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Visualize and Assess Classifier Performance in Classification Learner

After training classifiers in Classification Learner, you can compare models based on accuracy scores, visualize results by plotting class predictions, and check performance using the confusion matrix and ROC curve.

  • If you use k-fold cross-validation, then the app computes the accuracy scores using the observations in the k validation folds and reports the average cross-validation error. It also makes predictions on the observations in these validation folds and computes the confusion matrix and ROC curve based on these predictions.

    Note

    When you import data into the app, if you accept the defaults, the app automatically uses cross-validation. To learn more, see Choose Validation Scheme.

  • If you use holdout validation, the app computes the accuracy scores using the observations in the validation fold and makes predictions on these observations. The app also computes the confusion matrix and ROC curve based on these predictions.

  • If you use resubstitution validation, the score is the resubstitution accuracy based on all the training data, and the predictions are resubstitution predictions.

Check Performance in the Models Pane

After training a model in Classification Learner, check the Models pane to see which model has the best overall accuracy in percent. The best Accuracy (Validation) score is highlighted in a box. This score is the validation accuracy. The validation accuracy score estimates a model's performance on new data compared to the training data. Use the score to help you choose the best model.

  • For cross-validation, the score is the accuracy on all observations not set aside for testing, counting each observation when it was in a holdout (validation) fold.

  • For holdout validation, the score is the accuracy on the held-out observations.

  • For resubstitution validation, the score is the resubstitution accuracy against all the training data observations.

The best overall score might not be the best model for your goal. A model with a slightly lower overall accuracy might be the best classifier for your goal. For example, false positives in a particular class might be important to you. You might want to exclude some predictors where data collection is expensive or difficult.

To find out how the classifier performed in each class, examine the confusion matrix.

View Model Metrics in Summary Tab and Models Pane

You can view model metrics in the model Summary tab and the Models pane, and use these metrics to assess and compare models. Alternatively, you can use the Results Table tab to compare models. For more information, see Compare Model Information and Results in Table View.

The Training Results metrics are calculated on the validation set. The Test Results metrics, if displayed, are calculated on an imported test set. For more information, see Evaluate Test Set Model Performance.

Sample model Summary tab

Model Metrics

MetricDescriptionTip
AccuracyPercentage of observations that are correctly classifiedLook for larger accuracy values.
Total costTotal misclassification costLook for smaller total cost values. Make sure the accuracy value is still large.

You can sort models based on the different model metrics. To select a metric for model sorting, use the Sort by list at the top of the Models pane.

You can also delete unwanted models listed in the Models pane. Select the model you want to delete and click the Delete selected model button in the upper right of the pane, click Delete in the Models section of the Classification Learner tab, or right-click the model and select Delete. You cannot delete the last remaining model in the Models pane.

Compare Model Information and Results in Table View

Rather than using the Summary tab or the Models pane to compare model metrics, you can use a table of results. On the Classification Learner tab, in the Models section, click Results Table. In the Results Table tab, you can sort models by their training and test results, as well as by their options (such as model type, selected features, PCA, and so on). For example, to sort models by validation accuracy, click the sorting arrows in the Accuracy (Validation) column header. A down arrow indicates that models are sorted from highest accuracy to lowest accuracy.

To view more table column options, click the "Select columns to display" button at the top right of the table. In the Select Columns to Display dialog box, check the boxes for the columns you want to display in the results table. Newly selected columns are appended to the table on the right.

Select Columns to Display dialog box

Within the results table, you can manually drag and drop the table columns so that they appear in your preferred order.

You can mark some models as favorites by using the Favorite column. The app keeps the selection of favorite models consistent between the results table and the Models pane. Unlike other columns, the Favorite and Model Number columns cannot be removed from the table.

To remove a row from the table, right-click any entry within the row and click Hide row (or Hide selected row(s) if the row is highlighted). To remove consecutive rows, click any entry within the first row you want to remove, press Shift, and click any entry within the last row you want to remove. Then, right-click one of the highlighted entries and click Hide selected row(s). To restore all removed rows, right-click any entry in the table and click Show all rows. The restored rows are appended to the bottom of the table.

To export the information in the table, use one of the export buttons at the top right of the table. Choose between exporting the table to the workspace or to a file. The exported table includes only the displayed rows and columns.

Plot Classifier Results

Use a scatter plot to examine the classifier results. To view the scatter plot for a model, select the model in the Models pane. On the Classification Learner tab, in the Plot and Interpret section, click the arrow to open the gallery, and then click Scatter in the Validation Results group. After you train a classifier, the scatter plot switches from displaying the data to showing model predictions. If you are using holdout or cross-validation, then these predictions are the predictions on the held-out (validation) observations. In other words, the software obtains each prediction by using a model that was trained without the corresponding observation.

To investigate your results, use the controls on the right. You can:

  • Choose whether to plot model predictions or the data alone.

  • Show or hide correct or incorrect results using the check boxes under Model predictions.

