Self-associated concept mapping for representation, elicitation and inference of knowledge
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osstool for teaching, learning, evaluation, and curriculum planning. This paper presents self-associated concept mapping (SACM) whichextends the use of concept mapping by proposing the idea of self-construction and automatic problem solving to traditional conceptmaps. The SACM can be automatically constructed and dynamic updated. A Constrained Fuzzy Spreading Activation (CFSA) model
and organizing concepts into their cognitive structures
[25,34,40], teaching [2,12,22,31], assessing users under-standing [6,37,38], curriculum design [7,28], planning[11,36], etc. Numerous of tools and commercial software
discovery concept map in a repository  and so on.
changes of the maps. The construction of the maps is di-cult, time consuming and expensive. Moreover, the inter-pretation of concept maps rely on human who is notsuitable tool for computational inference.
On contrary to the current trend of the development ofconcept maps, this paper attempts to give the idea of
* Corresponding author. Tel.: +852 27667905; fax: +852 23625267.E-mail address: email@example.com (C.F. Cheung).
Available online at www.sciencedirect.com
Knowledge-Based Systems 2. New knowledge is assimilated into their cognitivestructures through construction and not merely acquired. Based on this learning theory, a method known asconcept maps was developed. Concept maps are widelyused as a means of visualizing ones inner cognitive struc-tures. Concept maps require users to identify, graphicallydisplay, and link key concepts by organizing and analyzinginformation. They make the structure of knowledge visual-ly explicit and conceptually coherent. There are numerousapplications for concept maps including communication
Moreover, several researchers have developed dierentmethodologies to extend the usage of concept map[5,6,17,18,24].
In the past, concept maps are manually constructed bythe users and the usages of concept maps are focused oneducational purpose. Although a number of concept map-ping tools are available, the construction and interpreta-tion of concept maps are still heavily relied on humanbeing. Traditional maps are static after the developmentprocess, which require human interventions for any lateris proposed to SACM for supporting rapid and automatic decisions. With the successful development of the SACM, the capability ofKnowledge-based systems (KBS) can be enhanced. The concept and operational feasibility of the SACM is realized through a case studyin a consultancy business. The theoretical results are found to agree well with the experimental results. 2006 Elsevier B.V. All rights reserved.
Keywords: Knowledge representation; Self-associated concept maps; Concept mapping; Knowledge management; Knowledge-based systems
Cognitive psychology stated that people do not learn bymemorizing, instead, they learn by summarizing, relating,
have been developed including construction tools of con-cept maps in dierent education and business settings[9,14,16,17,20,21,27,39], tools for handheld devicessupporting mobile learning , tools for navigation andSelf-associated concept mappinand inference
W.M. Wang, C.F. Cheun
Department of Industrial and Systems Engineering, The Hong
Received 18 March 2006; received in revised forAvailable online
Concept maps have been widely put to educational uses. They p0950-7051/$ - see front matter 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.knosys.2006.11.015for representation, elicitationf knowledge
*, W.B. Lee, S.K. Kwok
ng Polytechnic University, Hung Hum, Kowloon, Hong Kong
November 2006; accepted 16 November 2006December 2006
ess a number of appealing features which make them a promising
1 (2008) 5261
map, spreading activation (SA) is adopted. Similar to con-cept maps, the SA model also has its roots from its rela-tionship with human memory . It has often beenassociated with semantic networks. During spreading, theactivation input of a node in the network is calculatedbased on the following equation:
where Ij is the total input of node j, Oi is the output of nodei connected to node j, and wij is a weight associated to thelink connecting node i to node j.
After the input value of a node has been computed, the
e-Baconcept maps with self-construction ability and automaticproblem-solving ability. The extended concept map iscalled Self-Associated Concept Map (SACM). SACMscan be automatically constructed and dynamically updatedfrom a knowledge repository with structural historicalrecords. A Constrained Fuzzy Spreading Activation(CFSA) model is incorporated in the SACM which enablesthe decision supporting function for providing rapid andautomatic decisions. With SACM, the capability of Knowl-edge-based systems (KBS) can be enhanced and extended.The paper starts by reviewing the related work and thendescribes the proposed SACM. The capability of theSACM is realized by a case study in a consultancy business.The results indicate that the proposed idea of SACM is wellsuited for KBS with real-world data.
