By I. K. Sethi, Anil K. Jain
With the turning out to be complexity of development reputation comparable difficulties being solved utilizing synthetic Neural Networks, many ANN researchers are grappling with layout matters akin to the dimensions of the community, the variety of education styles, and function overview and boundaries. those researchers are always rediscovering that many studying methods lack the scaling estate; the systems easily fail, or yield unsatisfactory effects while utilized to difficulties of larger dimension. Phenomena like those are very common to researchers in statistical trend attractiveness (SPR), the place the
curse of dimensionality is a well known hindrance. concerns relating to the educational and try pattern sizes, function house dimensionality, and the discriminatory strength of other classifier varieties have all been commonly studied within the SPR literature. it sounds as if even though that many ANN researchers taking a look at development acceptance difficulties are usually not conscious of the binds among their box and SPR, and are for that reason not able to effectively make the most paintings that has already been performed in SPR. equally, many development acceptance and laptop imaginative and prescient researchers do not understand the potential for the ANN method of resolve difficulties equivalent to characteristic extraction, segmentation, and item acceptance. the current quantity is designed as a contribution to the larger interplay among the ANN and SPR examine groups
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Extra info for Artificial neural networks and statistical pattern recognition : old and new connections
H = 2; data set C: μτ = μ 2 ,£? = 4»'-1,i = 1,2, H = 8). 46 6. E F F E C T O F T H E N U M B E R O F N E U R O N S I N T H E H I D D E N L A Y E R ON T H E P E R F O R M A N C E OF A N N CLASSIFIERS It is obvious t h a t the classification error of an ideally trained neural network classifier cannot be increased by introducing new hidden layer neural elements. W i t h an increase in the number of hidden layer elements, the classification error of the ideally trained ANN classifier, P ^ , will fall sharply at first, then more slowly, and eventually, the addition of new elements will not effect P^.
Examples of such activation functions are hard limiting or soft limiting threshold functions and Huber's and Tukey's functions . T h e neurons in t h e input layer correspond to the components of t h e feature vector to be classified. In the feedforward network which will be discussed here, the inputs to the neurons in each successive layer are the outputs of the preceeding layer. T h e neurons in the output layer are usually associated with p a t t e r n class labels. T h e important design issues in building an ANN classifier are to find an appropriate network topology (number of hidden layers, number of neurons in each layer) and to learn the weights w^ for each neuron from t h e given training samples.
Let yi be t h e actual output and o, be the desired output of t h e ith neuron in the output layer of ANN. T h e most popular error function is the mean square error function defined as M SE = £ £ <ν» - °ο·) = Σ Σ(κ; - %·)2' j=li=l j=lt=l (2) where n is t h e number of training samples, p is t h e number of neurons in the output layer, and ε(·) denotes the error function. T h e ANN classifier can be analyzed as a special case of statistical p a t t e r n classifiers which are "data-driven", in the same spirit as Parzen-window classifiers and K-NN classifiers .