# Find Threshold (RapidMiner Studio Core)

## Synopsis

This operator finds the best threshold for crisp classification of soft classified data based on user defined costs. The optimization step is based on ROC analysis.

## Description

This operator finds the threshold for given prediction confidences of soft classified predictions in order to turn it into a crisp classification. The optimization step is based on ROC analysis. ROC is discussed at the end of this description.

The Find Threshold operator finds the threshold of a labeled ExampleSet to map a soft prediction to crisp values. The threshold is delivered through the threshold port. Mostly the Apply Threshold operator is used for applying a threshold after it has been delivered by the Find Threshold operator. If the confidence for the second class is greater than the given threshold the prediction is set to this class otherwise it is set to the other class. This can be easily understood by studying the attached Example Process.

Among various classification methods, there are two main groups of methods: soft and hard classification. In particular, a soft classification rule generally estimates the class conditional probabilities explicitly and then makes the class prediction based on the largest estimated probability. In contrast, hard classification bypasses the requirement of class probability estimation and directly estimates the classification boundary.

Receiver operating characteristic (ROC), or simply ROC curve, is a graphical plot of the true positive rate vs. false positive rate for a binary classifier system as its discrimination threshold is varied. The ROC can also be represented equivalently by plotting the fraction of true positives out of the positives (TP/P = true positive rate) vs. the fraction of false positives out of the negatives (FP/N = false positive rate). TP/P determines a classifier or a diagnostic test performance on classifying positive instances correctly among all positive samples available during the test. FP/N, on the other hand, defines how many incorrect positive results occur among all negative samples available during the test.

A ROC space is defined by FP/N and TP/P as x and y axes respectively, which depicts relative trade-offs between true positive (benefits) and false positive (costs). Each prediction result or one instance of a confusion matrix represents one point in the ROC space.The best possible prediction method would yield a point in the upper left corner or coordinate (0,1) of the ROC space, representing 100% TP/P and 0% FP/N. The (0,1) point is also called a perfect classification. A completely random guess would give a point along a diagonal line from the left bottom to the top right corners.

The diagonal divides the ROC space. Points above the diagonal represent good classification results, points below the line represent poor results. Note that the Find Threshold operator finds a threshold where points of bad classification are inverted to convert them to good classification.

## Input

• example set (Data Table)

This input port expects a labeled ExampleSet. The ExampleSet should have label and prediction attributes as well as attributes for the confidence of predictions.

## Output

• example set (Data Table)

The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.

• threshold

The threshold is delivered through this output port. Frequently, the Apply Threshold operator is used for applying this threshold on the soft classified data.

## Parameters

• define_labelsThis is an expert parameter. If set to true, the first and second label can be defined explicitly using the first label and second label parameters. Range: boolean
• first_labelThis parameter is only available when the define labels parameter is set to true. It explicitly defines the first label. Range: string
• second_labelThis parameter is only available when the define labels parameter is set to true. It explicitly defines the second label. Range: string
• misclassification_costs_firstThis parameter specifies the costs assigned when an example of the first class is misclassified as one of the second. Range: real
• misclassification_costs_secondThis parameter specifies the costs assigned when an example of the second class is misclassified as one of the first. Range: real
• show_roc_plotThis parameter indicates whether to display a plot of the ROC curve. Range: boolean
• use_example_weightsThis parameter indicates if example weights should be used. Range: boolean
• roc_biasThis is an expert parameter. It determines how the ROC (and AUC) are evaluated. Range: selection

## Tutorial Processes

### Introduction to the Find Threshold operator

This Example Process starts with a Subprocess operator. This subprocess provides the labeled ExampleSet. Double-click on the Subprocess operator to see what is happening inside although it is not directly relevant to the understanding of the Find Threshold operator. In the subprocess, the Generate Data operator is used for generation of testing and training data sets with binominal label. The SVM classification model is learned and applied on training and testing data sets respectively. The resultant labeled ExampleSet is output of this subprocess. A breakpoint is inserted after this subprocess so that you can have a look at the labeled ExampleSet before application of the Find Threshold operator. You can see that the ExampleSet has 500 examples. If you sort the results according to the confidence of positive prediction, and scroll through the data set, you will see that all examples with 'confidence(positive)' greater than 0.500 are classified as positive and all examples with 'confidence(positive)' less than 0.500 are classified as negative.

Now have a look at what is happening outside the subprocess. The Find Threshold operator is used for finding a threshold. All its parameters are used with default values. The Find Threshold operator delivers a threshold through the threshold port. This threshold is applied on the labeled ExampleSet using the Apply Threshold operator. We know that when the Apply Threshold operator is applied on an ExampleSet, if the confidence for the second class is greater than the given threshold the prediction is set to this class otherwise it is set to the other class. Have a look at the resultant ExampleSet. Sort the ExampleSet according to 'confidence(positive)' and scroll through the ExampleSet. You will see that all examples where 'confidence(positive)' is greater than 0.306 are classified as positive and all examples where 'confidence(positive)' is less than or equal to 0.306 are classified as negative. In the original ExampleSet the boundary value was 0.500 but the Find Threshold operator found a better threshold for a crisp classification of soft classified data. 