# sequentialfs

Sequential feature selection using custom criterion

## Syntax

## Description

selects a subset of features in `tf`

= sequentialfs(`fun`

,`X`

,`y`

)`X`

that are important for predicting
`y`

. The function defines a random nonstratified partition for 10-fold
cross-validation using `X`

and `y`

, and then
sequentially selects features based on the cross-validate prediction criterion values
computed by the `fun`

function. The initial feature set includes no
features. `sequentialfs`

adds one feature to the set at each iteration,
until adding a feature does not decrease the criterion value by greater than the termination
tolerance value. The output `tf`

is a logical vector that indicates the
selected features. For more details, see Algorithms.

specifies options using one or more name-value arguments in addition to any of the input
argument combinations in the previous syntaxes. For example, specify
`tf`

= sequentialfs(___,`Name,Value`

)`"Direction","backward"`

to perform recursive feature elimination (RFE).
The initial feature set includes all features. `sequentialfs`

removes one
feature from the set at each iteration, until removing a feature does not decrease the
prediction criterion.

## Examples

### Forward Feature Selection

Find important features by performing forward sequential feature selection using the wrapper type.

Load the `fisheriris`

data set.

`load fisheriris`

Display the variables in the data set.

whos

Name Size Bytes Class Attributes meas 150x4 4800 double species 150x1 18100 cell

The matrix `meas`

contains four measurements from three species of iris flowers for 150 different flowers. The variable `species`

lists the species for each flower.

Specify the predictor data `X`

and the response data y. Define `X`

to include the four measurements and six random variables. Place the measurement variables in columns 1, 3, 5, and 7.

rng("default") % For reproducibility X = randn(150,10); X(:,[1 3 5 7])= meas; y = species;

Define the function handle `myfun`

for an anonymous function that takes four inputs: training data (`XTrain`

and `yTrain`

) and test data (`XTest`

and `yTest`

). The anonymous function trains a classification model by using the training data, and returns a loss value on the test data for the trained model.

```
myfun = @(XTrain,yTrain,XTest,yTest) ...
size(XTest,1)*loss(fitcecoc(XTrain,yTrain),XTest,yTest);
```

The `loss`

function of a classification model object returns an average loss value, but `sequentialfs`

also divides the sum of the criterion values returned by `myfun`

by the total number of test observations. Therefore, the anonymous function must return the loss value multiplied by the number of test observations.

Create a random partition for stratified 10-fold cross-validation.

`cv = cvpartition(y,"KFold",10);`

Use the `sequentialfs`

function to sequentially select important features in `X`

based on the criterion value returned by `myfun`

. Specify to use the stratified partition `cv`

, and set the iteration option to display information about the feature selection process at each iteration.

opts = statset("Display","iter"); tf = sequentialfs(myfun,X,y,"CV",cv,"Options",opts);

Start forward sequential feature selection: Initial columns included: none Columns that can not be included: none Step 1, added column 7, criterion value 0.04 Step 2, added column 5, criterion value 0.0333333 Step 3, added column 1, criterion value 0.0266667 Step 4, added column 3, criterion value 0.0133333 Final columns included: 1 3 5 7

`sequentialfs`

correctly finds the important predictors in columns 1, 3, 5, and 7.

### Backward Feature Selection

Find important features by performing backward sequential feature selection, or recursive feature elimination (RFE), using the wrapper type.

Load the `hald`

data set, which measures the effect of cement composition on its hardening heat.

`load hald`

This data set includes the variables `ingredients`

and `heat`

. The matrix `ingredients`

contains the percent composition of four chemicals present in the cement. The vector `heat`

contains the values for the heat hardening after 180 days for each cement sample.

Use the `sequentialfs`

function to perform backward sequential feature selection based on the criterion value returned by `myfun`

. The code for the helper function `myfun`

appears at the end of this example. Specify the `Direction`

name-value argument as `"backward"`

to include all features in the initial feature set and then sequentially exclude one feature at each iteration. Set the iteration option to display information about the feature selection process at each iteration.

rng("default") % For reproducibility opts = statset("Display","iter"); tf = sequentialfs(@myfun,ingredients,heat, ... "Direction","backward","Options",opts);

Start backward sequential feature selection: Initial columns included: all Columns that must be included: none Step 1, used initial columns, criterion value 12.4989 Step 2, removed column 3, criterion value 6.25866 Final columns included: 1 2 4

`sequentialfs`

excludes the third variable from the features in `ingredients`

.

**Helper Function**

The `myfun`

function takes four inputs: training data (`XTrain`

and `yTrain`

) and test data (`XTest`

and `yTest`

). The function trains a regression model by using the training data, and returns the sum of squared errors on the test data for the trained model.

function criterion = myfun(XTrain,yTrain,XTest,yTest) mdl = fitrlinear(XTrain,yTrain); predictedYTest = predict(mdl,XTest); e = yTest - predictedYTest; criterion = e'*e; end

### Filter Type Feature Selection

Perform filter type feature selection based on the correlation coefficients for the features.

