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severe for small training sets In these cases, a k-fold cross-validation approach is sometimes used, in which cross validation is performed k different times, each time using a different partitioning of the data into training and validation sets, and the results are then averaged In one version of this approach, the m available examples are partitioned into k disjoint subsets, each of size m/k The crossvalidation procedure is then run k times, each time using a different one of these subsets as the validation set and combining the other subsets for the training set Thus, each example is used in the validation set for one of the experiments and in the training set for the other k - 1 experiments On each experiment the above cross-validation approach is used to determine the number of iterations i that yield the best performance on the validation set The mean i of these estimates for i is then calculated, and a final run of BACKPROPAGATION is performed training on all n examples for i iterations, with no validation set This procedure is closely related to the procedure for comparing two learning methods based on limited data, described in 5
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47 AN ILLUSTRATIVE EXAMPLE: FACE RECOGNITION
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To illustrate some of the practical design choices involved in applying BACKPROPAGATION, section discusses applying it to a learning task involving face recognithis tion All image data and code used to produce the examples described in this section are available at World Wide Web site http://wwwcscmuedu/-tomlmlbook html, along with complete documentation on how to use the code Why not try it yourself
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The learning task here involves classifying camera images of faces of various people in various poses Images of 20 different people were collected, including approximately 32 images per person, varying the person's expression (happy, sad, angry, neutral), the direction in which they were looking (left, right, straight ahead, up), and whether or not they were wearing sunglasses As can be seen from the example images in Figure 410, there is also variation in the background behind the person, the clothing worn by the person, and the position of the person's face within the image In total, 624 greyscale images were collected, each with a resolution of 120 x 128, with each image pixel described by a greyscale intensity value between 0 (black) and 255 (white) A variety of target functions can be learned from this image data For example, given an image as input we could train an ANN to output the identity of the person, the direction in which the person is facing, the gender of the person, whether or not they are wearing sunglasses, etc All of these target functions can be learned to high accuracy from this image data, and the reader is encouraged to try out these experiments In the remainder of this section we consider one particular task: learning the direction in which the person is facing (to their left, right, straight ahead, or upward) I
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Network weights after 100 iterations through each training example
FIGURE 410 Learning an artificial neural network to recognize face pose Here a 960 x 3 x 4 network is trained on grey-level images of faces (see top), to predict whether a person is looking to their left, right, ahead, or up After training on 260 such images, the network achieves an accuracy of 90% over a separate test set The learned network weights are shown after one weight-tuning iteration through the training examples and after 100 iterations Each output unit (left, straight, right, up) has four weights, shown by dark (negative) and light (positive) blocks The leftmost block corresponds to the weight wg, which determines the unit threshold, and the three blocks to the right correspond to weights on inputs from the three hidden units The weights from the image pixels into each hidden unit are also shown, with each weight plotted in the position of the corresponding image pixel
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