# predict

Predict labels using classification tree

## Description

uses
additional options specified by one or more `label`

= predict(`Mdl`

,`X`

,`Name,Value`

)`Name,Value`

pair
arguments. For example, you can specify to prune `Mdl`

to
a particular level before predicting labels.

`[`

uses any of the input argument
in the previous syntaxes and additionally returns:`label`

,`score`

,`node`

,`cnum`

]
= predict(___)

A matrix of classification scores (

`score`

) indicating the likelihood that a label comes from a particular class. For classification trees, scores are posterior probabilities. For each observation in`X`

, the predicted class label corresponds to the minimum expected misclassification cost among all classes.A vector of predicted node numbers for the classification (

`node`

).A vector of predicted class number for the classification (

`cnum`

).

## Input Arguments

`Mdl`

— Trained classification tree

`ClassificationTree`

model object | `CompactClassificationTree`

model object

Trained classification tree, specified as a `ClassificationTree`

or `CompactClassificationTree`

model
object. That is, `Mdl`

is a trained classification
model returned by `fitctree`

or `compact`

.

`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.

For a numeric matrix:

The variables making up the columns of

`X`

must have the same order as the predictor variables that trained`Mdl`

.If you trained

`Mdl`

using a table (for example,`Tbl`

), then`X`

can be a numeric matrix if`Tbl`

contains all numeric predictor variables. To treat numeric predictors in`Tbl`

as categorical during training, identify categorical predictors using the`CategoricalPredictors`

name-value pair argument of`fitctree`

. If`Tbl`

contains heterogeneous predictor variables (for example, numeric and categorical data types) and`X`

is a numeric matrix, then`predict`

throws an error.

For a table:

`predict`

does not support multicolumn variables or 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`fitctree`

. All predictor variables in`X`

must be numeric vectors.`X`

can contain additional variables (response variables, observation weights, etc.), but`predict`

ignores them.

**Data Types: **`table`

| `double`

| `single`

### Name-Value Arguments

Specify optional
comma-separated pairs of `Name,Value`

arguments. `Name`

is
the argument name and `Value`

is the corresponding value.
`Name`

must appear inside quotes. You can specify several name and value
pair arguments in any order as
`Name1,Value1,...,NameN,ValueN`

.

`Subtrees`

— Pruning level

0 (default) | vector of nonnegative integers | `'all'`

Pruning level, specified as the comma-separated pair consisting
of `'Subtrees'`

and a vector of nonnegative integers
in ascending order or `'all'`

.

If you specify a vector, then all elements must be at least `0`

and
at most `max(Mdl.PruneList)`

. `0`

indicates
the full, unpruned tree and `max(Mdl.PruneList)`

indicates
the completely pruned tree (i.e., just the root node).

If you specify `'all'`

, then `predict`

operates
on all subtrees (i.e., the entire pruning sequence). This specification
is equivalent to using `0:max(Mdl.PruneList)`

.

`predict`

prunes `Mdl`

to
each level indicated in `Subtrees`

, and then estimates
the corresponding output arguments. The size of `Subtrees`

determines
the size of some output arguments.

To invoke `Subtrees`

, the properties `PruneList`

and `PruneAlpha`

of `Mdl`

must
be nonempty. In other words, grow `Mdl`

by setting `'Prune','on'`

,
or by pruning `Mdl`

using `prune`

.

**Example: **`'Subtrees','all'`

**Data Types: **`single`

| `double`

| `char`

| `string`

## Output Arguments

`label`

— Predicted class labels

vector | array

Predicted
class labels, returned as a vector or array. Each entry of `label`

corresponds
to the class with minimal expected cost for the corresponding row
of `X`

.

Suppose `Subtrees`

is a numeric vector containing `T`

elements (for `'all'`

, see `Subtrees`

),
and `X`

has `N`

rows.

If the response data type is

`char`

and:`T`

= 1, then`label`

is a character matrix containing`N`

rows. Each row contains the predicted label produced by subtree`Subtrees`

.`T`

> 1, then`label`

is an`N`

-by-`T`

cell array.

Otherwise,

`label`

is an`N`

-by-`T`

array having the same data type as the response. (The software treats string arrays as cell arrays of character vectors.)

