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A connectionist approach for similarity assessment in case-based reasoning systems

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A connectionist approach for similarity assessment in case-based reasoning systems
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  ELSEVIER Decision Support Systems 19 (1997) 237-253 r 0o s sy ms A connectionist approach for similarity assessment in case-based reasoning systems Kalyan Moy Gupta a b Ali Reza Montazemi b a Atlantis Aerospace Corporation, 1 Kenview Boulevard, Brampton. Ontario. Canada. L6T 5E6 Michael G. DeGroote School ~f Business, McMaster Unieersity Hamilton, Ontario, Canada. LSS 4M4 Accepted 9 September 1996 Abstract Case-Based Reasoning (CBR) systems support ill-structured decision making. In ill-structured decision environments, decision makers (DMs) differ in their problem solving approaches. As a result, CBR systems would be more useful if they were able to adapt to the idiosyncrasies of individual decision makers. Existing implementations of CBR systems have been mainly symbolic, and symbolic CBR systems are unable to adapt to the preferences of decision makers (i.e., they are static). Retrieval of appropriate previous cases is critical to the success of a CBR system. Widely used symbolic retrieval functions, such as nearest-neighbor matching, assume independence of attributes and require specification of their importance lbr matching. To ameliorate these deficiencies connectionist systems have been proposed. However, these systems are limited in their ability to adapt and grow. To overcome this limitation, we propose a distributed connectionist-symbolic architecture that adapts to the preferences of a decision maker and that, additionally, ameliorates the limitations of symbolic matching. The proposed architecture uses a supervised learning technique to acquire the matching knowledge. The architecture allows the growth of a case base without the involvement of a knowledge engineer. Empirical investigation of the proposed architecture in an ill-structured diagnostic decision environment demonstrated a superior retrieval performance when compared to the nearest-neighbor matching function. © 1997 Elsevier Science B.V. Keywords: Case-based reasoning; Adaptive decision support systems; Connectionist networks; Information etrieval I. Introduction The paradigm of Case-Based Reasoning (CBR) has been used effectively in domains where decision problems are open ended and where no clear cut methods are available to solve them [ 19,31,42,49,65]. A CBR system reasons by remembering previous decision problems: it uses their outcome to evaluate new decision problems [34]. The processes followed * Corresponding author. Email: kgupta@atlantis.com. by a CBR system is as follows [53,62]: to assist a decision maker (DM), previous case(s) that closely resemble the new decision problem (new case) is(are) retrie~ ed. The solution of the previous case is then mapped as a solution for the new case. The mapped solution is adapted to account for the differences between a new case and a previous case. For future decision making, feedback of the success or failure of the solution is obtained from the DM. CBR systems support individual DMs faced with ill-structured decision problems. Ill-structured deci- sion problems are characterized by a large number of 0167-9236/97/ 17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0167-9236(96)00063-2  238 K.M. Gupta, A.R. Montazemi / Decision Support Systems 19 1997) 237-253 variables, incomplete information, and uncertainty of relationships among these variables. As a result, cut-and dried solution techniques for these problems do not exist, and solutions cannot be characterized as right or wrong [44,60]. In such decision environ- ments, DMs differ in their approaches to problem solving [37,41,43]. Therefore, DSSs that adapt to the idiosyncrasies of individual DMs are most desirable [39]. Existing implementations of CBR are mainly symbolic. However, symbolic CBR systems are static: they are unable to adapt to the preferences of DMs. The measure of the success of a CBR system depends on its ability to retrieve the most relevant previous cases in support of the solution of a new case [47]. One of the methodologies widely used in existing symbolic CBR systems to retrieve previous cases is that of the nearest-neighbor (NN) matching function [30]. The NN matching function is based on assumptions of the independence of attributes in previous cases and the availability of rules and pro- cedures for matching. However, little has been done to verify these assumptions in domains in which CBR has been applied [28]. Connectionist systems have been proposed to ameliorate deficiencies inherent in symbolic match- ing systems [5,67]. However, existing connectionist implementations of CBR systems are limited in their ability to grow and adapt. In this paper, we present a combination of connectionist and symbolic architec- ture that adapts to the preferences of DMs and that additionally ameliorates the assumptions of symbolic matching. An empirical investigation of our pro- posed connectionist architecture was performed by developing a CBR application for diagnosis and repair of A.C. motors. The remaining paper is structured as follows. In Section 2, we provide a brief overview of the methodologies for retrieving previous cases and the assumptions that underlie the existing retrieval methodologies. Section 3 provides an overview of connectionist retrieval methodologies. Section 4 pre- sents the proposed connectionist architecture for matching in a CBR system. Section 5 describes the empirical evaluation of the connectionist architec- ture. Findings of the empirical evaluation are pre- sented in Section 6 and are discussed in Section 7. Section 8 concludes the paper. 2 Retrieval in CBR systems The aim of case-based retrieval is to retrieve previous cases of most use towards solution of a new decision problem and to ignore irrelevant previous cases [32,36]. Retrieval in CBR consists of the fol- lowing steps (see Fig. 1): Based on a description of the new decision problem (i.e., the new case) the case-base is searched for candidate previous cases that have a potential to provide decision support. Searching increases the efficiency of the retrieval because only a subset of the case-base is examined. However, the effectiveness of the selection process toward choice of the most appropriate previous cases (i.e., the most appropriate cases may not be re- trieved) is not guaranteed. Effectiveness of retrieval is based on the matching process. 