Load the `carsmall`

data set.

`load carsmall`

Create the feature matrix `X`

containing six variables.

```
X = [Acceleration Cylinders Displacement ...
Horsepower Model_Year Weight];
```

Compute the matrix of the pairwise linear correlation coefficients between each pair of features in `X`

by using the `corr`

function. Specify the `Rows`

name-value argument as `"pairwise"`

to omit any rows containing `NaN`

on a pairwise basis for each two-column correlation coefficient calculation.

corr(X,"Rows","pairwise")

`ans = `*6×6*
1.0000 -0.6473 -0.6947 -0.6968 0.4843 -0.4879
-0.6473 1.0000 0.9512 0.8622 -0.6053 0.8844
-0.6947 0.9512 1.0000 0.9134 -0.5779 0.8895
-0.6968 0.8622 0.9134 1.0000 -0.6082 0.8733
0.4843 -0.6053 -0.5779 -0.6082 1.0000 -0.4964
-0.4879 0.8844 0.8895 0.8733 -0.4964 1.0000

`X`

contains highly correlated features. For example, the correlation between the second and third features (`Cylinders`

and `Displacement`

) is 0.9512.

Use the `sequentialfs`

function to rank the features in `X`

based on the correlation values. Specify these options when you call the `sequentialfs`

function:

Use the helper function

`mycorr`

, which returns the maximum absolute value of the off-diagonal elements in the matrix of correlation coefficients. The code for this helper function appears at the end of this example.Specify

`"Direction","backward"`

and`"NullModel",true`

so that`sequentialfs`

starts from the initial feature set containing all features and then excludes all features from the set, one feature at a time.Specify

`"CV","none"`

to perform feature selection without cross-validation.Set the iteration option to display information about the feature selection process at each iteration.

opts = statset("Display","iter"); [~,history] = sequentialfs(@mycorr,X, ... "Direction","backward","NullModel",true, ... "CV","none","Options",opts);

Start backward sequential feature selection: Initial columns included: all Columns that must be included: none Step 1, used initial columns, criterion value 0.951167 Step 2, removed column 3, criterion value 0.884401 Step 3, removed column 6, criterion value 0.862164 Step 4, removed column 4, criterion value 0.647346 Step 5, removed column 2, criterion value 0.484253 Step 6, removed column 1, criterion value 0 Step 7, removed column 5, criterion value 0 Final columns included: none

`sequentialfs`

returns the structure array `history`

with two fields (`In`

and `Crit`

) containing information about the feature selection process. The `In`

field contains a logical matrix where row `i`

indicates the features selected at iteration `i`

. A `true`

(logical `1`

) entry in a row indicates that the corresponding feature is in the feature set after the iteration.

history.In

`ans = `*7x6 logical array*
1 1 1 1 1 1
1 1 0 1 1 1
1 1 0 1 1 0
1 1 0 0 1 0
1 0 0 0 1 0
0 0 0 0 1 0
0 0 0 0 0 0

The `Crit`

field contains the criterion values computed at each iteration.

history.Crit

`ans = `*1×7*
0.9512 0.8844 0.8622 0.6473 0.4843 0 0

The last two criterion values are zero because the `mycorr`

function returns 0 if the input contains fewer than two features.

Extract the indices of the excluded features from the matrix in the `In`

field.

p = size(X,2); idx = NaN(1,p); for i = 1 : p idx(i) = find(history.In(i,:)~=history.In(i+1,:)); end idx

`idx = `*1×6*
3 6 4 2 1 5

Find the set of features whose criterion value is less than 0.8.

threshold = 0.8; iter_last_exclude = find(history.Crit(2:end)<threshold,1); idx_selected = idx(iter_last_exclude+1:end)

`idx_selected = `*1×3*
2 1 5

Compute the correlation coefficient matrix for the selected features.

corr(X(:,idx_selected),"Rows","pairwise")

`ans = `*3×3*
1.0000 -0.6473 -0.6053
-0.6473 1.0000 0.4843
-0.6053 0.4843 1.0000

The absolute values of the off-diagonal elements are less than the threshold value 0.8.

**Helper Function**

The `mycorr`

function takes a matrix that contains features in columns, and returns the maximum absolute value of the off-diagonal elements in the matrix of correlation coefficients. The off-diagonal elements are the correlations between two distinct features in the input data. Therefore, `mycorr`

returns zero if the input data does not have at least two distinct features.

function criterion = mycorr(X) if size(X,2) < 2 criterion = 0; else p = size(X,2); R = corr(X,"Rows","pairwise"); R(logical(eye(p))) = NaN; criterion = max(abs(R),[],"all"); end end

### Select Features in Table

Convert a table that contains both numeric and categorical variables to an array by using the `onehotencode`

and `table2array`

functions. Then, select important features in the array by using the `sequentialfs`

function.

