predict

Predict labels using discriminant analysis classification model

Syntax

label = predict(Mdl,X)

[label,score,cost] = predict(Mdl,X)

Description

label = predict(Mdl,X) returns a vector of predicted class labels for the predictor data in the table or matrix X, based on the trained discriminant analysis classification model Mdl.

[label,score,cost] = predict(Mdl,X) also returns:

• A matrix of classification scores (score) indicating the likelihood that a label comes from a particular class. For discriminant analysis, scores are posterior probabilities.

• A matrix of expected classification cost (cost). For each observation in X, the predicted class label corresponds to the minimum expected classification cost among all classes.

Input Arguments

Mdl — Discriminant analysis classification model

ClassificationDiscriminant model object | CompactClassificationDiscriminant model object

Discriminant analysis classification model, specified as a ClassificationDiscriminant or CompactClassificationDiscriminant model object returned by fitcdiscr.

X — Predictor data to be classified

numeric matrix | table

Predictor data to be classified, specified as a numeric matrix or table.

Each row of X corresponds to one observation, and each column corresponds to one variable. All predictor variables in X must be numeric vectors.

• For a numeric matrix, the variables that compose the columns of X must have the same order as the predictor variables that trained Mdl.

• For a table:

  • predict does not support multi-column variables and cell arrays other than cell arrays of character vectors.

  • If you trained Mdl using a table (for example, Tbl), then all predictor variables in X must have the same variable names and data types as those that trained Mdl (stored in Mdl.PredictorNames). However, the column order of X does not need to correspond to the column order of Tbl. Tbl and X can contain additional variables (response variables, observation weights, etc.), but predict ignores them.

  • If you trained Mdl using a numeric matrix, then the predictor names in Mdl.PredictorNames and corresponding predictor variable names in X must be the same. To specify predictor names during training, see the PredictorNames name-value pair argument of fitcdiscr. X can contain additional variables (response variables, observation weights, etc.), but predict ignores them.

Data Types: table | double | single

Output Arguments

label — Predicted class labels

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

Predicted class labels, returned as a categorical or character array, logical or numeric vector, or cell array of character vectors.

label:

• Is the same data type as the observed class labels (Y) that trained Mdl. (The software treats string arrays as cell arrays of character vectors.)

• Has length equal to the number of rows of X.

score — Predicted class posterior probabilities

numeric matrix

Predicted class posterior probabilities, returned as a numeric matrix of size N-by-K. N is the number of observations (rows) in X, and K is the number of classes (in Mdl.ClassNames). score(i,j) is the posterior probability that observation i in X is of class j in Mdl.ClassNames.

cost — Expected classification costs

numeric matrix

Expected classification costs, returned as a matrix of size N-by-K. N is the number of observations (rows) in X, and K is the number of classes (in Mdl.ClassNames). cost(i,j) is the cost of classifying row i of X as class j in Mdl.ClassNames.

Examples

Predict Class Labels Using Discriminant Analysis Model

Load Fisher's iris data set. Determine the sample size.

load fisheriris
N = size(meas,1);

Partition the data into training and test sets. Hold out 10% of the data for testing.

rng(1); % For reproducibility
cvp = cvpartition(N,'Holdout',0.1);
idxTrn = training(cvp); % Training set indices
idxTest = test(cvp);    % Test set indices

Store the training data in a table.

tblTrn = array2table(meas(idxTrn,:));
tblTrn.Y = species(idxTrn);

Train a discriminant analysis model using the training set and default options.

Mdl = fitcdiscr(tblTrn,'Y');

Predict labels for the test set. You trained Mdl using a table of data, but you can predict labels using a matrix.

labels = predict(Mdl,meas(idxTest,:));

Construct a confusion matrix for the test set.

confusionchart(species(idxTest),labels);

Mdl misclassifies one versicolor iris as virginica in the test set.

Plot Class Posterior Probability Regions

Load Fisher's iris data set. Consider training using the petal lengths and widths only.

load fisheriris
X = meas(:,3:4);

Train a quadratic discriminant analysis model using the entire data set.

