Contents:<\/h3>\n\n- Application type<\/a>.<\/li>\n
- Data set<\/a>.<\/li>\n
- Neural network<\/a>.<\/li>\n
- Training strategy<\/a>.<\/li>\n
- Model selection<\/a>.<\/li>\n
- Testing analysis<\/a>.<\/li>\n
- Model deployment<\/a>.<\/li>\n<\/ol>\n<\/section>\n
\n1. Application type<\/h2>\n
The model predicts a binary variable (disease region or not). Therefore, this is a classification<\/a> project.<\/p>\nThe goal here is to model the probability that a region of trees presents wilt, conditioned on the image features.<\/p>\n<\/section>\n\n2. Data set<\/h2>\nData source<\/h3>\n
The\u00a0dataset<\/a> comprises a data matrix, where<\/span>\u00a0columns represent variables and rows represent instances.<\/p>\nThe data file tree_wilt.csv<\/a> contains the information for creating the model. Here, the number of variables is 6, and the number of instances is 574.<\/p>\nVariables<\/h3>\n
The total number of variables<\/a> is 6:<\/p>\n\n- glcm<\/b>: Mean gray level co-occurrence matrix (GLCM) texture index.<\/li>\n
- green<\/b>: Mean green (G) value.<\/li>\n
- red<\/b>: Mean red (R) value.<\/li>\n
- nir<\/b>: Mean near-infrared (NIR) value.<\/li>\n
- pan_band<\/b>: Standard deviation.<\/li>\n
- class<\/b>: Diseased trees or all other land covers.<\/li>\n<\/ul>\n
Instances<\/h3>\n
The total number of instances<\/a> is 574. We divide them into training, generalization, and testing subsets. The number of training instances is 346 (60%), the number of selection instances is 114 (20%), and the number of testing instances is 114 (20%).<\/p>\nThis data represents satellite images of forest areas taken with four-channel imagery. This technique records the near-infrared frequencies, which vegetation reflects greatly for cooling purposes, as it absorbs most of the visible light as the energy source for photosynthesis.<\/p>\n
![\"Infrared](\"https:\/\/www.neuraldesigner.com\/images\/infrared_imagery.webp\")
<\/p>\n
Statistical analysis is always mandatory to detect possible issues related to the dataset. Therefore, a joint task before configuring the model is to check the data distribution. For example, the chart below shows the distribution across the sample of the instances of the green variable.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/wilt-green-distribution.webp\")
<\/p>\n
As we can see, there are outliers among our data. First, we must eliminate these instances. The following chart displays the distribution of the green variable after removing outliers from the data.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/wilt-green-distribution-after-outliers.webp\")
<\/p>\n
As expected, now the distribution of the green variable is correctly displayed. A uniform distribution of the data is always desired. This chart shows a normal distribution of the instances.<\/p>\n<\/section>\n\n3. Neural network<\/h2>\n
Now we have to configure the neural network<\/a> that represents the classification function.<\/p>\nThe number of inputs is 5, and the number of outputs is 1. Therefore, our neural network<\/a> will comprise 5 scaling neurons and one probabilistic neuron. We will assume three hidden neurons in the perceptron layer as a first guess.<\/p>\nThe binary probabilistic method<\/a> will be applied in this case, as we have a binary classification model. Nevertheless, choosing the continuous probabilistic method would also be a correct approach.<\/p>\nThe following picture shows a graph of the neural network for this example.<\/p>\n
![\"Neural](\"https:\/\/www.neuraldesigner.com\/images\/wilt_neural_network.webp\")
<\/p>\n<\/section>\n\n4. Training strategy<\/h2>\nLoss index<\/h3>\n
The loss index<\/a> defines the task the neural network must accomplish. The normalized squared error<\/a> with strong L2 regularization<\/a> is used here.<\/p>\nThe learning problem is finding a neural network that minimizes the loss index. A neural network fits the data set (error term) without undesired oscillations (regularization term).<\/p>\n
Optimization algorithm<\/h3>\n
The procedure used to carry out the learning process is called an optimization algorithm<\/a>. The model applies the optimization algorithm to the neural network to minimize the loss as much as possible. How the neural network’s parameters are set determines the type of training.<\/p>\nThe quasi-Newton method<\/a> is used here as the optimization algorithm in the training strategy.<\/p>\nTraining<\/h3>\n
The following chart illustrates how the training and selection errors decrease as the optimization algorithm epochs increase during the training process.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/wilt-training-results.webp\")
<\/p>\n
The final values are training error = 0.206\u00a0<\/b>and\u00a0selection error = 0.288<\/strong>, respectively, in terms of NSE<\/span>.<\/p>\n<\/section>\n\n5. Model selection<\/h2>\n
The objective of model selection<\/a> is to find a network architecture with the best generalization properties, which minimizes the error on the selected instances<\/a> of the data set.<\/p>\nMore specifically, we\u00a0aim to develop a neural network with a selection error of less than\u00a00.288<\/strong>, <\/span>the value we have achieved.<\/p>\nOrder selection<\/a> algorithms train several network architectures with different numbers of neurons and select the one with the smallest selection error.<\/p>\nThe incremental order<\/a> method starts with a few neurons and increases the complexity at each iteration. The following chart shows the training error (blue) and the selection error (orange) as a function of the number of neurons.<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/wilt-order-selection.webp\")
<\/p>\n
After model selection, an optimum selection error of 0.263 NSE<\/b> has been found for 2 hidden neurons.<\/p>\n
The final network architecture is displayed below.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/wilt-final-architecture.webp\")
