barcode in vb.net 2010 The KBANN Algorithm in Software

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1231 The KBANN Algorithm
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The KBANN algorithm exemplifies the initialize-the-hypothesisapproach to using domain theories It assumes a domain theory represented by a set of propositional, nonrecursive Horn clauses A Horn clause is propositional if it contains no variables The input and output of KBANN are as follows:
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KBANN(Domain-Theory, Training_Examples) Domain-Theory: Set of propositional, nonrecursive Horn clauses TrainingJxamples: Set of (input output) pairs of the targetfunction Analytical step: Create an initial network equivalent to the domain theory 1 For each instance attribute create a network input 2 For each Horn clause in the Domain-Theory, create a network unit as follows: 0 Connect the inputs of this unit to the attributes tested by the clause antecedents For each non-negated antecedent of the clause, assign a weight of W to the corresponding sigmoid unit input For each negated antecedent of the clause, assign a weight of -W to the corresponding sigmoid unit input 0 Set the threshold weight wo for this unit to -(n - 5)W, where n is the number of non-negated antecedents of the clause 3 Add additional connections among the network units, connecting each network unit at depth i from the input layer to all network units at depth i 1 Assign random near-zero weights to these additional connections Inductive step: Refine the initial network 4 Apply the BACKPROPAGATION algorithm to adjust the initial network weights to fit the Training-Examples
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TABLE 122 The KBANN algorithm The domain theory is translated into an equivalent neural network (steps algorithm (step 4) A typical value 1-3), which is inductively refined using the BACKPROPAGATION for the constant W is 40
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Given:
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A set of training examples A domain theory consisting of nonrecursive, propositional Horn clauses
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Determine:
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An artificial neural network that fits the training examples, biased by the domain theory
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The two stages of the KBANN algorithm are first to create an artificial neural network that perfectly fits the domain theory and second to use the BACKPROPACATION algorithm to refine this initial network to fit the training examples The details of this algorithm, including the algorithm for creating the initial network, are given in Table 122 and illustrated in Section 1232
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1 232
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An Illustrative Example
To illustrate the operation of KBANN, consider the simple learning problem summarized in Table 123, adapted from Towel1 and Shavlik (1989) Here each instance describes a physical object in terms of the material from which it is made, whether it is light, etc The task is to learn the target concept Cup defined over such physical objects Table 123 describes a set of training examples and a domain theory for the Cup target concept Notice the domain theory defines a C u p
Domain theory:
Cup t Stable, Lzpable, OpenVessel Stable t BottomIsFlat Lijiable t Graspable, Light Graspable t HasHandle OpenVessel t HasConcavity, ConcavityPointsUp
Training examples:
cups BottomIsFlat ConcavitjPointsUp Expensive Fragile HandleOnTop HandleOnSide HasConcavity HasHandle Light MadeOfCeramic MadeOfPaper MadeOfstyrofoam Non-Cups
J J J J J J J J J
J J J J J J
J J J
J J J
J J J J
2 / 4 4 J J J J J J J J J J J J J J J J J J J
J J J J J J J J J
TABLE 123 The Cup learning task An approximate domain theory and a set of training examples for the target concept Cup
as an object that is Stable, Liftable, and an OpenVessel The domain theory also defines each of these three attributes in terms of more primitive attributes, tenninating in the primitive, operational attributes that describe the instances Note the domain theory is not perfectly consistent with the training examples For example, the domain theory fails to classify the second and third training examples as positive examples Nevertheless, the domain theory forms a useful approximation to the target concept KBANN uses the domain theory and training examples together to learn the target concept more accurately than it could from either alone In the first stage of the KBANN algorithm (steps 1-3 in the algorithm), an initial network is constructed that is consistent with the domain theory For example, the network constructed from the Cup domain theory is shown in Figure 122 In general the network is constructed by creating a sigmoid threshold unit for each Horn clause in the domain theory KBANN follows the convention that a sigmoid output value greater than 05 is interpreted as True and a value below 05 as False Each unit is therefore constructed so that its output will be greater than 05 just in those cases where the corresponding Horn clause applies For each antecedent to the Horn clause, an input is created to the corresponding sigmoid unit The weights of the sigmoid unit are then set so that it computes the logical AND of its inputs In particular, for each input corresponding to a non-negated antecedent,
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