Load the `carbig`

data set.

`load carbig`

This data set contains variables that describe several aspects of cars, such as miles per gallon (`MPG`

), country of origin (`Origin`

), and number of cylinders (`Cylinders`

). You can create a regression model of `MPG`

using the other variables.

Specify the predictor data `tblX`

in a table, and specify the response data `y`

.

```
tblX = table(Acceleration,Cylinders,Displacement, ...
Horsepower,Model_Year,Weight,Origin);
y = MPG;
```

All variables in `tblX`

are numeric except the `Origin`

variable.

One-hot encode the `Origin`

variable by using the `onehotencode`

function.

tblOrigin = table(categorical(string(Origin))); tblOrigin = onehotencode(tblOrigin);

Remove the `Origin`

variable from `tblX`

, and add the encoded values to `tblX`

.

tblX.Origin = []; tblX = [tblX tblOrigin];

Convert the table `tblX`

to an array.

X = table2array(tblX);

Define the function handle `myfun`

for an anonymous function that takes four inputs: training data (`XTrain`

and `yTrain`

) and test data (`XTest`

and `yTest`

). The anonymous function trains a regression model by using the training data, and returns a loss value on the test data for the trained model.

```
myfun = @(XTrain,yTrain,XTest,yTest) ...
size(XTest,1)*loss(fitrtree(XTrain,yTrain),XTest,yTest);
```

The `loss`

function of a regression model object returns the mean squared error (MSE), but `sequentialfs`

also divides the sum of the criterion values returned by `myfun`

by the total number of test observations. Therefore, the anonymous function must return the loss value multiplied by the number of test observations.

Use the `sequentialfs`

function to sequentially select important features in `X`

based on the criterion value returned by `myfun`

.

rng("default") % For reproducibility tf = sequentialfs(myfun,X,y);

Display the variable names of the selected features.

tblX.Properties.VariableNames(tf)'

`ans = `*6x1 cell*
{'Cylinders' }
{'Displacement'}
{'Model_Year' }
{'Weight' }
{'Germany' }
{'Italy' }

## Input Arguments

`fun`

— Function to compute feature selection criterion

function handle

Function to compute the feature selection criterion, specified as a function handle.

For each candidate feature set, `sequentialfs`

computes the
cross-validated criterion value by repeatedly calling the `fun`

function as follows:

For each fold (a group of training and test data sets) defined by the

`CV`

name-value argument,`sequentialfs`

calls the`fun`

function to get the criterion value for the fold.`sequentialfs`

divides the sum of the criterion values by the total number of test observations.

If you specify `X`

and `y`

, then the
`fun`

function must have this form:

criterion = fun(XTrain,yTrain,XTest,yTest)

The

`fun`

function accepts the training data (`XTrain`

and`yTrain`

) and test data (`XTest`

and`yTest`

).`XTrain`

and`XTest`

contain a subset of the columns of`X`

that corresponds to the current candidate feature set.The

`fun`

function returns a scalar value`criterion`

.Typically,

`fun`

trains a model by using the training data (`XTrain`

,`yTrain`

), predicts response values for`XTest`

, and returns a loss of the predicted values compared to`yTest`

. Common loss measures include the sum of squared errors for regression models and the number of misclassified observations for classification models.For example, you can define the

`myFun`

function as follows, and then specify`fun`

as`@myFun`

.function criterion = myFun(XTrain,yTrain,XTest,yTest) mdl = fitcsvm(XTrain,yTrain); predictedYTest = predict(mdl,XTest); criterion = sum(~strcmp(yTest,predictedYTest)); end

Alternatively, you can define the function handle

`myFunHandle`

for an anonymous function as follows, and then specify`fun`

as`myFunHandle`

.`myFunHandle = @(XTrain,yTrain,XTest,yTest) ... loss(fitcsvm(XTrain,yTrain),XTest,yTest)*size(XTest,1);`

`sequentialfs`

divides the sum of the criterion values returned by`fun`

by the total number of test observations. So,`fun`

must not divide the loss value by the number of test observations. The`loss`

function of a classification or regression object returns an averaged loss value. Therefore,`fun`

must return the loss value multiplied by the number of test observations. If you define the`fun`

function to return the sum of squared errors or the number of misclassified observations, then the cross-validated criterion value is the mean squared error or the misclassification rate, respectively.

If you specify `X1,...,XN`

, `sequentialfs`

selects features from `X1`

only, but otherwise imposes no
interpretation on `X1,...,XN`

. The function `fun`

still must have this form:

criterion = fun(X1Train,⋯,XNTrain,X1Test,⋯,XNTest)

The

`fun`

function accepts the training data (`X1Train`

,…,`XNTrain`

) and test data (`X1Test`

,…,`XNTest`

).`X1Train`

and`X1Test`

contain a subset of the columns of`X1`

that corresponds to the current candidate feature set.The

`fun`

function returns a scalar value`criterion`

.

