Sort classes of confusion matrix chart

Create a confusion matrix chart and sort the classes of the chart according to the class-wise true positive rate (recall) or the class-wise positive predictive value (precision).

Load and inspect the `arrhythmia`

data set.

```
load arrhythmia
isLabels = unique(Y);
nLabels = numel(isLabels)
```

nLabels = 13

tabulate(categorical(Y))

Value Count Percent 1 245 54.20% 2 44 9.73% 3 15 3.32% 4 15 3.32% 5 13 2.88% 6 25 5.53% 7 3 0.66% 8 2 0.44% 9 9 1.99% 10 50 11.06% 14 4 0.88% 15 5 1.11% 16 22 4.87%

The data contains 16 distinct labels that describe various degrees of arrhythmia, but the response (`Y`

) includes only 13 distinct labels.

Train a classification tree and predict the resubstitution response of the tree.

Mdl = fitctree(X,Y); predictedY = resubPredict(Mdl);

Create a confusion matrix chart from the true labels `Y`

and the predicted labels `predictedY`

. Specify `'RowSummary'`

as `'row-normalized'`

to display the true positive rates and false positive rates in the row summary. Also, specify `'ColumnSummary'`

as `'column-normalized'`

to display the positive predictive values and false discovery rates in the column summary.

fig = figure; cm = confusionchart(Y,predictedY,'RowSummary','row-normalized','ColumnSummary','column-normalized');

Resize the container of the confusion chart so percentages appear in the row summary.

fig_Position = fig.Position; fig_Position(3) = fig_Position(3)*1.5; fig.Position = fig_Position;

To sort the confusion matrix according to the true positive rate, normalize the cell values across each row by setting the `Normalization`

property to `'row-normalized'`

and then use `sortClasses`

. After sorting, reset the `Normalization`

property back to `'absolute'`

to display the total number of observations in each cell.

cm.Normalization = 'row-normalized'; sortClasses(cm,'descending-diagonal') cm.Normalization = 'absolute';

To sort the confusion matrix according to the positive predictive value, normalize the cell values across each column by setting the `Normalization`

property to `'column-normalized'`

and then use `sortClasses`

. After sorting, reset the `Normalization`

property back to `'absolute'`

to display the total number of observations in each cell.

cm.Normalization = 'column-normalized'; sortClasses(cm,'descending-diagonal') cm.Normalization = 'absolute';

Create a confusion matrix chart by using the `confusionchart`

function, and sort the classes to cluster similar classes by using the `'cluster'`

option of the `sortClasses`

function. This example also shows how to cluster by using the `pdist`

, `linkage`

, and `optimalleaforder`

functions.

Generate a sample data set that contains eight distinct classes.

rng('default') % For reproducibility trueLabels = randi(8,1000,1); predictedLabels = trueLabels;

Insert confusion among classes {1,4,7}, {2,8}, and {5,6} for the first 200 samples.

rename = [4 8 3 7 6 5 1 2]; predictedLabels(1:100) = rename(predictedLabels(1:100)); rename = [7 8 3 1 6 5 4 2]; predictedLabels(101:200) = rename(predictedLabels(101:200));

Create a confusion matrix chart from the true labels `trueLabels`

and the predicted labels `predictedLabels`

.

figure cm1 = confusionchart(trueLabels,predictedLabels);

**Cluster Using 'cluster'**

Sort the classes to cluster similar classes by using the `'cluster'`

option.

`sortClasses(cm1,'cluster')`

**Cluster Using pdist, linkage, and optimalleaforder**

Instead of using the `'cluster'`

option, you can use the `pdist`

, `linkage`

, and `optimalleaforder`

functions to cluster confusion matrix values. You can customize clustering by using the options of these functions. For details, see the corresponding function reference pages.

Suppose you have a confusion matrix and class labels.

m = confusionmat(trueLabels,predictedLabels); labels = [1 2 3 4 5 6 7 8];

Compute the clustered matrix and find the corresponding class labels by using `pdist`

, `linkage`

, and `optimalleaforder`

. The `pdist`

function computes the Euclidean distance `D`

between pairs of the confusion matrix values. The `optimalleaforder`

function returns an optimal leaf ordering for the hierarchical binary cluster tree `linkage(D)`

using the distance `D`

.

D = pdist(m); idx = optimalleaforder(linkage(D),D); clusteredM = m(idx,idx); clusteredLabels = labels(idx);

Create a confusion matrix chart using the clustered matrix and the corresponding class labels. Then, sort the classes using the class labels.

cm2 = confusionchart(clusteredM,clusteredLabels); sortClasses(cm2,clusteredLabels)

The sorted confusion matrix chart `cm2`

, which you created by using `pdist`

, `linkage`

, and `optimalleaforder`

, is identical to the sorted confusion matrix chart `cm1`

, which you created by using the `'cluster'`

option.

Create a confusion matrix chart and sort the classes of the chart in a fixed order.

Load Fisher's iris data set.

```
load fisheriris
X = meas([51:150,1:50],:);
Y = species([51:150,1:50],:);
```

`X`

is a numeric matrix that contains four petal measurements for 150 irises. `Y`

is a cell array of character vectors that contains the corresponding iris species.

Train a *k*-nearest neighbor (KNN) classifier, where the number of nearest neighbors in the predictors (*k*) is 5. A good practice is to standardize numeric predictor data.

Mdl = fitcknn(X,Y,'NumNeighbors',5,'Standardize',1);

Predict the labels of the training data.

predictedY = resubPredict(Mdl);

Create a confusion matrix chart from the true labels `Y`

and the predicted labels `predictedY`

.

cm = confusionchart(Y,predictedY);

By default, `confusionchart`

sorts the classes into their natural order as defined by `sort`

. In this example, the class labels are character vectors, so `confusionchart`

sorts the classes alphabetically. Reorder the classes of the confusion matrix chart in a fixed order.

sortClasses(cm,["versicolor","setosa","virginica"])

`cm`

— Confusion matrix chart`ConfusionMatrixChart`

objectConfusion matrix chart, specified as a `ConfusionMatrixChart`

object. To create a confusion matrix chart, use `confusionchart`

,

`order`

— Order in which to sort classes`'auto'`

| `'ascending-diagonal'`

| `'descending-diagonal'`

| `'cluster'`

| arrayOrder in which to sort the classes of the confusion matrix chart, specified as one of these values:

`'auto'`

— Sorts the classes into their natural order as defined by the`sort`

function. For example, if the class labels of the confusion matrix chart are a string vector, then sort alphabetically. If the class labels are an ordinal categorical vector, then use the order of the class labels.`'ascending-diagonal'`

— Sort the classes so that the values along the diagonal of the confusion matrix increase from top left to bottom right.`'descending-diagonal'`

— Sort the classes so that the values along the diagonal of the confusion matrix decrease from top left to bottom right.`'cluster'`

— Sort the classes to cluster similar classes. You can customize clustering by using the`pdist`

,`linkage`

, and`optimalleaforder`

functions. For details, see Sort Classes to Cluster Similar Classes.Array — Sort the classes in a unique order specified by a categorical vector, numeric vector, string vector, character array, cell array of character vectors, or logical vector. The array must be a permutation of the

`ClassLabels`

property of the confusion matrix chart.

**Example: **`sortClasses(cm,'ascending-diagonal')`

**Example: **`sortClasses(cm,["owl","cat","toad"])`

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