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unsuspected relationships which are ofinterest or value to the databases owners, or data miners9. Due to the large number ofdimensionality and the huge volume ofdata, traditional statisticalmethods have their limitations in data mining. To meet the challenge ofdata mining, articialintelligence based humancomputer interactive techniques have been widely used in data mining3,16.*Conceptual construction on incomplete survey dataShouhong Wanga,*, Hai WangbaDepartmentofMarketing/BusinessInformationSystems,CharltonCollegeofBusiness,UniversityofMassachusettsDartmouth,285OldWestportRoad,NorthDartmouth,MA02747-2300,USAbDepartmentofComputerScience,UniversityofToronto,Toronto,ON,CanadaM5S3G4Received 22 March 2003; received in revised form 9 September 2003; accepted 20 October 2003Available online 26 November 2003AbstractThe raw survey data for data mining are often incomplete. The issues of missing data in knowledgediscovery are often ignored in data mining. This article presents the conceptual foundations of data miningwith incomplete survey data, and proposes query processing for knowledge discovery and a set of queryfunctions for the conceptual construction in survey data mining. Through a case, this paper demonstratesthat conceptual construction on incomplete data can be accomplished by using articial intelligence toolssuch as self-organizing maps.C211 2003 Elsevier B.V. All rights reserved.Keywords: Incomplete survey data; Survey data mining; Conceptual construction; Self-organizing maps; Clusteranalysis; Knowledge discovery; Query processing1. IntroductionData mining is the process oftrawling through data in the hope ofidentifying interpretablepatterns. Data mining is dierent from traditional statistical analysis in that it is aimed at /locate/datakData & Knowledge Engineering 49 (2004) 311323Corresponding author.E-mailaddresses: swang (S. Wang), hai (H. Wang).0169-023X/$ - see front matter C211 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.datak.2003.10.007ntsan eective method in dealing with high-dimensional data 6,12. More importantly, the SOMmethod provides a base for the visibility ofclusters ofhigh-dimensional data. This feature is not312 S.Wang,H.Wang/Data&KnowledgeEngineering49(2004)311323available in any other data analysis methods. It allows the data miner to analyze clusters based onthe problem domain.Survey is one ofthe common data acquisition methods for data mining 4. In data mining, onecan rarely nd a survey data set that contains complete entries ofeach observation for all ofthevariables. Commonly, surveys and questionnaires are often only partially completed by respon-dents. The extent ofdamage ofmissing data is unknown when it is virtually impossible to returnthe survey or questionnaires to the data source for completion, but is one of the most importantparts of knowledge for data mining to discover. In fact, missing data is an important debatableissue in the knowledge engineering eld 15.In mining a survey database with incomplete data through cluster analysis, patterns ofthemissing data as well as the potential impacts ofthese missing data on the mining results areknowledge. For instance, a data miner often wishes to know how reliable a cluster analysis is;when and why certain types ofvalues are often missing; what variables are correlated in terms ofhaving missing values at the same time. These valuable pieces ofknowledge can be discoveredonly after the missing part of the data set is fully explored.This paper discusses the issue ofmissing data in mining survey databases for knowledge dis-covery, presents the conceptual foundations of conceptual construction, and proposes a set ofquery functions for conceptual construction in SOM-based data mining. The rest of the paper isorganized as follows. Section 2 discusses the issues of missing data related to data mining. Section3 introduces SOM for conceptual construction on incomplete data. Section 4 suggests fourconcepts as knowledge discovery in data mining with incomplete data. It provides a scheme ofconceptual construction on incomplete data using SOM. Section 5 proposes a query tool that isused to manipulate SOM for conceptual construction. Section 6 presents a case study that appliesthe query tool to manipulate the SOM for the conceptual construction on a student opinionsurvey data set. Finally, Section 7 oers concluding remarks.2. Issues of missing dataIncomplete data sets are ubiquitous in data mining. There have been many treatments ofmissing data. One ofthe convenient solutions to incomplete data is to eliminate from the data setthose records that are missing values. This, however, ignores potentially useful information inthose records. In cases where the proportion ofmissing data is large, the conclusions drawn fromthe screened data set are more likely biased or misleading.There have been many non-statistical techniques for data mining. The self-organizing maps(SOM) method based on Kohonen neural network 12 is one ofthe promising techniques. SOM-based cluster techniques have advantages over other methods for data mining. Data miningtypically deals with very high-dimensional data. That is, an observation in the database for datamining is typically described by a large number ofvariables. The curse ofdimensionality turnsstatistical correlations ofdata insignicant, and thus makes statistical methods powerless. TheSOM method, however, does not rely on any assumptions ofstatistical tests, and is considered asntsS.Wang,H.Wang/Data&KnowledgeEngineering49(2004)311323 313Another simple approach ofdealing with missing data is to use generic unknown for allmissing data items. In data mining, unspecied unknown for all missing data items often causesconfusion and misinterpretation.The third solution to dealing with missing data is to estimate the missing value in the data eld.In the case oftime series data, interpolation