  • Choose features to plot using the X and Y lists under Predictors.

  • Visualize results by class by showing or hiding specific classes using the check boxes under Show.

  • Change the stacking order of the plotted classes by selecting a class under Classes and then clicking Move to Front.

  • Zoom in and out, or pan across the plot. To enable zooming or panning, place the mouse over the scatter plot and click the corresponding button on the toolbar that appears above the top right of the plot.

Scatter plot of the Fisher iris data. Correctly classified points are marked with an O. Incorrectly classified points are marked with an X.

See also Investigate Features in the Scatter Plot.

To export the scatter plots you create in the app to figures, see Export Plots in Classification Learner App.

Check Performance Per Class in the Confusion Matrix

Use the confusion matrix plot to understand how the currently selected classifier performed in each class. After you train a classification model, the app automatically opens the confusion matrix for that model. If you train an "All" model, the app opens the confusion matrix for the first model only. To view the confusion matrix for another model, select the model in the Models pane. On the Classification Learner tab, in the Plot and Interpret section, click the arrow to open the gallery, and then click Confusion Matrix (Validation) in the Validation Results group. The confusion matrix helps you identify the areas where the classifier performed poorly.

When you open the plot, the rows show the true class, and the columns show the predicted class. If you are using holdout or cross-validation, then the confusion matrix is calculated using the predictions on the held-out (validation) observations. The diagonal cells show where the true class and predicted class match. If these diagonal cells are blue, the classifier has classified observations of this true class correctly.

The default view shows the number of observations in each cell.

To see how the classifier performed per class, under Plot, select the True Positive Rates (TPR), False Negative Rates (FNR) option. The TPR is the proportion of correctly classified observations per true class. The FNR is the proportion of incorrectly classified observations per true class. The plot shows summaries per true class in the last two columns on the right.

Tip

Look for areas where the classifier performed poorly by examining cells off the diagonal that display high percentages and are orange. The higher the percentage, the darker the hue of the cell color. In these orange cells, the true class and the predicted class do not match. The data points are misclassified.

Confusion matrix assessing a model that predicts the country of origin for cars in the carbig data set

In this example, which uses the carbig data set, the fifth row from the top shows all cars with the true class Japan. The columns show the predicted classes. Of the cars from Japan, 77.2% are correctly classified, so 77.2% is the true positive rate for correctly classified points in this class, shown in the blue cell in the TPR column.

The other cars in the Japan row are misclassified: 5.1% of the cars are incorrectly classified as from Germany, 5.1% are classified as from Sweden, and 12.7% are classified as from the USA. The false negative rate for incorrectly classified points in this class is 22.8%, shown in the orange cell in the FNR column.

If you want to see numbers of observations (cars, in this example) instead of percentages, under Plot, select Number of observations.

If false positives are important in your classification problem, plot results per predicted class (instead of true class) to investigate false discovery rates. To see results per predicted class, under Plot, select the Positive Predictive Values (PPV), False Discovery Rates (FDR) option. The PPV is the proportion of correctly classified observations per predicted class. The FDR is the proportion of incorrectly classified observations per predicted class. With this option selected, the confusion matrix now includes summary rows below the table. Positive predictive values are shown in blue for the correctly predicted points in each class, and false discovery rates are shown in orange for the incorrectly predicted points in each class.

If you decide there are too many misclassified points in the classes of interest, try changing classifier settings or feature selection to search for a better model.

To export the confusion matrix plots you create in the app to figures, see Export Plots in Classification Learner App.

Check ROC Curve

View a receiver operating characteristic (ROC) curve after training a model. In the Plot and Interpret section, click the arrow to open the gallery, and then click ROC Curve (Validation) in the Validation Results group. The app creates a ROC curve by using the rocmetrics function.

ROC curve for a binary classification problem

The ROC curve shows the true positive rate (TPR) versus the false positive rate (FPR) for different thresholds of classification scores, computed by the currently selected classifier. The Model Operating Point shows the false positive rate and true positive rate corresponding to the threshold used by the classifier to classify an observation. For example, a false positive rate of 0.4 indicates that the classifier incorrectly assigns 40% of the negative class observations to the positive class. A true positive rate of 0.9 indicates that the classifier correctly assigns 90% of the positive class observations to the positive class.

The AUC (area the under curve) value corresponds to the integral of a ROC curve (TPR values) with respect to FPR from FPR = 0 to FPR = 1. The AUC value is a measure of the overall quality of the classifier. The AUC values are in the range 0 to 1, and larger AUC values indicate better classifier performance. Compare classes and trained models to see if they perform differently in the ROC curve.

You can create a ROC curve for a specific class using the Show check boxes under Plot. However, you do not need to examine ROC curves for both classes in a binary classification problem. The two ROC curves are symmetric, and the AUC values are identical. A TPR of one class is a true negative rate (TNR) of the other class, and TNR is 1–FPR. Therefore, a plot of TPR versus FPR for one class is the same as a plot of 1–FPR versus 1–TPR for the other class.

