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# confusionmat

Confusion matrix

## Syntax

``C = confusionmat(group,grouphat)``
``C = confusionmat(group,grouphat,'Order',grouporder)``
``[C,order] = confusionmat(___)``

## Description

example

````C = confusionmat(group,grouphat)` returns the confusion matrix `C` determined by the known and predicted groups in `group` and `grouphat`, respectively. ```

example

````C = confusionmat(group,grouphat,'Order',grouporder)` uses `grouporder` to order the rows and columns of `C`. ```

example

````[C,order] = confusionmat(___)` also returns the order of the rows and columns of `C` in the variable `order` using any of the input arguments in previous syntaxes.```

## Examples

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Display the confusion matrix for data with two misclassifications and one missing classification.

Create vectors for the known groups and the predicted groups.

```g1 = [3 2 2 3 1 1]'; % Known groups g2 = [4 2 3 NaN 1 1]'; % Predicted groups```

Return the confusion matrix.

`C = confusionmat(g1,g2)`
```C = 4×4 2 0 0 0 0 1 1 0 0 0 0 1 0 0 0 0 ```

The indices of the rows and columns of the confusion matrix `C` are identical and arranged by default in the sorted order of `[g1;g2]`, that is, `(1,2,3,4)`.

The confusion matrix shows that the two data points known to be in group 1 are classified correctly. For group 2, one of the data points is misclassified into group 3. Also, one of the data points known to be in group 3 is misclassified into group 4. `confusionmat` treats the `NaN` value in the grouping variable `g2` as a missing value and does not include it in the rows and columns of `C`.

Display the confusion matrix for data with two misclassifications and one missing classification, and specify the group order.

Create vectors for the known groups and the predicted groups.

```g1 = [3 2 2 3 1 1]'; % Known groups g2 = [4 2 3 NaN 1 1]'; % Predicted groups```

Specify the group order and return the confusion matrix.

`C = confusionmat(g1,g2,'Order',[4 3 2 1])`
```C = 4×4 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 2 ```

The indices of the rows and columns of the confusion matrix `C` are identical and arranged in the order specified by the group order, that is, `(4,3,2,1)`.

The second row of the confusion matrix `C` shows that one of the data points known to be in group 3 is misclassified into group 4. The third row of `C` shows that one of the data points belonging to group 2 is misclassified into group 3, and the fourth row shows that the two data points known to be in group 1 are classified correctly. `confusionmat` treats the `NaN` value in the grouping variable `g2` as a missing value and does not include it in the rows and columns of `C`.

Perform classification on a sample of the `fisheriris` data set and display the confusion matrix for the resulting classification.

`load fisheriris`

Randomize the measurements and groups in the data.

```rng(0,'twister'); % For reproducibility numObs = length(species); p = randperm(numObs); meas = meas(p,:); species = species(p);```

Train a discriminant analysis classifier by using measurements in the first half of the data.

```half = floor(numObs/2); training = meas(1:half,:); trainingSpecies = species(1:half); Mdl = fitcdiscr(training,trainingSpecies);```

Predict labels for the measurements in the second half of the data by using the trained classifier.

```sample = meas(half+1:end,:); grouphat = predict(Mdl,sample);```

Specify the group order and display the confusion matrix for the resulting classification.

```group = species(half+1:end); [C,order] = confusionmat(group,grouphat,'Order',{'setosa','versicolor','virginica'})```
```C = 3×3 29 0 0 0 22 2 0 0 22 ```
```order = 3x1 cell array {'setosa' } {'versicolor'} {'virginica' } ```

The confusion matrix shows that the measurements belonging to setosa and virginica are classified correctly, while two of the measurements belonging to versicolor are misclassified as virginica. The output `order` contains the order of the rows and columns of the confusion matrix in the sequence specified by the group order` {'setosa','versicolor','virginica'}`.

Perform classification on a tall array of the `fisheriris` data set and display the confusion matrix for the known and predicted tall labels.

`load fisheriris`

Convert the in-memory arrays, `meas` and `species`, to tall arrays.

`tx = tall(meas);`
```Starting parallel pool (parpool) using the 'local' profile ... connected to 12 workers. ```
`ty = tall(species);`

Find the number of observations in the tall array.

`numObs = gather(length(ty)); % gather collects tall array into memory`
```Evaluating tall expression using the Parallel Pool 'local': Evaluation completed in 0 sec ```

Set the random number stream for reproducibility, and randomly select training samples.

