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A three -layer network used in forecasting
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Figure 33 Three-layer network used in forecasting
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The disadvantages of having too many hidden nodes (two times the inputs and above) are excessive training time and memorization of training patterns Since hidden nodes are one of the parameters that may play a role in ANN performance, we try two con gurations one with the number of hidden nodes equal to the number of inputs 1, and the other with the number of hidden nodes equal to twice the number of inputs 1 After some initial experimentation (experiment #1), we identify a better con guration and use it for our DEA-based data preprocessing experimentation (experiment #2) We do admit that better designs, in terms of selecting the number of hidden nodes, are possible but such issues are considered beyond the scope of the current research ANNs are data-driven techniques; thus high-quality training data for the ANN implementation cannot be overstressed The quality and structure of the input data largely determine the success or failure of an ANN implementation High-quality data do not necessarily mean data that are free of noise (eg, errors, inaccuracies, outlying values) In fact, it has been shown that ANNs are highly noise tolerant in comparison to other forecasting methods A study comparing the forecasting performance of ANNs to linear regression under circumstances of varying data accuracy concluded that ANN-based forecasts were more robust as the data accuracy degraded Several studies point out the fact that, for ANNs, providing high-quality training input data is not as simple as cleaning inaccuracies from data or eliminating extreme outliers On the contrary, it has been suggested that a valuable technique for improving the quality of training data is to add noise to the network inputs The addition of noise is shown to strengthen the generalizability of ANNs, and the absence of noise in the training data forces the network to memorize speci c patterns rather than abstract the essential features from the examples
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There are three essential requirements for high-quality training data (1) the data should adequately represent the fundamental features that the network must detect in order to obtain correct outputs; (2) the training data set should provide suf cient variation to allow generalization and discourage memorization; and (3) the training data should not contain contradictory examples (ie, examples with identical inputs but different outputs) In regard to the rst and second requirements, we caution that pattern variations (noise), while helpful in the training process, must be controlled to avoid swamping the essential features in the input data The need to nd a balance between these two requirements has been described as the noise-saturation dilemma The dilemma can be expressed in terms of communications theory as follows: some xed dynamic range will always exist within which the components of a system can operate; that is, any signal below a certain baseline level will become lost in system noise, and any signal above a certain level will cause the components to become saturated at their maximum value To successfully resolve the noisesaturation dilemma, an ANN must be able to process the dominating patterns without allowing the weaker patterns to become lost in system noise At the same time, an ANN must be able to process weak patterns without allowing the dominating patterns to saturate the processing units There are several proposed approaches for training tasks in ANNs The various approaches can be grouped into the following categories: (1) statistical and other data analysis techniques, (2) data transformation and preprocessing, (3) analysis of feedback obtained by interpreting the connection weights, and (4) hybrid techniques It has been proposed that statistical and numerical approaches can be useful in selecting and preprocessing training data for ANNs One approach is to apply signi cant measures (correlation coef cients and plots) to assess the strength of the relationship between data elements; linear regression is used to examine the degree of contribution a candidate data element makes to the model as a whole In cases where two data elements are highly correlated, one of the elements is eliminated Another approach is to calculate correlation coef cients between the error terms of a model prediction and each individual unused candidate variable A high correlation between an unused variable and the error terms suggests that including that variable in the model might add explanatory power (resulting in improved ANN performance) Data aggregation approaches, such as the use of histograms, are proposed to facilitate inspection of the data These approaches sometimes reveal unusual characteristics or complex relationships and outliers in the data Stein pointed out that outliers and odd patterns in the data do not necessarily indicate that data should be eliminated or modi ed Such patterns can be indicators of important relationships in the data, and further analysis of these areas can lead to improved input selections as the ANN model is re ned Several other studies focused on training data transformation and preprocessing The studies included both formal (applying a nonlinear transform to nonnormal data) and heuristic approaches (If you are unsure about including a certain type of data,
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