# predict

Predict labels using discriminant analysis classification model

## Description

`[`

also
returns:`label`

,`score`

,`cost`

]
= predict(`Mdl`

,`X`

)

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 multicolumn 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`

:

`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*
{'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 *x* belongs to class
*k* is the product of the prior probability and the multivariate normal
density. The density function of the multivariate normal with 1-by-*d* mean
*μ _{k}* and

*d*-by-

*d*covariance Σ

*at a 1-by-*

_{k}*d*point

*x*is

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

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`k`

th 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:

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

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. You can use models trained on either in-memory or tall data with this function.

For more information, see Tall Arrays.

### C/C++ Code Generation

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

Usage notes and limitations:

Use

`saveLearnerForCoder`

,`loadLearnerForCoder`

, and`codegen`

(MATLAB Coder) 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.To generate single-precision C/C++ code for

`predict`

, specify the name-value argument`'DataType','single'`

when you call the`loadLearnerForCoder`

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`

`X`

must be a single-precision or double-precision matrix or a table containing numeric variables.The number of rows, or observations, in

`X`

can be a variable size, but the number of columns in`X`

must be fixed.If you want to specify

`X`

as a table, then your model must be trained using a table, and your entry-point function for prediction must:Accept data as arrays.

Create a table from the data input arguments and specifies the variable names in the table.

Pass the table to

`predict`

.

For an example of this table workflow, see Generate Code to Classify Data in Table. For more information on using tables in code generation, see Code Generation for Tables (MATLAB Coder) and Table Limitations for Code Generation (MATLAB Coder).

For more information, see Introduction to Code Generation.

## See Also

`ClassificationDiscriminant`

| `CompactClassificationDiscriminant`

| `fitcdiscr`

| `edge`

| `loss`

| `margin`

**Introduced in R2011b**

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