based on two adjacent data points that are observedis possible. In general cases, one may use some expected value in the data eld based on statisticalmeasures 7. However, in data mining, survey data are commonly ofthe types ofranking, cat-egory, multiple choices, and binary. Interpolation and use ofan expected value for a particularmissing data variable in these cases are generally inadequate. More importantly, research 2indicates that a meaningful treatment ofmissing data shall always be independent ofthe problembeing investigated.More recently, there have been mathematical methods for nding the aggregate conceptualdirections ofa data set with missing data (e.g., 1,10). These methods make themselves distinctfrom the traditional approaches of treating missing data by focusing on the collective eects of themissing data instead ofindividual missing values. This superior feature ofthese methods can bebest built up for data mining on incomplete data. However, these statistical methods have limi-tations. First, it is assumed that missing values occur in a random fashion or follow a certaindistribution functions. Their strong assumptions about the distributions of data are often invalidespecially for cases of survey with incomplete data. Second, these mathematical models are data-driven, instead ofproblem-domain-driven. In fact, a single generic conceptual constructionalgorithm is insucient to handle a variety ofgoals ofdata mining since a goal ofdata mining isoften related to its specic problem domain.Knowledge discovery in databases is the non-trivial process ofidentifying valid, novel,potentially useful, and ultimately understandable patterns of data 8. Following this denition,this research emphasizes two aspects ofconcept construction in data mining with incomplete data.First, the criteria ofvalidity, novelty, usefulness ofthe concepts to be constructed in data miningwith incomplete data could be problem-dependent. That is, the interest ofa data pattern dependson the data miner and does not solely depend on the estimated statistical strength ofthe pattern14. Second, the conceptual construction based on the incomplete data is accomplished throughheuristic search in combinatorial spaces built on computer and human cognitive theories 13.Humancomputer collaboration concept construction is the interactive process between the dataminer and computer to extract novel, plausible, useful, relevant, and interesting knowledgeassociated with the missing data.In our view, data mining diers from traditional statistics in dealing missing data in manyways.(1) Data mining attempts to extract unsuspected and potentially useful patterns from the data forthe data miners with novel goals related to the missing data, rather than to estimate the indi-vidual values ofthe missing data.(2) Data mining is a human centered process implemented through knowledge discovery loopscoupled with humancomputer interaction to perceive the impact ofthe missing data at anaggregate level, rather than a one-way mathematical derivation based on unveried assump-tions.nts3. Tool for conceptual construction: self-organizing maps (SOM)Given a large set ofhigh-dimensional survey samples, there usually be a signicant number ofobservations have missing values; however, not all missing data are relevant to the data minerC213sinterest. Hence, any simple brute-force search method for missing data is not only infeasible for ahuge amount ofdata, but also helpless when the data miner is to identify problems, or developconcepts, through data mining. To identify problems or develop concepts, the data miner needs atool to observe unsuspected patterns ofthe available data and the missing parts.Self-organizing maps (SOM) 12 have been widely used for clustering, since SOM are morecomputationally ecient than the popular k-means clustering algorithm. More importantly, SOMprovide data visualization for the data miner to view high-dimensional data 11. Research 14,16314 S.Wang,H.Wang/Data&KnowledgeEngineering49(2004)311323indicates that SOM are eective in data mining for the identication of unsuspected pattern of thedata. Specically, SOM can be used for cluster analysis on multivariate survey data. This studytakes one step further and uses SOM as a tool for concept construction related to missing data.Conceptual construction on incomplete data is to investigate the patterns ofthe missing data aswell as the potential impacts ofthese missing data on the mining results based only on thecomplete data. As seen later in our illustrative examples, SOM provide a mechanism for humancomputer collaboration to construct concepts from the data with missing values.SOM can learn certain useful features found in their input patterns through the unsupervised(competitive) learning process, and map the high-dimensional data onto low-dimensional pic-tures, allowing the data miner to view the map with clusters. The neural network depicted in Fig. 1is the two-layer SOM used in this study. The nodes at the lower layer (input nodes) receive inputspresented by the sample data points. The nodes at the upper layer (output nodes) will representthe organization map ofthe input patterns after the unsupervised learning process. Every lowlayer node is connected to every upper layer node via a variable connection weight.The unsupervised learning process in SOM can be briey described as follows. The connectionweights are assigned with small random numbers at the beginning. The incoming input vectorpresented by a sample data point is received by the input nodes. The input vector is transmitted tothe output nodes via the connections. The activation ofthe output nodes depends upon the input.In a winner-take-all competition, the output node with the weights most similar to the inputvector becomes active. In the learning stage, the weights are updated following Kohonen learningFig. 