The instances<\/a> are randomly split into 60% training (144), 20% validation (48), and 20% testing (48).<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n We can calculate the distributions<\/a> of all variables.<\/p>\n The following figure is the pie chart for the star types.<\/p>\n As we can see, the target is well-distributed.<\/p>\n<\/section>\n The second step is to choose a neural network<\/a>.<\/p>\n For classification problems, it is usually composed of:<\/p>\n The scaling layer<\/a> contains the statistics on the inputs calculated from the data file and the method for scaling the input variables.<\/p>\n The number of perceptron layers<\/a> is 1. This perceptron layer has 22 inputs and 6 neurons.<\/p>\n The probabilistic layer<\/a> allows the outputs to be interpreted as probabilities. This means that all the outputs are between 0 and 1, and their sum is 1.<\/p>\n The softmax probabilistic method<\/a> is used here. The neural network has six outputs since the target variable contains six classes (Red Dwarf, Brown Dwarf, White Dwarf, Main Sequence, Supergiants, and Hypergiants).<\/p>\n<\/section>\n The fourth step is to set the training strategy<\/a>.<\/p>\n It is composed of:<\/p>\n The loss index<\/a> chosen for this application is the\u00a0normalized squared error<\/a>\u00a0with L1 regularization<\/a>.<\/p>\n The error term<\/a> fits the neural network to the training instances<\/a> of the data set.<\/p>\n The regularization term<\/a> makes the model more stable and improves generalization.<\/p>\n The optimization algorithm<\/a> searches for the neural network parameters that minimize the loss index.<\/p>\n The quasi-Newton method<\/a> is chosen here.<\/p>\n The following chart shows how training and selection errors decrease with the epochs during training.<\/p>\n The final values are training error = 0.091 NSE<\/b> (blue) and selection error = 0.073 NSE<\/b> (orange).<\/p>\n<\/section>\n The objective of model selection<\/a> is to find the network architecture with the best generalization properties.<\/p>\n That is the model that minimizes the error on the selected instances<\/a> of the data set.<\/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 purpose of the testing analysis<\/a> is to validate the generalization performance of the model.<\/p>\n Here, we compare the neural network outputs to the corresponding targets in the testing instances<\/a> of the data set.<\/p>\n As we can see, the model correctly predicts 48 instances (100%). Therefore, there are no misclassified cases.<\/p>\n This shows that our predictive model has excellent accuracy.<\/p>\n<\/section>\n The neural network is now ready to predict outputs for inputs it has never seen.\u00a0This process is called model deployment<\/a>.<\/p>\n To classify any given star, we calculate the neural network outputs<\/a> from the different variables: temperature, luminosity, relative radius, absolute magnitude, color, and spectral class.<\/p>\n For example, if we introduce the following values for each input:<\/p>\nVariables distributions<\/h3>\n
![\"The](\"https:\/\/www.neuraldesigner.com\/images\/star-type-pie-chart.webp\")
<\/p>\n3. Neural network<\/h2>\n
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4. Training strategy<\/h2>\n
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Loss index<\/h3>\n
Optimization algorithm<\/h3>\n
Training<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/star-type-quasi-newton.webp\")
<\/p>\n5. Model selection<\/h2>\n
6. Testing analysis<\/h2>\n
Confusion matrix<\/h3>\n
\n\n
\n <\/th>\n Predicted
\nRed Dwarf<\/th>\nPredicted
\nBrown Dwarf<\/th>\nPredicted
\nWhite Dwarf<\/th>\nPredicted
\nMain Sequence<\/th>\nPredicted
\nSupergiants<\/th>\nPredicted
\nHypergiants<\/th>\n<\/tr>\n\n Real Red Dwarf<\/th>\n 7(14.6%)<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n<\/tr>\n \n Real Brown Dwarf<\/th>\n 0<\/td>\n 10 (20.8%)<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n<\/tr>\n \n Real White Dwarf<\/th>\n 0<\/td>\n 0<\/td>\n 7 (14.6%)<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n<\/tr>\n \n Real Main Sequence<\/th>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 10 (20.8%)<\/td>\n 0<\/td>\n 0<\/td>\n<\/tr>\n \n Real Supergiants<\/th>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 6 (12.5%)<\/td>\n 0<\/td>\n<\/tr>\n \n Real Hypergiants<\/th>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 0<\/td>\n 8 (16.7%)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n 7. Model deployment<\/h2>\n
![\"classification](\"https:\/\/www.neuraldesigner.com\/images\/HRdiagram.webp\")
<\/p>\n