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The meaning of similarity always depends on the underlying context of a particular application, and it does not convey a xed characteristic that applies to any comparative context. In CBR, the computation of similarity becomes a very important issue in the case retrieval process. The effectiveness of a similarity measurement is determined by the usefulness of a retrieved case in solving a new problem. Therefore, establishing an appropriate similarity function is an attempt at handling the deeper or hidden relationships between the relevant objects associated with the cases. There are (broadly) two major retrieval approaches [9]. The rst is based on the computation of distance between cases, where the most similar case is determined by evaluation of a similarity measure (i.e., a metric). The second approach is related more to the representational/indexing structures of the cases. The indexing structure can be traversed to search for a similar case. We describe next the basic concepts and features of some of the distance measures used in this regard. 3.2.1 Weighted Euclidean Distance



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A central function of the grid is to provide real power requirements of the load The real power loads at the substations are indicated by the letter P For example, at substation S1 the real power requirement is 900 MW In the schematic in Figure 37 there are eight generators within the control area and three generators outside the control area The control area is the region within the dotted lines The real power generated by each generator is indicated by the accompanying letter P In addition to the generators and distribution buses within the schematic, there are generators and load centers in neighboring control areas that in uence the delivery system but are not a part of the schematic The transmission system is necessary for providing real power to load Transmission systems must be designed to perform this ef ciently.





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ever, because of the relation Ksp(AgCl) = a(Ag+)a(Cl ), the potential is determined by the activity of the chloride ion: E E 0 Ag =Ag 0:0592 log Ksp 0:0592 log a Cl E 0 AgCl=Ag 0:0592 log a Cl 25 8C where E0(AgCl/Ag) is the standard potential of the silver-silver chloride electrode. The silver-silver chloride electrode is an indicator electrode for chloride ion activity (or concentration). However, more importantly, the silver-silver chloride electrode in saturated (or 3.5 M) KCl is the most popular reference electrode (see below).

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partition of S into k clusters by assigning each point to the point in T that is the closest and breaking the ties using a xed (but otherwise arbitrary) order on the set of points The clustering function de ned by (d, g), denoted by f g maps d to this partition The k-median clustering function is obtained by choosing g(x) = x for x R 0 ; the k-means clustering function is obtained by taking g(x) = x2 for x R 0 De nition 9 Let be a partition of S and let d, d DS The de nite dissimilarity d is a -transformation of d if the following conditions are satis ed: (i) If x y, then d (x, y) d(x, y); (ii) If x y, then d (x, y) > d(x, y).

Many transaction data sets produce huge number of frequent item sets, and therefore, huge number of association rules particularly when the levels of support and con dence required are relatively low. Moreover, it is well known (see the work by Tan et al. [17]) that limiting the analysis of association rules to the support/con dence framework can lead to dubious conclusions. The data mining literature contains many references that attempt to derive interestingness measures for association rules in order to focus data analysis of those rules that may be more relevant (see, other works [4,6,8,11,12,16]).

In other words, d is a -transformation of d if for two objects that belong to the same -cluster d (x, y) is smaller than d(x, y), while for two objects that belong to two distinct clusters d (x, y) is larger than d(x, y) Next, we consider three desirable properties of a clustering function De nition 10 Let S be a set and let f : DS PART(S) be a clustering function.

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