1. Self-organizing maps.ntszero, the learning process will eventually converge.First, SOM are applied to the data set with complete data to reveal the unusual patterns oftheinvestigated. Two indices can be applied to this concept.C1: SM=SCwhere SMis the number ofdata samples with missing values, and SCis the number ofdata samples with complete values used for clusters identication. Apparently, the higher SM=SCis, the lower the reliability ofthe observation ofthe clusters would be.C2: VMi=VCi where VMi is the number ofmissing values in variable i, and VCi isthe number ofsamples used for the clusters identication in variable i. Again, in terms ofvari-able i, the higher VMi=VCi is, the lower the reliability ofthe observation ofthe clusters wouldbe.4.2.HidingThe concept ofhiding reveals how likely an observation with a certain range ofvalues in onedata by presenting clusters. Based on those clusters, unsuspected patterns ofthe data are iden-tied, and the problem is articulated by the data miner. Second, the incomplete data with missingvalues related to the clusters in question are used to construct new concepts. In this phase, thedata miner evaluates the impacts ofmissing data on the problem identied and developsknowledge related to the missing data. The task ofthe rst phase is the same as most applicationsofSOM in clusters identication (e.g., 16). This study places the focal point on the second phaseand proposes techniques ofconceptual construction for data mining with incomplete data. Next,we propose four concepts as knowledge discovery in data mining with incomplete data. As shownlater in this paper, these concepts can be constructed through humancomputer collaboration andSOM-based data visualization.4.1.ReliabilityThe reliability concept reveals the scope ofthe missing data in terms ofthe problem beingAfter enough input vectors have been presented, weights will specify clusters such that the localdensity function of the cluster centers tends to approximate the probability density function ofthe input vectors 12. The weights will be organized such that nodes that share a topologicalresemblance are sensitive to inputs that are similar. The output nodes in SOM will thus be or-ganized and represent the real clusters in the self-organizing map without knowing a priori clustercenters. The reader is referred to 12 for a more detailed discussion.4. Conceptual construction on incomplete dataIn this study, conceptual construction on incomplete data is carried out through two phases.rule 12. The weight update only occurs for the active output node and its topological neighbors(Fig. 1). In this one-dimensional output case, we assume a linear neighborhood. The neighbor-hood starts large and slowly decreases in size over time. Because the learning rate is reduced toS.Wang,H.Wang/Data&KnowledgeEngineering49(2004)311323 315variable is to have a missing value in another variable.ntsthe same time.C4: VMi; j=VMi where VMi; j is the number ofmissing values in both variables i and j, andVMi is the number ofmissing values in variable i. This concept discloses the correlation oftwovariables in terms ofmissing values. The higher the value VMi; j=VMi is, the stronger thecorrelation ofmissing values would be.4.4.ConditionaleectsThe concept ofconditional eects reveals the potential changes ofthe clusters identied ifthemissing values had completed.C5: DPj8zik where DP is the changes ofthe clusters perceived by the data miner, 8zirepresents all missing values ofvariable i, and k is the possible value variable i might have for thesurvey. Typically, k fmax; min;pg where max is the maximal value ofthe scale, min is theminimal value ofthe scale, and p is the random variable with the same distribution function ofthe values in the complete data. By setting dierent possible values of k for the missing values, thedata miner is able to observe the changes ofclusters and redene the problem.In summary, conceptual construction on incomplete data is a knowledge development process.To construct new concepts on incomplete data, the data miner needs to identify a particularproblem as a base for the construction. Four concepts on missing data are reliability, hiding,complementing, and conditional eects. Next, we develop a set ofqueries for conceptual con-struction on incomplete data. Our objective ofthese queries is to allow the data miner to conductthe experimental process through the use ofSOM in order to construct new concepts related tothe problem.5. Query processing for conceptual constructionQuery tools are characterized by structured query language (SQL), the standard query languagefor relational database management systems. For data mining, as the ultimate objective ofinformation retrieval from the database is the formulation of knowledge through the use of avariety oftechniques, it is unlikely that a single standard query language can be created for allpurposes ofdata mining. Nevertheless, to support humancomputer collaboration eectively,visualized query processing is necessary in data mining 5. This study develops a set ofqueryfunctions that assist the data miner to construct concepts related to the missing data through theC3: VMijxja; b where VMi is the number ofmissing values in variable i, xj is the valueofvariable j, and a; b is the range ofvalues of xj.This index discloses the degree ofuncertainty ofanswers to the survey question, such as donot know and neutral, or the intention ofsystematical missing data, such as do not want totell.4.3.ComplementingThe concept ofcomplementing reveals what variables are more likely to have missing values at316 S.Wang,H.Wang/Data&KnowledgeEngineering49(2004)311323SOM-based clustering analysis.ntsThe computing environment ofthe SOM-based data mining system is Microsoft Excel. Thismakes it possible to integrate the data base, the SOM program, data visualization, and queryprocessing into a single computing environment. Using Microsoft Excel, data base is held by thespreadsheet, the SOM program is implement