2. A comparison between Traditional Concept Mapping and
Self-Associated Concept Mapping
2.1. Traditional concept maps
Concept map has its root from its relationship to mem-ory and learning theory. Semantic memory theory believesthat knowledge is stored in a network format where con-cepts are connected to each other . The more tightlyinterconnected the knowledge representation, the morelikely it is that a person will recall information at theappropriate time. As a result, a network representationcan be used to show the integration of dierent concepts.The theory has resulted in dierent terms being used todescribe concept maps including semantic networks[13,15] and knowledge maps .
In 1984, Novak proposed concept map to representknowledge . It is an instructional method that inte-grates new information into an old knowledge structure.It promotes conceptual understanding by displaying mean-ingful patterns of ideas. Knowledge is graphically displayedas a network of nodes and links. A concept map consists ofsets of propositions. Each proposition is made up of a pairof nodes and a link connecting them. The labeling of nodescontains the concepts. The labeling of the links providesinformation about the nature of the relationships. Cross-links sometimes appear to show the connections betweenand among concepts, create an interdisciplinary space forinquiry and learning, or provide examples for clarifyingthe meaning of a given concept. Concept maps are varyingon the basis of an individual area of interest and style. Fig. 1shows an example of concept map. There are propositionsin the concept map: (Concept Map consists of Concepts),(Concept Map consists of Relations), (Concepts denotedby Nodes), (Relations denoted by Links).
Several research studies have developed dierent meth-odologies to extend the usage of concept map. Lin et al. introduce a concept map focusing on the propositionswith weights, which is named weighted concept map.
W.M. Wang et al. / KnowledgChen et al.  proposed an extended concept maps calledattributed concept maps (ACM). ACM associates itsconcept nodes and relation links with attribute valueswhich indicate the relative signicance of concepts andrelationships in knowledge representation. A Two-PhaseConcept Map Construction (TP-CMC) algorithm is pro-posed by Sue et al.  to automatically construct a con-cept map of a course by historical testing records. Theyapply Fuzzy Set Theory to transform the numeric testingrecords of learners into symbolic, apply Education Theoryto further rene it, and apply Data Mining approach tond its grade fuzzy association rules. Then, they use multi-ple rule types to further analyze the mined rules and a heu-ristic algorithm is proposed to automatically construct theconcept map according to the results of the analysis.
Recently, more and more researches are applying con-cept maps on knowledge management. Concept mappingis provided as a knowledge management tool so thatconcepts can be captured, queried, and perhaps mostimportantly connections discovered and reasoned about. Current research work is focusing on the constructionof theoretical frameworks and design of humanmachineinterfaces (e.g. [19,26]). They provide tools for creating cus-tom templates, publishing the maps as web pages, associat-ing documents and URLs with concepts and some queryand search capabilities. However, this is insucient for per-forming such knowledge management activities since mostof the work is still relied on human being. It seeks for a toolwith the ability to automatically discover implicit connec-tions, generate new maps, maintain evolution of maps, rea-soning, and inferencing.
In order to support the automatic inference of concept
Fig. 1. An example of concept map.
sed Systems 21 (2008) 5261 53activation level of the node is determined by a function ofthe input:
until a termination condition has been met.
nodes and the degree of importance of conceptis assigned.
If the value of elds of the new record is sym-bolic, a concept node is added and its corre-sponding degree of importance of the addedconcept is assigned to be 1.
If the value of elds of the new record is numeric,more than one concept nodes may be addedaccording to the value. For example, if the valueis Quantity (0.7 High, 0.2 Medium, 0 Low),then two new concept nodes: Quantity: Highand Quantity: Medium are added. The corre-sponding degree of importance of the added con-cepts Quantity: High and Quantity:Medium are 0.7 and 0.2, respectively.
Assign the degree of importance of relation foreach pair of concepts.
Step 2: Combining the temporary SACM with the originalSACM.
-Baset theory on measuring the grading of the historicalrecords, while SACM applies fuzzy set theory on dividingthe concepts within the historical records which increasethe ability of inference. For knowledge inference, a newmodel named Constrained Fuzzy Spreading Activation(CFSA) is proposed. It integrates fuzzy logic and CSA soas to provide more precise, rapid and automatic solutions.
