The final errors are 0.966 WSE for training and 0.933 WSE for validation.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n<\/section>\n The objective of model selection<\/a> is to find the 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\u00a00.933 WSE<\/strong>, the current best value we have achieved<\/span>.<\/p>\n Order selection<\/a> algorithms train several network architectures with a different number 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.<\/p>\n<\/section>\n The last step is to test the generalization performance of the trained neural network.<\/p>\n The objective of the testing analysis<\/a> is to validate the generalization performance of the trained neural network. To validate a classification technique, we need to compare the values provided by this technique to the observed values.<\/p>\n We can use the ROC curve<\/a> as it is the standard testing method for binary classification projects.<\/p>\n5. Model selection<\/h2>\n
6. Testing analysis<\/h2>\n
ROC curve<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/forest-fires-ROC.webp\")
<\/p>\nConfusion matrix<\/h3>\n
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
This is a classification<\/a> project since the variable to be predicted is binary (fire or no fire).<\/p>\nThe goal is to model the probability of a fire occurring according to the day, month, certain meteorological variables, and a series of indices developed by the FWI system.<\/p>\n<\/section>\n\n2. Data set<\/h2>\n
The data set<\/a> comprises a data matrix in which columns represent variables and rows represent instances.<\/p>\nThe data file forestfires.csv<\/a> contains the data needed to create the model.<\/p>\nHere, the number of variables is 9, and the number of instances is 515.<\/p>\n
Variables<\/h3>\n
This data set contains the following variables<\/a> that contain data measured in the northeast region of Portugal:<\/p>\nTemporal variable<\/h4>\n\n- \n
month<\/strong> \u2013 Month of observation.<\/p>\n<\/li>\n<\/ul>\nFWY system indices<\/h4>\n\n- FFMC<\/strong> \u2013 Fine Fuel Moisture Code.<\/li>\n
- DMC<\/strong> \u2013 Duff Moisture Code.<\/li>\n
- DC<\/strong> \u2013 Drought Code.<\/li>\n
- ISI<\/strong> \u2013 Initial Spread Index.<\/li>\n<\/ul>\n
Weather variables<\/h4>\n\n- temp<\/strong> \u2013 Temperature (\u00b0C).<\/li>\n
- RH<\/strong> \u2013 Relative humidity (%).<\/li>\n
- wind<\/strong> \u2013 Wind speed (km\/h).<\/li>\n<\/ul>\n
Target variable<\/h4>\n\n- \n
class<\/strong> \u2013 Fire occurrence (1 = fire, 0 = not fire).<\/p>\n<\/li>\n<\/ul>\nInstances<\/h3>\n
Each instance<\/a>\u00a0in the dataset represents the fire weather conditions of a specific area and month, including fuel moisture indices, temperature, humidity, wind speed, and whether a fire occurred.<\/p>\nThe dataset contains 515 instances, split into 333 for training (80%), 45 for validation (10%), and 45 for testing (10%).<\/p>\n
Statistics<\/h3>\n
We can perform a few related analytics once the data set is set up. First, we check the provided information and ensure that the data is of high quality.<\/p>\n
You can calculate data statistics<\/a> and create a table with the minimum, maximum, mean, and standard deviation for each variable.<\/p>\nThe table below shows these values.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/forest-fires-statistics.webp\")
<\/p>\n
Distributions<\/h3>\n
Also, we can calculate the distributions<\/a> for all variables. The following figure shows a pie chart with the proportion of fire (positives) and no fire (negatives) following our dataset.<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/forest-fires-pie-chart.webp\")
<\/p>\n
As we can see, the number of fire cases is 45.4% of the samples, and non-fire fire represent approximately 54.6% of the pieces.<\/p>\n
Input-target correlations<\/h3>\n
Finally, the input-target correlations<\/a> might indicate what factors most influence fires.<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/forest-fires-correlations.webp\")
<\/p>\n
Here, the different variables are a little correlated. Indeed, a forest fire depends on many factors simultaneously.<\/p>\n<\/section>\n\n3. Neural network<\/h2>\n
The second step is to set a neural network<\/a> representing the classification function. For this class of applications, the neural network is composed of:<\/p>\n\n- Scaling layer.<\/li>\n
- Perceptron layers.<\/li>\n
- Probabilistic layer.<\/li>\n<\/ul>\n
Scaling layer<\/h3>\n
The scaling layer<\/a> stores the input statistics from the data file and the chosen scaling method.<\/p>\nIn this case, the min\u2013max method is used, though mean\u2013std scaling would give similar results.<\/p>\n
Dense layers<\/h3>\n
The number of perceptron layers<\/a> is 1. This perceptron layer has 8 inputs and 8 neurons.<\/p>\nFinally, we will set the binary probabilistic method<\/a> for the probabilistic layer<\/a>, as we want the predicted target variable to be binary.<\/p>\nNeural network graph<\/h3>\n
The following picture shows a graph of the neural network for this example.<\/p>\n
![\"Neural](\"https:\/\/www.neuraldesigner.com\/images\/forest-fires-neural-network.webp\")
<\/p>\n
The yellow circles represent scaling neurons, the blue circles perceptron neurons, and the red circles probabilistic neurons. The number of inputs is 8, and the number of outputs is 1.<\/p>\n<\/section>\n\n4. Training strategy<\/h2>\n
The procedure used to carry out the learning process is called a training strategy<\/a>. The training strategy is applied to the neural network to obtain the best possible performance. The type of training is determined by how the parameters in the neural network are adjusted.<\/p>\nThis process is composed of two terms:<\/p>\n