For a multiclass classifier, the app formulates a set of one-versus-all binary classification problems to have one binary problem for each class, and finds a ROC curve for each class using the corresponding binary problem. Each binary problem assumes that one class is positive and the rest are negative. The model operating point on the plot shows the performance of the classifier for each class in its one-versus-all binary problem.

ROC curves for a multiclass classification problem

For more information, see rocmetrics and ROC Curve and Performance Metrics.

To export the ROC curve plots you create in the app to figures, see Export Plots in Classification Learner App.

Interpret Model Using Partial Dependence Plots

Partial dependence plots (PDPs) allow you to visualize the marginal effect of each predictor on the predicted scores of a trained classification model. After you train a model in Classification Learner, you can view a partial dependence plot for the model. On the Classification Learner tab, in the Plot and Interpret section, click the arrow to open the gallery. In the Interpretation Results section, click Partial Dependence. When computing partial dependence values, the app uses the final model, trained on the full data set (including training and validation data, but excluding test data).

To investigate your results, use the controls on the right.

  • Under Data, choose whether to plot results using Training set data or Test set data. The training set refers to the data used to train the final model and includes all the observations that are not reserved for testing.

  • Under Feature, choose the feature to plot using the X list. The x-axis tick marks in the plot correspond to the unique predictor values in the selected data set.

    If you use PCA to train a model, you can select principal components from the X list.

  • Visualize the predicted scores by class. Each line in the plot corresponds to the average predicted scores across the predictor values for a specific class. Show or hide a plotted line by checking or clearing the corresponding Show box under Classes. Make a plotted line thicker by clicking the corresponding Class name under Classes.

  • Zoom in and out, or pan across the plot. To enable zooming or panning, place the mouse over the PDP and click the corresponding button on the toolbar that appears above the top right of the plot.

Partial dependence plot that compares model scores to displacement values using the training data set

For an example, see Interpret Classifiers Trained in Classification Learner App. For more information on partial dependence plots, see plotPartialDependence.

To export PDPs you create in the app to figures, see Export Plots in Classification Learner App.

Compare Model Plots by Changing Layout

Visualize the results of models trained in Classification Learner by using the plot options in the Plot and Interpret section of the Classification Learner tab. You can rearrange the layout of the plots to compare results across multiple models: use the options in the Layout button, drag and drop plots, or select the options provided by the Document Actions arrow located to the right of the model plot tabs.

For example, after training two models in Classification Learner, display a plot for each model and change the plot layout to compare the plots by using one of these procedures:

  • In the Plot and Interpret section, click Layout and select Compare models.

  • Click the second model tab name, and then drag and drop the second model tab to the right.

  • Click the Document Actions arrow located to the far right of the model plot tabs. Select the Tile All option and specify a 1-by-2 layout.

    Selections for a side-by-side model comparison using the Document Actions arrow

Note that you can click the Hide plot options button at the top right of the plots to make more room for the plots.

Evaluate Test Set Model Performance

After training a model in Classification Learner, you can evaluate the model performance on a test set in the app. This process allows you to check whether the validation accuracy provides a good estimate for the model performance on new data.

  1. Import a test data set into Classification Learner. Alternatively, reserve some data for testing when importing data into the app (see (optional) Reserve Data for Testing).

    • If the test data set is in the MATLAB® workspace, then in the Test section on the Classification Learner tab, click Test Data and select From Workspace.

    • If the test data set is in a file, then in the Test section, click Test Data and select From File. Select a file type in the list, such as a spreadsheet, text file, or comma-separated values (.csv) file, or select All Files to browse for other file types such as .dat.

    In the Import Test Data dialog box, select the test data set from the Test Data Set Variable list. The test set must have the same variables as the predictors imported for training and validation. The unique values in the test response variable must be a subset of the classes in the full response variable.

  2. Compute the test set metrics.

    • To compute test metrics for a single model, select the trained model in the Models pane. On the Classification Learner tab, in the Test section, click Test All and select Test Selected.

    • To compute test metrics for all trained models, click Test All and select Test All in the Test section.

    The app computes the test set performance of each model trained on the full data set, including training and validation data (but excluding test data).

  3. Compare the validation accuracy with the test accuracy.

    In the model Summary tab, the app displays the validation metrics and test metrics in the Training Results section and Test Results section, respectively. You can check if the validation accuracy gives a good estimate for the test accuracy.

    You can also visualize the test results using plots.

    • Display a confusion matrix. In the Plot and Interpret section on the Classification Learner tab, click the arrow to open the gallery, and then click Confusion Matrix (Test) in the Test Results group.

    • Display a ROC curve. In the Plot and Interpret section, click the arrow to open the gallery, and then click ROC Curve (Test) in the Test Results group.

For an example, see Check Classifier Performance Using Test Set in Classification Learner App. For an example that uses test set metrics in a hyperparameter optimization workflow, see Train Classifier Using Hyperparameter Optimization in Classification Learner App.

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