Mdl = fitcdiscr(X,species,'DiscrimType','quadratic');

Define a grid of values in the observed predictor space. Predict the posterior probabilities for each instance in the grid.

xMax = max(X);
xMin = min(X);
d = 0.01;
[x1Grid,x2Grid] = meshgrid(xMin(1):d:xMax(1),xMin(2):d:xMax(2));

[~,score] = predict(Mdl,[x1Grid(:),x2Grid(:)]);
Mdl.ClassNames

ans = 3x1 cell array
    {'setosa'    }
    {'versicolor'}
    {'virginica' }

score is a matrix of class posterior probabilities. The columns correspond to the classes in Mdl.ClassNames. For example, score(j,1) is the posterior probability that observation j is a setosa iris.

Plot the posterior probability of versicolor classification for each observation in the grid and plot the training data.

figure;
contourf(x1Grid,x2Grid,reshape(score(:,2),size(x1Grid,1),size(x1Grid,2)));
h = colorbar;
caxis([0 1]);
colormap jet;
hold on
gscatter(X(:,1),X(:,2),species,'mcy','.x+');
axis tight
title('Posterior Probability of versicolor'); 
hold off

The posterior probability region exposes a portion of the decision boundary.

More About

Posterior Probability

The posterior probability that a point z belongs to class j is the product of the prior probability and the multivariate normal density. The density function of the multivariate normal with mean μ_j and covariance Σ_j at a point z is

$$P\left(x|k\right)=\frac{1}{{\left(2\pi \left|{\Sigma }_k\right|\right)}^{1/2}}\exp \left(-\frac{1}{2}{\left(x-{\mu }_k\right)}^T{\Sigma }_k^{-1}\left(x-{\mu }_k\right)\right),$$

where $$\left|{\Sigma }_k\right|$$ is the determinant of Σ_k, and $${\Sigma }_k^{-1}$$ is the inverse matrix.

Let P(k) represent the prior probability of class k. Then the posterior probability that an observation x is of class k is

$$\widehat{P}\left(k|x\right)=\frac{P\left(x|k\right)P\left(k\right)}{P\left(x\right)},$$

where P(x) is a normalization constant, the sum over k of P(x|k)P(k).

Prior Probability

The prior probability is one of three choices:

• 'uniform' — The prior probability of class k is one over the total number of classes.

• 'empirical' — The prior probability of class k is the number of training samples of class k divided by the total number of training samples.

• Custom — The prior probability of class k is the kth element of the prior vector. See fitcdiscr.

After creating a classification model (Mdl) you can set the prior using dot notation:

Mdl.Prior = v;

where v is a vector of positive elements representing the frequency with which each element occurs. You do not need to retrain the classifier when you set a new prior.

Cost

The matrix of expected costs per observation is defined in Cost.

Predicted Class Label

predict classifies so as to minimize the expected classification cost:

$$\widehat{y}=\underset{y=1,\mathrm{...},K}{\arg \min }{\displaystyle \sum _{k=1}^K\widehat{P}\left(k|x\right)C\left(y|k\right)},$$

where

• $$\widehat{y}$$ is the predicted classification.

• K is the number of classes.

• $$\widehat{P}\left(k|x\right)$$ is the posterior probability of class k for observation x.

• $$C\left(y|k\right)$$ is the cost of classifying an observation as y when its true class is k.

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

This function fully supports tall arrays. For more information, see Tall Arrays (MATLAB).

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• Use saveLearnerForCoder, loadLearnerForCoder, and codegen to generate code for the predict function. Save a trained model by using saveLearnerForCoder. Define an entry-point function that loads the saved model by using loadLearnerForCoder and calls the predict function. Then use codegen to generate code for the entry-point function.

• This table contains notes about the arguments of predict. Arguments not included in this table are fully supported.

  Argument	Notes and Limitations
  Mdl	For the usage notes and limitations of the model object, see Code Generation of the CompactClassificationDiscriminant object.
  X	Must be a single-precision or double-precision matrix and can be variable-size. However, the number of columns in X must be numel(Mdl.PredictorNames). Rows and columns must correspond to observations and predictors, respectively.

For more information, see Introduction to Code Generation.