\n- A loss index.<\/li>\n
- An optimization algorithm.<\/li>\n<\/ul>\n
Loss index<\/h3>\n
The loss index<\/a> that we use is the weighted squared error<\/a> with L2 regularization<\/a>. This is the default loss index for binary classification applications.<\/p>\nThe learning problem is finding a neural network that minimizes the loss index. That is a neural network that fits the data set (error term<\/a>) and does not oscillate (regularization term<\/a>).<\/p>\nOptimization algorithm<\/h3>\n
The optimization algorithm<\/a> that we use is the quasi-Newton method<\/a>. This is also the standard optimization algorithm for this type of problem.<\/p>\nTraining<\/h3>\n
The following chart shows how errors decrease with the iterations during training.<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/forest-fires-quasi-newton.webp\")
<\/p>\n\n\n\n\n\n\n\n
1. Application type<\/h2>\n
This is a classification<\/a> project since the variable to be predicted is binary (fire or no fire).<\/p>\n The goal is to model the probability of a fire occurring according to the day, month, certain meteorological variables, and a series of indices developed by the FWI system.<\/p>\n<\/section>\n The data set<\/a> comprises a data matrix in which columns represent variables and rows represent instances.<\/p>\n The data file forestfires.csv<\/a> contains the data needed to create the model.<\/p>\n Here, the number of variables is 9, and the number of instances is 515.<\/p>\n This data set contains the following variables<\/a> that contain data measured in the northeast region of Portugal:<\/p>\n month<\/strong> \u2013 Month of observation.<\/p>\n<\/li>\n<\/ul>\n class<\/strong> \u2013 Fire occurrence (1 = fire, 0 = not fire).<\/p>\n<\/li>\n<\/ul>\n Each instance<\/a>\u00a0in the dataset represents the fire weather conditions of a specific area and month, including fuel moisture indices, temperature, humidity, wind speed, and whether a fire occurred.<\/p>\n The dataset contains 515 instances, split into 333 for training (80%), 45 for validation (10%), and 45 for testing (10%).<\/p>\n We can perform a few related analytics once the data set is set up. First, we check the provided information and ensure that the data is of high quality.<\/p>\n You can calculate data statistics<\/a> and create a table with the minimum, maximum, mean, and standard deviation for each variable.<\/p>\n The table below shows these values.<\/p>\n Also, we can calculate the distributions<\/a> for all variables. The following figure shows a pie chart with the proportion of fire (positives) and no fire (negatives) following our dataset.<\/p>\n As we can see, the number of fire cases is 45.4% of the samples, and non-fire fire represent approximately 54.6% of the pieces.<\/p>\n Finally, the input-target correlations<\/a> might indicate what factors most influence fires.<\/p>\n Here, the different variables are a little correlated. Indeed, a forest fire depends on many factors simultaneously.<\/p>\n<\/section>\n The second step is to set a neural network<\/a> representing the classification function. For this class of applications, the neural network is composed of:<\/p>\n The scaling layer<\/a> stores the input statistics from the data file and the chosen scaling method.<\/p>\n In this case, the min\u2013max method is used, though mean\u2013std scaling would give similar results.<\/p>\n The number of perceptron layers<\/a> is 1. This perceptron layer has 8 inputs and 8 neurons.<\/p>\n Finally, we will set the binary probabilistic method<\/a> for the probabilistic layer<\/a>, as we want the predicted target variable to be binary.<\/p>\n The following picture shows a graph of the neural network for this example.<\/p>\n The yellow circles represent scaling neurons, the blue circles perceptron neurons, and the red circles probabilistic neurons. The number of inputs is 8, and the number of outputs is 1.<\/p>\n<\/section>\n The procedure used to carry out the learning process is called a training strategy<\/a>. The training strategy is applied to the neural network to obtain the best possible performance. The type of training is determined by how the parameters in the neural network are adjusted.<\/p>\n This process is composed of two terms:<\/p>\n The loss index<\/a> that we use is the weighted squared error<\/a> with L2 regularization<\/a>. This is the default loss index for binary classification applications.<\/p>\n The learning problem is finding a neural network that minimizes the loss index. That is a neural network that fits the data set (error term<\/a>) and does not oscillate (regularization term<\/a>).<\/p>\n The optimization algorithm<\/a> that we use is the quasi-Newton method<\/a>. This is also the standard optimization algorithm for this type of problem.<\/p>\n The following chart shows how errors decrease with the iterations during training.<\/p>\n2. Data set<\/h2>\n
Variables<\/h3>\n
Temporal variable<\/h4>\n
\n
FWY system indices<\/h4>\n
\n
Weather variables<\/h4>\n
\n
Target variable<\/h4>\n
\n
Instances<\/h3>\n
Statistics<\/h3>\n
<\/p>\nDistributions<\/h3>\n
<\/p>\nInput-target correlations<\/h3>\n
<\/p>\n3. Neural network<\/h2>\n
\n
Scaling layer<\/h3>\n
Dense layers<\/h3>\n
Neural network graph<\/h3>\n
<\/p>\n4. Training strategy<\/h2>\n
\n
Loss index<\/h3>\n
Optimization algorithm<\/h3>\n
Training<\/h3>\n
<\/p>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/Potugal-map-risk.webp\")
<\/pre>\n