In the latter two cases, column * j*
of

`label`

contains the vector of predicted labels produced
by subtree `Subtrees(``j`

)

.`score`

— Posterior probabilities

numeric matrix

Posterior probabilities, returned as a numeric matrix of size `N`

-by-`K`

,
where `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 row `i`

of `X`

is
of class `j`

.

If `Subtrees`

has `T`

elements,
and `X`

has `N`

rows, then `score`

is
an `N`

-by-`K`

-by-`T`

array,
and `node`

and `cnum`

are `N`

-by-`T`

matrices.

`cnum`

— Class numbers

numeric vector

Class numbers corresponding to the predicted `labels`

,
returned as a numeric vector. Each entry of `cnum`

corresponds
to a predicted class number for the corresponding row of `X`

.

## Examples

### Predict Labels Using a Classification Tree

Examine predictions for a few rows in a data set left out of training.

Load Fisher's iris data set.

`load fisheriris`

Partition the data into training (50%) and validation (50%) sets.

n = size(meas,1); rng(1) % For reproducibility idxTrn = false(n,1); idxTrn(randsample(n,round(0.5*n))) = true; % Training set logical indices idxVal = idxTrn == false; % Validation set logical indices

Grow a classification tree using the training set.

Mdl = fitctree(meas(idxTrn,:),species(idxTrn));

Predict labels for the validation data. Count the number of misclassified observations.

```
label = predict(Mdl,meas(idxVal,:));
label(randsample(numel(label),5)) % Display several predicted labels
```

`ans = `*5x1 cell*
{'setosa' }
{'setosa' }
{'setosa' }
{'virginica' }
{'versicolor'}

numMisclass = sum(~strcmp(label,species(idxVal)))

numMisclass = 3

The software misclassifies three out-of-sample observations.

### Estimate Class Posterior Probabilities Using a Classification Tree

Load Fisher's iris data set.

`load fisheriris`

Partition the data into training (50%) and validation (50%) sets.

n = size(meas,1); rng(1) % For reproducibility idxTrn = false(n,1); idxTrn(randsample(n,round(0.5*n))) = true; % Training set logical indices idxVal = idxTrn == false; % Validation set logical indices

Grow a classification tree using the training set, and then view it.

Mdl = fitctree(meas(idxTrn,:),species(idxTrn)); view(Mdl,'Mode','graph')

The resulting tree has four levels.

Estimate posterior probabilities for the test set using subtrees pruned to levels 1 and 3.

```
[~,Posterior] = predict(Mdl,meas(idxVal,:),'SubTrees',[1 3]);
Mdl.ClassNames
```

`ans = `*3x1 cell*
{'setosa' }
{'versicolor'}
{'virginica' }

Posterior(randsample(size(Posterior,1),5),:,:),... % Display several posterior probabilities

ans = ans(:,:,1) = 1.0000 0 0 1.0000 0 0 1.0000 0 0 0 0 1.0000 0 0.8571 0.1429 ans(:,:,2) = 0.3733 0.3200 0.3067 0.3733 0.3200 0.3067 0.3733 0.3200 0.3067 0.3733 0.3200 0.3067 0.3733 0.3200 0.3067

The elements of `Posterior`

are class posterior probabilities:

Rows correspond to observations in the validation set.

Columns correspond to the classes as listed in

`Mdl.ClassNames`

.Pages correspond to the subtrees.

The subtree pruned to level 1 is more sure of its predictions than the subtree pruned to level 3 (i.e., the root node).

## More About

### Predicted Class Label

`predict`

classifies by minimizing the expected
misclassification cost:

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

where:

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

*K*is the number of classes.$$\widehat{P}\left(j|x\right)$$ is the posterior probability of class

*j*for observation*x*.$$C\left(y|j\right)$$ is the cost of classifying an observation as

*y*when its true class is*j*.

### Score (tree)

For trees, the *score* of a classification
of a leaf node is the posterior probability of the classification
at that node. The posterior probability of the classification at a
node is the number of training sequences that lead to that node with
the classification, divided by the number of training sequences that
lead to that node.

For example, consider classifying a predictor `X`

as `true`

when `X`

< `0.15`

or `X`

> `0.95`

, and `X`

is
false otherwise.

