Also, we use the data science and machine learning platform\u00a0Neural Designer<\/a>\u00a0to build the model. You can follow this example step by step using the\u00a0free trial<\/a>.<\/p>\n The heart_failure.csv<\/a> file contains the data for this example. Target variables can only have two values in a classification model: 0 (false, alive) or 1 (true, deceased), depending on the event’s occurrence. The number of patients (rows) in the data set is 299, and the number of variables (columns) is 12.<\/p>\n The following list summarizes the variables’<\/a> information:<\/p>\n<\/section>\n age<\/strong> \u2013 Age of the patient.<\/p>\n<\/li>\n sex<\/strong> \u2013 Woman or man.<\/p>\n<\/li>\n smoking<\/strong> \u2013 1 if the patient smokes, 0 otherwise.<\/p>\n<\/li>\n diabetes<\/strong> \u2013 1 if the patient has diabetes, 0 otherwise.<\/p>\n<\/li>\n high_blood_pressure<\/strong> \u2013 1 if the patient has hypertension, 0 otherwise.<\/p>\n<\/li>\n anaemia<\/strong> \u2013 Low red blood cell or hemoglobin count.<\/p>\n<\/li>\n<\/ul>\n creatinine_phosphokinase<\/strong> \u2013 Level of CPK enzyme in the blood.<\/p>\n<\/li>\n ejection_fraction<\/strong> \u2013 Percentage of blood pumped out with each heartbeat.<\/p>\n<\/li>\n platelets<\/strong> \u2013 Platelet count in the blood.<\/p>\n<\/li>\n serum_creatinine<\/strong> \u2013 Creatinine level in the blood.<\/p>\n<\/li>\n serum_sodium<\/strong> \u2013 Sodium level in the blood.<\/p>\n<\/li>\n<\/ul>\n The number of input variables<\/a>, or attributes for each sample, is 11.<\/p>\n The target variable<\/a> is 1, death_event (1 or 0), indicating whether the patient has died or survived.<\/p>\n Instances<\/span><\/p>\n Also, we can calculate the distributions<\/a> for all variables. The following figure is a pie chart showing which patients are dead (1) or alive (0) in the data set.<\/p>\n The image shows that dead patients represent 32.107% of the samples, while live patients represent 67.893%.<\/p>\n The inputs-targets correlations<\/a> might indicate which factors have the most univariate influence on whether or not a patient will live.<\/p>\n Here, the most correlated variables with survival status are serum_creatinine<\/b>, age<\/b>, serum_sodium,<\/b> and ejection_fraction.<\/b><\/p>\n<\/section>\n The next step is to set up 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> contains the statistics on the inputs calculated from the data file and the method for scaling the input variables. Here, the minimum-maximum method<\/a> has been set. As we use 11 input variables, the scaling layer has 11 inputs.<\/p>\n We won’t use a perceptron layer<\/a> to stabilize and simplify our model.<\/p>\n The probabilistic layer<\/a> only contains the method for interpreting the outputs as probabilities. Moreover, as the output layer’s activation function is logistic, that output can already be interpreted as a probability of class membership. The following figure is a graphical representation of this neural network.<\/p>\n The fourth step is to set the training strategy<\/a>, which is composed of two terms:<\/p>\n The loss index<\/a> is the weighted squared error<\/a> with L2 regularization<\/a>, the default loss index for binary classification applications.<\/p>\n We can state the learning problem as 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>, which 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>\n The final errors are 0.632 WSE for training and 0.899 WSE for selection.<\/p>\n<\/section>\n The curves have converged, but since the selection error is higher, the model could still be improved to further reduce errors.<\/p>\n The objective of model selection<\/a> is to find the network architecture that minimizes the error, that is, with the best generalization properties for the selected instances<\/a> of the data set.<\/p>\n Order selection<\/a> algorithms train several network architectures with different numbers of neurons and select that with the smallest selection error. We have removed our perceptron layer to stabilize our model, so we cannot use this feature.<\/p>\n However, we will use input selection<\/a> to select features in the data set that provide the best generalization capabilities.<\/p>\n The following image shows the training and selection errors as a function of the number of inputs using this method.<\/p>\n In the end, we obtain a training error = 0.693 WSE<\/b> and a selection error = 0.823 WSE<\/b>, respectively. Also, we have reduced the number of inputs to only 5 features. Our network is now like this:<\/p>\n The objective of 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>\n A random classifier has an AUC of 0.5, while a perfect one reaches 1. With an AUC of 0.803, this model shows good performance.<\/p>\n The following table shows the confusion matrix<\/a>, including true positives, false positives, false negatives, and true negatives for the variable diagnosis.<\/p>\n The binary classification tests<\/a> are parameters for measuring the performance of a classification problem with two classes:<\/p>\n Once we have tested the neural network’s generalization performance, we can save it for future use in the so-called model deployment<\/a> mode.<\/p>\n<\/section>\nContents<\/h3>\n
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1. Application type<\/h2>\n
2. Data set<\/h2>\n
Data source<\/h3>\n
Variables<\/h3>\n
Patient information<\/h4>\n
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Clinical measurements<\/h4>\n
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Target variable<\/h4>\n
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Variables distributions<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/HApie.webp\")
<\/p>\nInputs-targets correlations<\/h3>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/HAcorrelationsChart.webp\")
<\/p>\n3. Neural network<\/h2>\n
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\nThe probabilistic layer has 11 inputs. It has one output, representing the probability of a patient being dead or alive.<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/HAneuralNetwork.webp\")
<\/p>\n<\/section>\n4. Training strategy<\/h2>\n
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![](\"https:\/\/www.neuraldesigner.com\/images\/HAerrorsHistory.webp\")
<\/p>\n5. Model selection<\/h2>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/HAselectionErrorsPlot.webp\")
<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/HAnetworkAfterInputSelection.webp\")
<\/p>\n<\/section>\n6. Testing analysis<\/h2>\n
![](\"https:\/\/www.neuraldesigner.com\/images\/HAROCchart.webp\")
<\/p>\n![](\"https:\/\/www.neuraldesigner.com\/images\/HAConfusionTable.webp\")
<\/p>\n\n
7. Model deployment<\/h2>\n
References<\/h2>\n