```s = RandStream('mlfg6331_64'); % For reproducibility numTrain = floor(numObs/2); [txTrain,trIdx] = datasample(s,tx,numTrain,'Replace',false); tyTrain = ty(trIdx); ```

Fit a decision tree classifier model on the training samples.

`mdl = fitctree(txTrain,tyTrain); `
```Evaluating tall expression using the Parallel Pool 'local': Evaluation completed in 1 sec Evaluating tall expression using the Parallel Pool 'local': Evaluation completed in 1 sec Evaluating tall expression using the Parallel Pool 'local': Evaluation completed in 0 sec Evaluating tall expression using the Parallel Pool 'local': Evaluation completed in 0 sec Evaluating tall expression using the Parallel Pool 'local': Evaluation completed in 0 sec ```

Predict labels for the test samples by using the trained model.

```txTest = tx(~trIdx,:); label = predict(mdl,txTest);```

Display the confusion matrix for the resulting classification.

```tyTest = ty(~trIdx); [C,order] = confusionmat(tyTest,label)```
```C = 3x3 tall double matrix 20 0 0 0 27 2 0 1 25 order = 3x1 tall cell array {'setosa' } {'versicolor'} {'virginica' } ```

The confusion matrix shows that two measurements in the versicolor class are misclassified as virginica, and one measurement in the virginica class is misclassified as versicolor. All the measurements belonging to setosa are classified correctly.

## Input Arguments

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Known groups for categorizing observations, specified as a numeric vector, logical vector, character array, string array, cell array of character vectors, or categorical vector.

`group` is a grouping variable of the same type as `grouphat`. The `group` argument must have the same number of observations as `grouphat`, as described in Grouping Variables. The `confusionmat` function treats character arrays and string arrays as cell arrays of character vectors. Additionally, `confusionmat` treats `NaN`, empty, and `'undefined'` values in `group` as missing values and does not count them as distinct groups or categories.

Example: `{'Male','Female','Female','Male','Female'}`

Data Types: `single` | `double` | `logical` | `char` | `string` | `cell` | `categorical`

Predicted groups for categorizing observations, specified as a numeric vector, logical vector, character array, string array, cell array of character vectors, or categorical vector.

`grouphat` is a grouping variable of the same type as `group`. The `grouphat` argument must have the same number of observations as `group`, as described in Grouping Variables. The `confusionmat` function treats character arrays and string arrays as cell arrays of character vectors. Additionally, `confusionmat` treats `NaN`, empty, and `'undefined'` values in `grouphat` as missing values and does not count them as distinct groups or categories.

Example: `[1 0 0 1 0]`

Data Types: `single` | `double` | `logical` | `char` | `string` | `cell` | `categorical`

Group order, specified as a numeric vector, logical vector, character array, string array, cell array of character vectors, or categorical vector.

`grouporder` is a grouping variable containing all the distinct elements in `group` and `grouphat`. Specify `grouporder` to define the order of the rows and columns of `C`. If `grouporder` contains elements that are not in `group` or `grouphat`, the corresponding entries in `C` are `0`.

By default, `grp2idx` computes the group order using `grp2idx(s)`, where ```s = [group;grouphat]```. The group order depends on the data type of `s`.

• For numeric and logical vectors, the order is the sorted order of `s`.

• For categorical vectors, the order is the order returned by `categories(s)`.

• For other data types, the order is the order of first appearance in `s`.

Example: `'order',{'setosa','versicolor','virginica'}`

Data Types: `single` | `double` | `logical` | `char` | `string` | `cell` | `categorical`

## Output Arguments

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Confusion matrix, returned as a square matrix with size equal to the total number of distinct elements in the `group` and `grouphat` arguments. `C(i,j)` is the count of observations known to be in group `i` but predicted to be in group `j`.

The rows and columns of `C` have identical ordering of the same group indices, computed by `grp2idx` using `grp2idx([group;grouphat])` or specified by `grouporder`.

The `confusionmat` function treats `NaN`, empty, and `'undefined'` values in the grouping variables as missing values and does not include them in the rows and columns of `C`.

Order of rows and columns in `C`, returned as a numeric vector, logical vector, categorical vector, or cell array of character vectors. If `group` and `grouphat` are character arrays, string arrays, or cell arrays of character vectors, then the variable `order` is a cell array of character vectors. Otherwise, `order` is of the same type as `group` and `grouphat`.