Machine learning examples

Urinary inflammation diagnosis

The goal of this example is to design a model that can diagnose the disease of the acute inflammations/nephritises of urinary bladder.

This is a medical diagnosis application.

The main idea of this data set is to prepare the algorithm for the expert, who will perform the presumptive diagnosis of two diseases of urinary system.

Acute inflammation of urinary bladder is characterised by sudden occurrence of pains in the abdomen region and the urination in form of constant urine pushing, micturition pains and sometimes lack of urine keeping. Temperature of the body rises, however most often not above 38C. The excreted urine is turbid and sometimes bloody.

At proper treatment, symptoms decay usually within several days. However, there is inclination to returns. At persons with acute inflammation of urinary bladder, we should expect that the illness will turn into protracted form.

Acute nephritis of renal pelvis origin occurs considerably more often at women than at men. It begins with sudden fever, which reaches, and sometimes exceeds 40C. The fever is accompanied by shivers and one- or both-side lumbar pains, which are sometimes very strong. Symptoms of acute inflammation of urinary bladder appear very often. Quite not infrequently there are nausea and vomiting and spread pains of whole abdomen.

Contents:

  1. Application type.
  2. Data set.
  3. Neural network.
  4. Training strategy.
  5. Model selection.
  6. Testing analysis.
  7. Model deployment.

1. Application type

This is a classification project, since the variables to be predicted are binary.

The goal here is to model the probability of nephritises of urinary bladder and inflammation of the urinary bladder, conditioned on the patient symptoms.

Since both variables are binary and independent, we will use the model to predict the diseases one at a time. In this example, the model will be build to predict the acute inflammation of urinary bladder.

2. Data set

The data file urinary_inflammation.csv contains 120 rows and 8 columns.

This data set contains the following variables:

As the objective is to get a model that can diagnose one of the diseases, the variable of acute nephritises diagnosis will be set as unused.

The instances are divided into a training, a selection and a testing subsets. They represent 60% (72) , 20% (24) and 20% (24) of the original instances, respectively, and are splitted at random.

Before configuring the model, it is recommended to perform an analysis of the data we have. For classification projects, it is important to know the distribution of the target variable in the dataset. The next picture shows a pie chart for the inflammation_of_urinary_bladder variable.

As we can observe, the data is quite well balanced. This information will later be used to define the parameters of the neural network.

Another relevant information to keep in mind, is the correlation of each of the inputs with the target variable. Below a chart with this information is displayed.

From the above picture we can conclude that all the variables have a considerable influence on the target variable.

3. Neural network

The second step is to choose a neural network to represent the classification function. For classification problems, it is composed by:

For the scaling layer, the mean and standard deviation scaling method is set.

We set 2 perceptron layers, one hidden layer with 3 neurons as a first guess and one output layer with 1 neuron, both layers having the logistic activation function.

At last, we will set the binary probabilistic method for the probabilistic layer, since we want the predicted target variable to be binary.

The next figure is a diagram for the neural network used in this example.

4. Training strategy

The fourth step is to set the training strategy, which is composed by:

The loss index chosen for this application is the normalized squared error with L2 regularization.

The learning problem can be stated as to find a neural network which minimizes the loss index, i.e., a neural network that fits the data set (error term) and that does not oscillate (regularization term).

The optimization algorithm set for the model is the quasi-Newton method.

The final training and selection errors are training error = 0.0009 WSE and selection error = 0.0008 WSE, respectively. In the next section we will try to improve the generalization performance by reducing the selection error.

5. Model selection

The objective of model selection is to improve the generalization capabilities of the neural network or, in other words, to reduce the selection error.

Since the selection error that we have achieved so far is very small (0.0008 WSE), we don't need to apply Order selection nor inputs selection here.

6. Testing analysis

An exhausttive testing analysis is performed to validate the generalization performance of the trained neural network. To validate a classification model, we need to compare the values provided by this technique to the actually observed values.

The following table contains the elements of the confusion matrix. It contains the true positives, the false positives, the false negatives, the true negatives for the variable diagnose.

Predicted positive Predicted negative
Real positive 12 0
Real negative 0 12

The number of correctly classified instances is 24, and the number of misclassified instances is 0. From this table we can calculate the binary classification tests.

The binary classification tests are parameters for measuring the performance of a classification problem with two classes:

From the above results, we can say that the model is predicting perfectly.

7. Model deployment

The neural network is now ready to predict outputs for inputs that it has never seen.

We calculate the neural network outputs to diagnose inflammation of urinary bladder from the features of a new patient. The next list shows some values for the inputs and the corresponding output for that patient.

We can export the mathematical expression of the neural network to any clinical software used for diagnosing this diseases. This expression is listed below.

scaled_temperature = (temperature-38.7242)/1.81913;
scaled_occurrence_of_nausea = (occurrence_of_nausea-0.241667)/0.429888;
scaled_lumbar_pain = (lumbar_pain-0.583333)/0.495074;
scaled_urine_pushing = (urine_pushing-0.666667)/0.473381;
scaled_micturition_pains = (micturition_pains-0.491667)/0.502027;
scaled_burning_of_urethra = (burning_of_urethra-0.416667)/0.495074;
y_1_1 = Logistic (0.202475+ (scaled_temperature*0.456805)+ (scaled_occurrence_of_nausea*-0.793165)+ (scaled_lumbar_pain*1.47038)+ (scaled_urine_pushing*-1.76085)+ (scaled_micturition_pains*-0.81808)+ (scaled_burning_of_urethra*0.145468));
y_1_2 = Logistic (-0.254725+ (scaled_temperature*-0.224772)+ (scaled_occurrence_of_nausea*0.605717)+ (scaled_lumbar_pain*-1.1313)+ (scaled_urine_pushing*1.62554)+ (scaled_micturition_pains*0.801991)+ (scaled_burning_of_urethra*-0.267477));
y_1_3 = Logistic (-0.307314+ (scaled_temperature*-0.245913)+ (scaled_occurrence_of_nausea*0.733341)+ (scaled_lumbar_pain*-1.26759)+ (scaled_urine_pushing*1.63105)+ (scaled_micturition_pains*0.83814)+ (scaled_burning_of_urethra*-0.159719));
non_probabilistic_inflammation_of_urinary_bladder = Logistic (-1.16282+ (y_1_1*-3.39269)+ (y_1_2*2.99384)+ (y_1_3*3.00634));
inflammation_of_urinary_bladder = binary(non_probabilistic_inflammation_of_urinary_bladder);

logistic(x){
   return 1/(1+exp(-x))
}

binary(x){
   if x < decision_threshold
       return 0
   else
       return 1
}
        

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