Generate 100 random points and classify them:

rng(0,'twister') % for reproducibility X = rand(100,1); Y = (abs(X - .55) > .4); tree = fitctree(X,Y); view(tree,'Mode','Graph')

Prune the tree:

tree1 = prune(tree,'Level',1); view(tree1,'Mode','Graph')

The pruned tree correctly classifies observations that are less
than 0.15 as `true`

. It also correctly classifies
observations from .15 to .94 as `false`

. However,
it incorrectly classifies observations that are greater than .94 as `false`

.
Therefore, the score for observations that are greater than .15 should
be about .05/.85=.06 for `true`

, and about .8/.85=.94
for `false`

.

Compute the prediction scores for the first 10 rows of `X`

:

[~,score] = predict(tree1,X(1:10)); [score X(1:10,:)]

`ans = `*10×3*
0.9059 0.0941 0.8147
0.9059 0.0941 0.9058
0 1.0000 0.1270
0.9059 0.0941 0.9134
0.9059 0.0941 0.6324
0 1.0000 0.0975
0.9059 0.0941 0.2785
0.9059 0.0941 0.5469
0.9059 0.0941 0.9575
0.9059 0.0941 0.9649

Indeed, every value of `X`

(the right-most
column) that is less than 0.15 has associated scores (the left and
center columns) of `0`

and `1`

,
while the other values of `X`

have associated scores
of `0.91`

and `0.09`

. The difference
(score `0.09`

instead of the expected `.06`

)
is due to a statistical fluctuation: there are `8`

observations
in `X`

in the range `(.95,1)`

instead
of the expected `5`

observations.

### True Misclassification Cost

The true misclassification cost is the cost of classifying an observation into an incorrect class.

You can set the true misclassification cost per class by using the `'Cost'`

name-value argument when you create the classifier. `Cost(i,j)`

is the cost
of classifying an observation into class `j`

when its true class is
`i`

. By default, `Cost(i,j)=1`

if
`i~=j`

, and `Cost(i,j)=0`

if `i=j`

.
In other words, the cost is `0`

for correct classification and
`1`

for incorrect classification.

### Expected Cost

The expected misclassification cost per observation is an averaged cost of classifying the observation into each class.

Suppose you have `Nobs`

observations that you want to classify with a trained
classifier, and you have `K`

classes. You place the observations
into a matrix `X`

with one observation per row.

The expected cost matrix `CE`

has size
`Nobs`

-by-`K`

. Each row of
`CE`

contains the expected (average) cost of classifying
the observation into each of the `K`

classes.
`CE(`

is*n*,*k*)

$$\sum _{i=1}^{K}\widehat{P}\left(i|X(n)\right)C\left(k|i\right)},$$

where:

*K*is the number of classes.$$\widehat{P}\left(i|X(n)\right)$$ is the posterior probability of class

*i*for observation*X*(*n*).$$C\left(k|i\right)$$ is the true misclassification cost of classifying an observation as

*k*when its true class is*i*.

### Predictive Measure of Association

The *predictive measure of association* is
a value that indicates the similarity between decision rules that
split observations. Among all possible decision splits that are compared
to the optimal split (found by growing the tree), the best surrogate decision
split yields the maximum predictive measure of association.
The second-best surrogate split has the second-largest predictive
measure of association.

Suppose *x _{j}* and

*x*are predictor variables

_{k}*j*and

*k*, respectively, and

*j*≠

*k*. At node

*t*, the predictive measure of association between the optimal split

*x*<

_{j}*u*and a surrogate split

*x*<

_{k}*v*is

$${\lambda}_{jk}=\frac{\text{min}\left({P}_{L},{P}_{R}\right)-\left(1-{P}_{{L}_{j}{L}_{k}}-{P}_{{R}_{j}{R}_{k}}\right)}{\text{min}\left({P}_{L},{P}_{R}\right)}.$$

*P*is the proportion of observations in node_{L}*t*, such that*x*<_{j}*u*. The subscript*L*stands for the left child of node*t*.*P*is the proportion of observations in node_{R}*t*, such that*x*≥_{j}*u*. The subscript*R*stands for the right child of node*t*.$${P}_{{L}_{j}{L}_{k}}$$ is the proportion of observations at node

*t*, such that*x*<_{j}*u*and*x*<_{k}*v*.$${P}_{{R}_{j}{R}_{k}}$$ is the proportion of observations at node

*t*, such that*x*≥_{j}*u*and*x*≥_{k}*v*.Observations with missing values for

*x*or_{j}*x*do not contribute to the proportion calculations._{k}

*λ _{jk}* is a value
in (–∞,1]. If

*λ*> 0, then

_{jk}*x*<

_{k}*v*is a worthwhile surrogate split for

*x*<

_{j}*u*.

