# confusionmat

Compute confusion matrix for classification problem

## Syntax

## Description

uses `C`

= confusionmat(`group`

,`grouphat`

,`'Order'`

,`grouporder`

)`grouporder`

to order the rows and columns of `C`

.

## Examples

### Calculate Confusion Matrix

Load a sample of predicted and true labels for a classification problem. `trueLabels`

are the true labels for an image classification problem and `predictedLabels`

are the predictions of a convolutional neural network.

load('Cifar10Labels.mat','trueLabels','predictedLabels');

Calculate the numeric confusion matrix. `order`

is the order of the classes in the confusion matrix.

[m,order] = confusionmat(trueLabels,predictedLabels)

`m = `*10×10*
923 4 21 8 4 1 5 5 23 6
5 972 2 0 0 0 0 1 5 15
26 2 892 30 13 8 17 5 4 3
12 4 32 826 24 48 30 12 5 7
5 1 28 24 898 13 14 14 2 1
7 2 28 111 18 801 13 17 0 3
5 0 16 27 3 4 943 1 1 0
9 1 14 13 22 17 3 915 2 4
37 10 4 4 0 1 2 1 931 10
20 39 3 3 0 0 2 1 9 923

`order = `*10x1 categorical*
airplane
automobile
bird
cat
deer
dog
frog
horse
ship
truck

You can use `confusionchart`

to plot the confusion matrix as a confusion matrix chart.

figure cm = confusionchart(m,order);

You do not need to calculate the confusion matrix first and then plot it. Instead, plot a confusion matrix chart directly from the true and predicted labels. You can also add column and row summaries and a title.

figure cm = confusionchart(trueLabels,predictedLabels, ... 'Title','My Title', ... 'RowSummary','row-normalized', ... 'ColumnSummary','column-normalized');

The `ConfusionMatrixChart`

object stores the numeric confusion matrix in the `NormalizedValues`

property and classes in the `ClassLabels`

property.

cm.NormalizedValues

`ans = `*10×10*
923 4 21 8 4 1 5 5 23 6
5 972 2 0 0 0 0 1 5 15
26 2 892 30 13 8 17 5 4 3
12 4 32 826 24 48 30 12 5 7
5 1 28 24 898 13 14 14 2 1
7 2 28 111 18 801 13 17 0 3
5 0 16 27 3 4 943 1 1 0
9 1 14 13 22 17 3 915 2 4
37 10 4 4 0 1 2 1 931 10
20 39 3 3 0 0 2 1 9 923

cm.ClassLabels

`ans = `*10x1 categorical*
airplane
automobile
bird
cat
deer
dog
frog
horse
ship
truck

## Input Arguments

`group`

— Known groups

numeric vector | logical vector | character array | string array | cell array of character vectors | categorical vector

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 (Statistics and Machine Learning Toolbox). 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`

`grouphat`

— Predicted groups

numeric vector | logical vector | character array | string array | cell array of character vectors | categorical vector

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 (Statistics and Machine Learning Toolbox). 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`

`grouporder`

— Group order

numeric vector | logical vector | character array | string array | cell array of character vectors | categorical vector

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, the group order depends on the data type of `s = [group;grouphat]`

:

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

`C`

— Confusion matrix

matrix

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. By default, the group order depends on the data type of `s = [group;grouphat]`

:

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`

.

To change the order, specify `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`

— Order of rows and columns

numeric vector | logical vector | categorical vector | cell array of character vectors

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`

.

## Alternative Functionality

Use

`confusionchart`

to calculate and plot a confusion matrix. Additionally,`confusionchart`

displays summary statistics about your data and sorts the classes of the confusion matrix according to the class-wise precision (positive predictive value), class-wise recall (true positive rate), or total number of correctly classified observations.

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