Simple applications of neural nets 1 Character recognition 2
Character recognition 3 Backpropagation issues 4
Backpropagation issues 5 Demonstration - classification of crabs 6 In this demo, we will train a neural network to classify rock crabs as either male or female. The data was taken from Campbell & Mahon (1974) and is contained within the Excel worksheet "Crab Data". There are 5 male and 5 female specimens for each of two species (blue form and orange form) for a total of 2 specimens. The columns labeled "Species", "Frontal Lip", "Rear Width", "Length", "Width", and "Depth" will serve as inputs to the neural network and the columns labeled "Male" and "Female" will serve as the desired outputs. versus.7.6.5.4.3 Training Cross Validation.2.1 1 2 39 58 77 96 115 134 153 172 191
Demonstration - classification of crabs 7 Tested with the training examples Output / Desired Male Female Male 65.. Female 1. 54. Tested with unseen test examples Output / Desired Male Female Male 21.. Female 2. 27. Demonstration - classification of crabs Training process with different set of initial weights 8 versus.7.6.5.4.3 Training Cross Validation.2.1 1 2 39 58 77 96 115.7 134 153 172 191.6 versus.5.4.3 Training Cross Validation.2.1 1 2 39 58 77 96 115 134 153 172 191
Demonstration - breast cancer data 9 This demo will develop a model for diagnosing breast cancer. Ten features (radius, texture, perimeter, area, smoothness, compactness, concavity, concave points, symmetry, and fractal dimension) have been computed from a digitized image of a fine needle aspirate of a breast mass. The inputs to the neural network model consist of the mean, standard error, and "worst" (mean of the three largest values) for each of these 1 features resulting in 3 total inputs for each image. This data is contained within the Excel worksheet named "Breast Cancer Data" located behind this slide. The first 3 columns have been pretagged as "Input", the last 2 columns have been pre-tagged as "Desired", and the first 1 rows have been pre-tagged as "Training". A two hidden layer MLP will be used as the neural network model. Train a network multiple times with the same set of data to extract the best possible mapping and set of parameters. Training 1.7.6.5.4.3.2.1 Run #1 Run #2 Run #3 Run #4 Run #5 1 5 9 13 17 21 25 29 33 37 41 Training 45 49.8.7.6.5.4.3.2 Run #1 Run #2 Run #3 Run #4 Run #5.1 1 5 9 13 17 21 25 29 33 37 41 45 49
Demonstration - iris plant classification 11 The problem for this demo is to develop a neural network classifier for classifying Iris plants as one of three distinct types. The inputs to the network are sepal length, sepal width, petal length, and petal width (all in cm) and the three classes of Iris plants (which are used as the desired outputs) are Setosa, Versicolour, and Virginica. There are 5 samples of each class for a total of 15 samples. The 15 samples have been pre-randomized. Furthermore, 1 samples have been tagged as "Training" and 5 samples have been tagged as "Testing". This data is contained within the worksheet named "Iris Data Randomized" located behind this slide. Average Training for 3 Runs 12 Average.7.6.5.4.3.2.1 Hidden 1 PEs = 1 Hidden 1 PEs = 2 Hidden 1 PEs = 3 Hidden 1 PEs = 4.7.6 Average Training for 3 Runs 1 5 9 13 17 21 25 29 33 37 41 45 49 Average.5.4.3.2.1 Hidden 1 PEs = 1 Hidden 1 PEs = 2 Hidden 1 PEs = 3 Hidden 1 PEs = 4 1 5 9 13 17 21 25 29 33 37 41 45 49
13 Testing of the network Output / Desired Setosa Versicolour Virginica Setosa 14... Versicolour. 22.. Virginica. 1. 13. Testing a linear network Output / Desired Setosa Versicolour Virginica Setosa 13... Versicolour 1. 7.. Virginica. 16. 13. Sensitivity study 14 In this demo we will develop a model for real estate appraisal in the Boston area. We will use 13 indicators as inputs to this model. These indicators are per capita crime rate by town (CRIM), proportion of residential land zoned for lots over 25, sq.ft. (ZN), proportion of nonretail business acres per town (INDUS), bounds Charles River (CHAS), nitric oxides concentration (NOX), average number of rooms per dwelling (RM), proportion of owner-occupied units built prior to 194 (AGE), weighted distances to five Boston employment centers (DIS), index of accessibility to radial highways (RAD), full-value property-tax rate per $1, (TAX), pupil-teacher ratio by town (PTRATIO), 1(Bk -.63)^2 where Bk is the proportion of blacks by town (B), % lower status of the population (LSTAT). The desired output for this model is the Median value of owner-occupied homes (in $1's). There are 4 total samples. Three hundred of them have been tagged as "Training" and the other 1 have been tagged as "Testing".
Sensitivity study 15 Desired Output and Actual Network Output 6 5 4 Output 3 2 1 1 1 19 28 37 46 55 64 73 82 91 1 Exe m plar MEDV Desired MEDV Output Sensitivity study 16 Sensitivity About the Mean 4. 3.5 3. Sensitivity 2.5 2. 1.5 1. MEDV.5. CRIM ZN INDUS CHAS NOX RM AGE DIS RAD TAX PTRATIO B LSTAT Input Name Notice that according to the sensitivity analysis, the six most important inputs are whether the property bounds the Charles River (CHAS), nitric oxides concentration (NOX), average number of rooms per dwelling (RM), weighted distances to five Boston employment centers (DIS), pupil-teacher ratio by town (PTRATIO), and % lower status of the population (LSTAT).
D esired Output and Actual N etw ork Output 17 6 5 Seven most important features Output 4 3 2 MEDV MEDV Output 1 1 1 19 28 37 Desired 46 55Output 64 and 73 Actual 82 91 Network 1 Output Exemplar 6 5 4 Output 3 2 All features 1 MEDV Desired 1 1 19 28 37 46 55 64 73 82 91 1 MEDV Output Exe m plar