## Algorithms

`predict`

generates predictions by following
the branches of `Mdl`

until it reaches a leaf node
or a missing value. If `predict`

reaches a leaf node,
it returns the classification of that node.

If `predict`

reaches a node with a missing value
for a predictor, its behavior depends on the setting of the `Surrogate`

name-value
pair when `fitctree`

constructs `Mdl`

.

(default) —`Surrogate`

=`'off'`

`predict`

returns the label with the largest number of training samples that reach the node.—`Surrogate`

=`'on'`

`predict`

uses the best surrogate split at the node. If all surrogate split variables with positive*predictive measure of association*are missing,`predict`

returns the label with the largest number of training samples that reach the node. For a definition, see Predictive Measure of Association.

## Alternative Functionality

### Simulink Block

To integrate the prediction of a classification tree model into Simulink^{®}, you can use the ClassificationTree
Predict block in the Statistics and Machine Learning Toolbox™ library or a MATLAB^{®} Function block with the `predict`

function. For
examples, see Predict Class Labels Using ClassificationTree Predict Block and Predict Class Labels Using MATLAB Function Block.

When deciding which approach to use, consider the following:

If you use the Statistics and Machine Learning Toolbox library block, you can use the

**Fixed-Point Tool (Fixed-Point Designer)**to convert a floating-point model to fixed point.Support for variable-size arrays must be enabled for a MATLAB Function block with the

`predict`

function.If you use a MATLAB Function block, you can use MATLAB functions for preprocessing or post-processing before or after predictions in the same MATLAB Function block.

## 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:

You can generate C/C++ code for both

`predict`

and`update`

by using a coder configurer. Or, generate code only for`predict`

by using`saveLearnerForCoder`

,`loadLearnerForCoder`

, and`codegen`

.Code generation for

`predict`

and`update`

— Create a coder configurer by using`learnerCoderConfigurer`

and then generate code by using`generateCode`

. Then you can update model parameters in the generated code without having to regenerate the code.Code generation for

`predict`

— 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`

(MATLAB Coder) 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.You can also generate fixed-point C/C++ code for

`predict`

. Fixed-point code generation requires an additional step that defines the fixed-point data types of the variables required for prediction. Create a fixed-point data type structure by using the data type function generated by`generateLearnerDataTypeFcn`

, and use the structure as an input argument of`loadLearnerForCoder`

in an entry-point function. Generating fixed-point C/C++ code requires MATLAB Coder™ and Fixed-Point Designer™.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

`CompactClassificationTree`

object.`X`

For general code generation,

`X`

must be a single-precision or double-precision matrix or a table containing numeric variables, categorical variables, or both.In the coder configurer workflow,

`X`

must be a single-precision or double-precision matrix.For fixed-point code generation,

`X`

must be a fixed-point matrix.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).

`label`

If the response data type is `char`

and`codegen`

cannot determine that the value of`Subtrees`

is a scalar, then`label`

is a cell array of character vectors.`'Subtrees'`

Names in name-value pair arguments must be compile-time constants. For example, to allow user-defined pruning levels in the generated code, include

`{coder.Constant('Subtrees'),coder.typeof(0,[1,n],[0,1])}`

in the`-args`

value of`codegen`

(MATLAB Coder), where`n`

is`max(Mdl.PruneList)`

.The

`'Subtrees'`

name-value pair argument is not supported in the coder configurer workflow.For fixed-point code generation, the

`'Subtrees'`

value must be`coder.Constant('all')`

or have an integer data type.

For more information, see Introduction to Code Generation.

### GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Usage notes and limitations:

`predict`

executes on a GPU in these cases:The input argument

`X`

is a`gpuArray`

or a table containing`gpuArray`

predictor variables.The input argument

`mdl`

was fitted with GPU array input arguments.

If the tree model was trained with surrogate splits, these limitations apply:

You cannot specify the input argument

`X`

as a`gpuArray`

.You cannot specify the input argument

`X`

as a table containing`gpuArray`

elements.

For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

## See Also

`fitctree`

| `compact`

| `prune`

| `loss`

| `edge`

| `margin`

| `CompactClassificationTree`

| `ClassificationTree`

**Introduced in R2011a**

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