# Performance (Costs) (AI Studio Core)

## Synopsis

This operator provides the ability to evaluate misclassification costs for performance evaluation of classification tasks.## Description

The Performance (Costs) operator provides the ability to evaluate misclassification costs. A cost matrix should be specified through the *cost matrix* parameter. The cost matrix is similar in structure to a confusion matrix because it has predicted classes in one dimension and actual classes on the other dimension. Therefore the cost matrix can denote the costs for every possible classification outcome: predicted label vs. actual label. Actually this matrix is a matrix of misclassification costs because you can specify different weights for certain classes misclassified as other classes. Weights can also be assigned to correct classifications but they are not taken into account for evaluating misclassification costs. The classes in the matrix are labeled as Class 1, Class 2 etc where classes are numbered according to their order in the internal mapping. The *class order definition* parameter allows you to specify the class order for the matrix in which case classes are ordered according to the order specified in this parameter (instead of internal mappings). For a better understanding of this operator please study the attached Example Process.

## Input

- example set (Data Table)
This input port expects a labeled ExampleSet. The Apply Model operator is a good example of such operators that provide labeled data. Make sure that the ExampleSet has label and prediction attributes. Please see the Set Role operator for more details about attribute roles.

## 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.

- performance (Performance Vector)
This port delivers a Performance Vector which has information about the misclassification costs.

## Parameters

- cost_matrixThis parameter is used for specifying the cost matrix. The cost matrix is similar in structure to a confusion matrix because it has predicted classes in one dimension and actual classes on the other dimension. Therefore the cost matrix can denote the costs for every possible classification outcome: predicted label vs. actual label. Actually this matrix is a matrix of misclassification costs because you can specify different weights for certain classes misclassified as other classes. Weights can also be assigned to correct classifications but they are not taken into account for evaluating misclassification costs. The classes in the matrix are labeled as Class 1, Class 2 etc where classes are numbered according to their order in the internal mapping. The
*class order definition*parameter can be used for specifying the class order for the matrix (instead of internal mappings). Range: string - class_order_definitionThe
*class order definition*parameter allows you to specify the class order for the cost matrix in which case classes are ordered according to the order specified in this parameter (instead of internal mappings). Range: enumeration

## Tutorial Processes

### Measuring Misclassification costs of a classifier

The 'Golf' data set is loaded using the Retrieve operator. The Split Validation operator is applied on it for training and testing a classification model. The Naive Bayes operator is applied in the training subprocess of the Split Validation operator. The Naive Bayes operator trains a classification model. The Apply Model operator is used in the testing subprocess to apply this model. A breakpoint is inserted here so that you can have a look at the labeled ExampleSet. As you can see, out of 4 examples of the testing data set only 1 has been misclassified. The misclassified example was classified as 'class = yes' while actually it was 'class = no'.

The resultant labeled ExampleSet is used by the Performance (Costs) operator for measuring the misclassification costs of the model. Have a look at the parameters of the Performance (Costs) operator. The class order definition parameter specifies the order of classes in the cost matrix. The classes 'yes' and 'no' are placed in first and second rows respectively. Thus class 'yes' is Class 1 and class 'no' is Class 2 in the cost matrix. Now have a look at the cost matrix in the cost matrix parameter. The case where Class 2 (i.e. class = no) is misclassified as Class 1 (i.e. class = yes) has been given weight 2.0. The case where Class 1 (i.e. class = yes) is misclassified as Class 2 (i.e. class = no) has been given weight 1.0.

Now let us see how this cost matrix is used for evaluating misclassification costs of the labeled ExampleSet. As 1 of the 4 classifications was wrong, one should expect the classification cost to be 1/4 or 0.250. But as this misclassification has weight 2.0 (because class = no is misclassified as class = yes) instead of 1.0 the cost for this misclassification is doubled. Therefore the cost in this case is 0.500. The misclassification cost can be seen in the Results Workspace.

Now set the sampling type parameter of the Split Validation operator to 'linear sampling' and run the process again. Have a look at the labeled ExampleSet generated by the Apply Model operator. 2 out of 4 examples have been misclassified. One example with class = no has been misclassified as class = yes (i.e. weight = 2.0) and one example with class = yes has been misclassified as class = no (i.e. weight = 1.0). The resultant misclassification cost is ((1 x 1.0)+(1 x 2.0))/4 which results to 0.750. The misclassification cost can be seen in the Results Workspace.