2.2. Self-Associated Concept Mapping
2.2.1. Knowledge representation
The graphical representation provides insights fordescribing the relationships among dierent knowledgeconcepts. A SACM is represented by a simple graph withnodes and edges. The nodes represent concepts relevant toa given domain and the association relationships betweenthem are depicted by directed edges. An example of SACMis shown in Fig. 2. The importance of the concepts and theassociations between dierent concepts are indicated by thedepth of color i.e. darker color indicates higher importance.(The detail symbolic representation of knowledge represen-tation, knowledge elicitation, and knowledge inference isput in the appendix for interested readers.)
2.2.2. Knowledge elicitation
With the advanced development of computer technolo-gy and Knowledge-based system (KBS) in the recent dec-ade, organizations are able to record the workingactivities of each worker at a dramatically lower cost. SomeKBSs have been developed to serve this purpose. Theknowledge of knowledge workers can be assimilated andThe most salient fault of pure SA is that the activationtends to quickly spread over the entire network . Theshortcoming can be partially overcome by the implementa-tion of rules to control the activation. This new model iscalled Constrained Spreading Activation (CSA). Somecommon constraints are distance constraint, fan-out con-straint, path constraint and activation constraint .
In this paper, the authors attempt to propose a newextended concept map: Self-associated Concept Map(SACM). It has a knowledge representation which is simi-lar to the ACM mentioned above. Contrasting to manuallyconstructed ACM, SACM can be automatically construct-ed and dynamically updated from a knowledge repositorywith structural historical records. On the other hand, theautomatic construction method of SACM is dierent toTP-CMC that mentioned above. TP-CMC applies fuzzyAj f I j 2where Aj is the activation level of node j, f is the activationfunction, and Ij is the input of node j.
The output of the node, Oj, is usually its activation level,Aj. The output value of the node is red to all nodes con-nected to it. Hence, the activation spreads pulse after pulse
54 W.M. Wang et al. / Knowledgestored in a structured format into the knowledge reposito-ries of KBSs when they use the KBSs for performing theirdaily work . This enables the oer of vast new mines ofinformation on individual working knowledge automati-cally and objectively. By following the learning theory,individuals abilities to work depend on whether they havean appropriate concept map of working. In the proposedapproach, the concept map of each individual is construct-ed based on the information in the knowledge repositoriesof the KBS and it enables dynamic update by adding newrecords to the knowledge repository.
The elicitation algorithm consists of 3 steps:
Step 1: Constructing a temporary SACM based on theinputs of the new record. Distinct concepts are extracted from the newrecord for the construction of a set of concept
Fig. 2. An example of SACM.
sed Systems 21 (2008) 5261 The nodes and relations of the temporarySACM are matched with that of the original
the temporary SACM.
activation level is computed by defuzziion by the
Product Type contains symbolic values. Diameter and UnitPrice contain numerical values. The membership functionsof Diameter and Unit Price are shown in Figs. 3 and 4,respectively. In this example, Diameter is represented by3 fuzzy regions which are Small, Medium and Large,respectively. The Unit Price is represented by 3 fuzzyregions which are Low, Medium and High, respectively.
In order to construct a new SACM, all distinct conceptsfrom the rst record are rstly extracted for the construc-tion of a set of concept nodes C, the set of degrees ofimportance of concept F are assigned, and the set ofdegrees of importance of relations L for each pair of con-cepts are assigned, based on the step 1 of knowledge elici-tation that described in Section 2.2.2. The results are shown
Table 1A simplied knowledge repository
Case ID Product type Diameter Unit Price
1 Prototype Lens 7 14002 Mould Insert 12 2000
Fig. 4. The membership functions of Unit Price.
Table 2Temporary results of SACM that assimilates 1 record
e-Based Systems 21 (2008) 5261 55centre of gravity (COG) method. If the extracted concept node is symbolic, theconcept node with the highest activation level isselected to be the result.
2.4. An application example
In this section, an application example is used to illus-trate the proposed methodology. This is a simple exampleto show how a SACM is constructed and how a SACMinfers quantitative prediction. Table 1 shows a simpliedknowledge repository that stores 2 quotation records. EachStep 3: The parameters of the combined SACM is adjustedand the comb...