2 1 Matching Matching assesses the degree of similarity of a candidate previous case with a new case as follows: case can be considered as a schema that consists of a set of attribute value pairs (i.e., descriptors) [18,30]. For example, in a credit assessment decision sce- nario, a Loan Manager assesses several descriptor pairs (e.g., descriptor Character of the applicant has a value of average ). Matching involves establishing the similarity of the schema of the new case with the Description of the New Case Search for Candidate Prey ous cases Ranking of Candidate j Previous cases Fig. 1. Component processes in CBR retrieval.  K.M. Gupta, A.R. Montazemi / Decision Support Systems 19 1997) 237-253 39 schema of the previous case (e.g., See SIZZLE [45]). Matching proceeds as follows (see Fig. 1). First, the pair-wise similarity along the descriptors of the schemata of the new case and the previous case is assessed. Similarity of schemata of two cases along descriptors can be assessed using domain knowledge in the form of heuristics and domain specific matching rules (e.g., JULIA [33], and PRO- TOS [50,63]). For example, a matching rule deter- mines that the descriptor color of the object with value orange is very similar to the descriptor with value red. Second, a matching function is used to assess the overall similarity of the schemata of a new case with a previous case. Here, we focus on methodologies for assessing overall similarity. The overall similarity of a new case with the previous case is assessed by aggregation of pair-wise similarity along descriptors. Overall similarity can be determined by the follow- ing two functions: (1) Tversky s matching function [69], and (2) Nearest-Neighbor (NN) matching func- tion [15]. Tversky s matching function has been ap- plied successfully in a CBR system for model man- agement [48]. However, it has not been used in other domains because the pair-wise similarity is consid- ered as binary and does not incorporate domain knowledge. In complex ill-structured decision prob- lems, the use of domain knowledge is necessary for good retrieval performance of the CBR system [7], [20]. Therefore, in this paper, we do not consider the Tversky s matching function. The NN matching function incorporates domain knowledge and has been widely used in the existing CBR systems (e.g., [10,14,25,30]). The overall simi- larity (OS) determined by NN matching function is mathematically represented as follows: ~ ~w sim(a~ ap* osNN (n,pk) : ,, , (1) Y , wi i=l where, a~ is the ith descriptor of the new case; a p~ is the ith descriptor of the kth candidate previous case; the superscripts n and p refer to the new case and the previous case respectively; sire(-) is a func- tion, rule, or heuristic that determines the pair-wise similarity along a descriptor; and w i is the weight representing degree of importance of the ith descrip- tor towards the decision problem. The NN matching function is based on four as- sumptions. The first assumption is in regard to the mutual independence of descriptors of a case, and the next three assumptions are related to the use and acquisition of weights in NN matching function. These four assumptions are as follows: 1. The linear combination assumes mutual indepen- dence of the descriptors of a case, and that the overall similarity is an additive combination of pair-wise similarity. However, the goal of CBR is to support ill-structured decision making in do- mains where descriptors have complex interrela- tionships. Under these circumstances, the number of descriptors and their possible values are poten- tially large, and the matching along descriptors is fuzzy and partial. Often, the dependence among descriptors is conditional on their values. There- fore, in order to reduce their effect on the assess- ment of overall similarity, statistical techniques cannot be used for determining these dependen- cies. For example, let us consider a complex decision domain such as the problem of diagnos- ing an A.C. motor fault. In a domain of this complexity the troubleshooter has to consider multiple faults scenarios. In these types of envi- ronments, non-linearity can arise when matching a previous case with multiple faults, such as Damaged Shaft and Overload . Since Over- load is sometimes) caused by Damaged Shaft , they are related. Hence for this previous case, the feature Overload is of greater importance when Damaged Shaft is investigated. Errors can be introduced when using a linear combination of pair-wise similarity because relationships among descriptors can be ignored [22]. Therefore, a matching technique that can deal with non-linear relationships among the descriptors would be most useful. 2. The importance of descriptors is acquired by a knowledge engineer from experts or by a machine learning technique such as explanation-based learning [7,12]. A heuristic is used to transform the subjective notion of importance into numbers, and trial and error is used to refine these numbers to give a satisfactory performance. The underly-  240 K.M. Gupta, A.R. Montazemi / Decision Support Systems 19 1997) 237-253 ing assumption is that the DM can provide an explanation of the degree of importance of a descriptor. However, the goal of CBR is to sup- port ill-structured decision making where domain knowledge is noisy and weak. Therefore, it is difficult for a DM to provide an accurate assess- ment of the degree of importance of pertinent descriptors. The question arises whether it is pos- sible to determine the importance of weights without explicit input from the DM. 3. In the existing CBR systems, the weights used are always positive. This is because of the singular emphasis on similarity. However, it would be much more useful if the presence of a descriptor in the new case that had an adverse effect on the usefulness of a candidate previous case be weighted