type I ad Type II errors are always the same, the value that results i the miimum expected misrepresetatio cost ecessarily leads to the miimum total expected error cost. This helps us reach the followig propositio: Propositio : With the quadratic error cost fuctio, the value i a retrieval iterval that is the closest to the expected true value of a attribute is always the cost-miimizig value from that iterval. (Proof omitted. For istace, if the expected true Icome value for Richard Smith is $35,000, the the best value from the first retrieval iterval I : [mivalue, 79,999] is $79,999, because this value is the closest to the expected true value. Similarly, we ca obtai the cost-miimizig values for the other four retrieval itervals I 2 I 5 as $99,999, $9,999, $35,000, ad $50,000. The best overall Icome value for Richard Smith ca be chose from this pool of cadidate values. (Observed I I 2 I 3 I 4 I 5 I I 2 (True I 3 I 4 I 5 P P 2 P 3 P 4 P 5 P 2 P 22 P 23 P 24 P 25 P 3 P 32 P 33 P 34 P 35 P 4 P 42 P 43 P 44 P 45 P 5 P 52 P 53 P 54 P 55 Figure 2. Distortio Matrix for Icome

8 Retrieval iterval is also a atural choice for use as value itervals for the purpose of estimatio of error patters i each data source. For istace, we ca sample each data source to costruct a distortio matrix for the attribute Icome, as show i Figure 2. Oce these probabilities of errors are estimated, they ca be plugged ito Equatio (3 to help estimate the probability that the true Icome value falls withi a particular iterval. Besides sigificatly reducig the umber of probabilities to estimate durig samplig, the use of retrieval itervals as value itervals for the purpose of probability estimatio has two importat advatages: first, the errors occurrig withi each retrieval iterval do ot cause ay Type I or Type II error, therefore the loss of precisio as a result of usig value itervals istead of idividual values is miimized; secod, the probabilities eeded to calculate the Type I ad Type II error costs ca be easily obtaied. For the purpose of calculatig the misrepresetatio error cost ad the expect value of a attribute, we ca treat the media of a retrieval iterval as the value represetig the iterval, ad the probability for the etire iterval as the probability for its represetative value. 5. DETERMINING THE BEST VALUE Suppose that by followig the proposed samplig ad probability estimatio procedure, we obtai the followig probabilities for Richard Smith: P(I = 0.2, P(I 2 = 0.32, P(I 3 = 0.35, P(I 4 = 0.9, ad P(I 5 = Based o these probabilities, the expected true Icome value is $09,250. Therefore, the cadidate values for the five retrieval itervals are $79,999, $99,999, $09,250, $20,000, ad $50,000, respectively. To calculate the expected costs of errors, we set the values of the type I ad Type II costs to $00 for both Q ad Q2, ad the coefficiet of misrepresetatio error cost to for both Q2 ad Q3. We also assume that Q3 will select Richard Smith. Usig the give parameter values, we obtai the expected error costs associated with all five cadidate values, ad fid that the value $20,000 results i the lowest expected error cost of $3. I compariso, the expected error costs associated with the cadidate values from the two most likely itervals (I2 ad I3 are $28.95 ad 20.27, respectively. It is iterestig to ote that the best value is ot from the two most likely retrieval itervals. With the proposed framework, approximately oe teth of cost ca be saved. If $20,000, the cost-miimizig value is stored i the cosolidated database, Richard Smith will be selected as a target customer by the direct marketig campaig represeted by Q, but ot by the campaig represeted by Q2. 6. DISCUSSION AND FUTURE RESEARCH If the umber of queries is p, the umber of cadidate values to be cosidered is r, ad the umber of etity istaces with values to be recociled is l, the the worst-case complexity of the proposed framework is O(lpr2. From the expressio, we ca see that the adoptio of retrieval itervals sigificatly reduces the computatioal overhead of the procedure. We are i the process of desigig a simulated experimet to evaluate the performace of our framework i relatio to other ad-hoc approaches. We expect this framework to outperform other approaches because by costructio, our framework produces values that miimizes the expect error costs, while other approaches igores errors ad error costs altogether. I additio, we pla to examie more complex scearios ivolvig multiple ucertai attributes ad queries with more tha oe selectio coditios. Refereces Bleiholder, J. ad F. Nauma. (2006. Coflict hadlig strategies i a itegrated iformatio system. WWW Workshop i Iformatio Itegratio o the Web (IIWeb 2006, Ediburgh, UK.

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