<\/p>\n<\/section>\n\n6. Testing analysis<\/h2>\n
The last step is to test the generalization performance of the trained neural network.<\/p>\n
Confusion matrix<\/h3>\n\n\n\n\n\n\n\n\n\n<\/th>\n Predicted positive<\/th>\n Predicted negative<\/th>\n<\/tr>\n \nReal positive<\/th>\n 42 (37.8%)<\/td>\n 5 (4.5%)<\/td>\n<\/tr>\n \nReal negative<\/th>\n 7 (6.31%)<\/td>\n 57 (51.4%)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nClassification metrics<\/h3>\n
The following list depicts the binary classification tests<\/a> for this application:<\/p>\n
1. Application type<\/h2>\n
The model predicts a binary variable (disease region or not). Therefore, this is a classification<\/a> project.<\/p>\n The goal here is to model the probability that a region of trees presents wilt, conditioned on the image features.<\/p>\n<\/section>\n The\u00a0dataset<\/a> comprises a data matrix, where<\/span>\u00a0columns represent variables and rows represent instances.<\/p>\n The data file tree_wilt.csv<\/a> contains the information for creating the model. Here, the number of variables is 6, and the number of instances is 574.<\/p>\n The total number of variables<\/a> is 6:<\/p>\n The total number of instances<\/a> is 574. We divide them into training, generalization, and testing subsets. The number of training instances is 346 (60%), the number of selection instances is 114 (20%), and the number of testing instances is 114 (20%).<\/p>\n This data represents satellite images of forest areas taken with four-channel imagery. This technique records the near-infrared frequencies, which vegetation reflects greatly for cooling purposes, as it absorbs most of the visible light as the energy source for photosynthesis.<\/p>\n Statistical analysis is always mandatory to detect possible issues related to the dataset. Therefore, a joint task before configuring the model is to check the data distribution. For example, the chart below shows the distribution across the sample of the instances of the green variable.<\/p>\n As we can see, there are outliers among our data. First, we must eliminate these instances. The following chart displays the distribution of the green variable after removing outliers from the data.<\/p>\n As expected, now the distribution of the green variable is correctly displayed. A uniform distribution of the data is always desired. This chart shows a normal distribution of the instances.<\/p>\n<\/section>\n Now we have to configure the neural network<\/a> that represents the classification function.<\/p>\n The number of inputs is 5, and the number of outputs is 1. Therefore, our neural network<\/a> will comprise 5 scaling neurons and one probabilistic neuron. We will assume three hidden neurons in the perceptron layer as a first guess.<\/p>\n The binary probabilistic method<\/a> will be applied in this case, as we have a binary classification model. Nevertheless, choosing the continuous probabilistic method would also be a correct approach.<\/p>\n The following picture shows a graph of the neural network for this example.<\/p>\n The loss index<\/a> defines the task the neural network must accomplish. The normalized squared error<\/a> with strong L2 regularization<\/a> is used here.<\/p>\n The learning problem is finding a neural network that minimizes the loss index. A neural network fits the data set (error term) without undesired oscillations (regularization term).<\/p>\n The procedure used to carry out the learning process is called an optimization algorithm<\/a>. The model applies the optimization algorithm to the neural network to minimize the loss as much as possible. How the neural network’s parameters are set determines the type of training.<\/p>\n The quasi-Newton method<\/a> is used here as the optimization algorithm in the training strategy.<\/p>\n The following chart illustrates how the training and selection errors decrease as the optimization algorithm epochs increase during the training process.<\/p>\n The final values are training error = 0.206\u00a0<\/b>and\u00a0selection error = 0.288<\/strong>, respectively, in terms of NSE<\/span>.<\/p>\n<\/section>\n The objective of model selection<\/a> is to find a network architecture with the best generalization properties, which minimizes the error on the selected instances<\/a> of the data set.<\/p>\n More specifically, we\u00a0aim to develop a neural network with a selection error of less than\u00a00.288<\/strong>, <\/span>the value we have achieved.<\/p>\n Order selection<\/a> algorithms train several network architectures with different numbers of neurons and select the one with the smallest selection error.<\/p>\n The incremental order<\/a> method starts with a few neurons and increases the complexity at each iteration. The following chart shows the training error (blue) and the selection error (orange) as a function of the number of neurons.<\/p>\n After model selection, an optimum selection error of 0.263 NSE<\/b> has been found for 2 hidden neurons.<\/p>\n The final network architecture is displayed below.<\/p>\n The last step is to test the generalization performance of the trained neural network.<\/p>\n The following list depicts the binary classification tests<\/a> for this application:<\/p>\n2. Data set<\/h2>\n
Data source<\/h3>\n
Variables<\/h3>\n
\n
Instances<\/h3>\n
<\/p>\n<\/p>\n<\/p>\n3. Neural network<\/h2>\n
<\/p>\n<\/section>\n4. Training strategy<\/h2>\n
Loss index<\/h3>\n
Optimization algorithm<\/h3>\n
Training<\/h3>\n
<\/p>\n5. Model selection<\/h2>\n
<\/p>\n<\/p>\n<\/section>\n6. Testing analysis<\/h2>\n
Confusion matrix<\/h3>\n
\n\n
\n <\/th>\n Predicted positive<\/th>\n Predicted negative<\/th>\n<\/tr>\n \n Real positive<\/th>\n 42 (37.8%)<\/td>\n 5 (4.5%)<\/td>\n<\/tr>\n \n Real negative<\/th>\n 7 (6.31%)<\/td>\n 57 (51.4%)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n Classification metrics<\/h3>\n