negatively. This is similar to the notion of confirmatory and disconfirmatory evidence in evidential reasoning systems [57]. Evidential rea- soning has been incorporated into CBR systems, in part, by including deep knowledge in form of validity constraints [17,58,68] censors [50], exclu- sion criteria [30] and causal models [35]. How- ever, such systems assume that the constraints, censors, and exclusion criteria are known with certainty. Furthermore, the application of more than one constraint is not considered and the assumption is that constraints are independent of each other. For instance, in the A.C. motors deci- sion domain, a previous case of overheating and tripping is considered appropriate towards the diagnosis of a motor of 'size' medium when the value of descriptor 'voltage drop' is greater than 15 of rated voltage and the value of descriptor 'current drawn' is greater than 10 of the rated current. However, these constraints take on differ- ent degrees of importance when the appropriate- ness of the same previous case toward a new case with a motor of 'size' large is assessed. This is because of the interrelationship of constraints on descriptors 'voltage drop' and 'current drawn' with the descriptor 'motor size'. Accurate assess- ment of these constraints is difficult due to their interrelationships with other descriptors. The question is how might we take into account the interaction effect among constraints. 4. It is not only the similarity between the new case and the previous case that determines usefulness of a previous case towards a new case, but also the similarities and differences among the candi- date previous cases [1]. Therefore, the usefulness of a previous case towards solution of the new case is dependent on the presence of other candi- date previous cases (i.e., matching is competitive). For instance, in the domain of A.C. motors, a previous case explaining 'failure of thermal pro- tection mechanism' with a higher degree of over- all similarity is considered secondary to a previ- ous case with lower degree of overall similarity that explains 'winding failure'. The underlying reason is that 'winding failure' is considered as a catastrophic failure, and 'failure of thermal pro- tection mechanism' a failure of less severity. In addition, these failures can have common causes. Matching techniques in most existing CBR sys- tems assume that each candidate previous case is independent of the other. The interrelationship of previous cases is considered in HYPO by compar- ing them with each other based on each of the descriptors necessary to partially order the candi- date previous cases [2]. However, this methodol- ogy has not been used in other application do- mains because of the difficulties inherent in deter- mining the basis of ordering. Likewise, in PRO- TOS, explicit difference links are traversed to explain the new case [3]. Nonetheless, these dif- ferences are not used to determine the importance of descriptors in the context of a new case. The question arises as to what methodologies can be used to determine importance weights that take into consideration the presence of other candidate previous  K.M. Gupta, A.R. Montazemi / Decision Support Systems 19 1997) 237 253 241 means to capitalize on strengths and overcome weak- nesses [25,70]. In the following section, we provide a brief overview of connectionist networks. 3. Connectionist networks Connectionist networks are composed of rela- tively simple, neuron-like processing elements that store their knowledge in the strengths of connections between processors [26]. The connectionist networks are based on an analogy with the biological structure of the brain which functions as a highly complex, non-linear, parallel information processing system [54]. The capabilities of connectionist networks in- clude: 1) the ability to determine non-linear rela- tionships among objects descriptors) in a domain; 2) to map a set of inputs to a set of outputs; 3) to learn or adapt to the changes in environment by alteration of connection strengths and by processing information that is incomplete and noisy; and 4) to incorporate the effect of contextual information [23]. These capabilities of connectionist networks can overcome the limitations of retrieval in symbolic CBR systems. Connectionist network representations can be cat- egorized as [26] see Fig. 2): 1) Localist, and 2) distributed. Localist representations are those in which each processing element corresponds to a meaningful concept i.e., descriptor), and each con- nection corresponds to a defined relationship. The localist representation is suitable for representing structured knowledge e.g., semantic networks [56]). In a distributed representation, each processing unit may correspond to many descriptors, and vice-versa. Consequently, the structure of a distributed network does not correspond to the structure of relationships among the descriptors. However, distributed net- works are capable of implicitly learning the relation- ships that best perform its intended function. Dis- tributed networks adapt their reasoning process to the decision environment by changing the strength of their connections. A number of learning procedures have been developed for distributed representations. In contrast, structured localist networks lack suitable learning methodologies [26]. A few implementations of connectionist based CBR systems are reported in the literature. However, these implementations use localist representation techniques, and thereby they do not learn or adapt to decision environments. An overview of the connec- tionist implementations of CBR systems is presented next. 3.1. Connectionist implementation of CBR systems The existing connectionist implementations of CBR systems have attempted to accomplish three objectives. The first objective was to improve the speed of retrieval and search. An example is PARADYME, which is a parallel implementation of its symbolic counterpart JULIA [33]. In a Localist representation b Distn~outed representation Reg..~ I ^ l Rel~ V c I ° ° I [ 2 I--[ . J [ ,, ][ Fig. 2. Categories of connectionist representation: a) Localist representation; b) Distributed representation.
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