confusionmat

Compute confusion matrix for classification problem

Syntax

C = confusionmat(group,grouphat)

C = confusionmat(group,grouphat,'Order',grouporder)

[C,order] = confusionmat(___)

Description

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

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

[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

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');

Calcualte 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 array
     airplane 
     automobile 
     bird 
     cat 
     deer 
     dog 
     frog 
     horse 
     ship 
     truck 

You can use confusionchart to plot a 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 array
     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.