**Data Types: **`function_handle`

`X`

— Feature data

numeric matrix

Feature data, specified as a numeric matrix. The rows of `X`

correspond to observations, and the columns of `X`

correspond to
features. `X`

and `y`

must have the same number of
rows.

The custom function defined by the `fun`

argument must accept a
group of training and test data sets defined by splitting `X`

. For
details, see the `fun`

argument and `CV`

name-value argument.

**Data Types: **`single`

| `double`

`y`

— Responses (labels)

column vector

Responses (labels), specified as a column vector. `X`

and
`y`

must have the same number of rows.

The custom function defined by the `fun`

argument must accept a
group of training and test data sets defined by splitting `y`

. For
details, see the `fun`

argument and `CV`

name-value argument.

**Data Types: **`single`

| `double`

| `logical`

| `char`

| `string`

| `cell`

| `categorical`

`X1,...,XN`

— Input data

matrices

Input data, specified as matrices. The matrices must have the same number of rows.

`sequentialfs`

selects features from `X1`

only,
but otherwise imposes no interpretation on `X1,...,XN`

.

The custom function defined by the `fun`

argument must accept a
group of training and test data sets defined by splitting
`X1,...,XN`

. For details, see the `fun`

argument
and `CV`

name-value argument.

**Data Types: **`single`

| `double`

| `logical`

| `char`

| `string`

| `cell`

| `categorical`

### Name-Value Arguments

Specify optional pairs of arguments as
`Name1=Value1,...,NameN=ValueN`

, where `Name`

is
the argument name and `Value`

is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.

**Example: **`KeepIn=[1 0 0 0],KeepOut=[0 0 0 1]`

always includes the first
feature and excludes the last feature.

*
Before R2021a, use commas to separate each name and value, and enclose*
`Name`

*in quotes.*

**Example: **`"KeepIn",[1 0 0 0],"KeepOut",[0 0 0 1]`

`CV`

— Cross-validation option

10 (default) | positive integer | `cvpartition`

object | `"resubstitution"`

| `"none"`

Cross-validation option to compute the criterion for each candidate feature
subset, specified as a positive integer, `cvpartition`

object, `"resubstitution"`

, or
`"none"`

.

For each candidate feature subset, `sequentialfs`

uses the
partition specified by this argument to cross-validate the criterion value returned by
the `fun`

function.

Positive integer

`k`

—`sequentialfs`

uses a random nonstratified partition for`k`

-fold cross-validation.`cvpartition`

object —`sequentialfs`

uses a partition specified in the`cvpartition`

object. You can specify a stratified partition, a partition for holdout validation, or a partition for leave-one-out cross-validation. For details, see`cvpartition`

.`"resubstitution"`

—`sequentialfs`

does not partition the input data. Both the training set and the test set contain all of the original observations. For example, if you specify`X`

and`y`

, then`sequentialfs`

calls`fun`

as`criterion = fun(X,y,X,y)`

.`"none"`

—`sequentialfs`

does not validate the criterion value and calls`fun`

as`criterion = fun(X,y)`

, without separating the training and test sets.

**Example: **`"CV","none"`

`MCReps`

— Number of Monte Carlo repetitions for cross-validation

`1`

(default) | positive integer

Number of Monte Carlo repetitions for cross-validation, specified as a positive integer.

If you specify a positive integer greater than `1`

,
`sequentialfs`

repeats the cross-validation computation for the
specified number of repetitions for each candidate feature subset.

If `CV`

is `"none"`

,
`"resubstitution"`

, a `cvpartition`

object of type
`"resubstitution"`

, a `cvpartition`

object of type
`"leaveout"`

, or a custom `cvpartition`

object (with
the `IsCustom`

property set to `1`

), then the
software sets the `MCReps`

value to `1`

.

**Example: **`"MCReps",10`

**Data Types: **`single`

| `double`

`Direction`

— Direction of sequential search

`"forward"`

(default) | `"backward"`

Direction of the sequential search, specified as `"forward"`

or
`"backward"`

.

`"forward"`

— The initial feature set includes no features, and the`sequentialfs`

function sequentially adds features to the set.`"backward"`

— The initial feature set includes all features, and the`sequentialfs`

function sequentially removes features from the set. That is, the`sequentialfs`

function performs recursive feature elimination (RFE).

**Example: **`"Direction","backward"`

**Data Types: **`char`

| `string`

`KeepIn`

— Features to include

`[]`

(default) | logical vector | vector of positive integers

Features to include, specified as `[]`

, a logical vector, or a
vector of positive integers.

By default, `sequentialfs`

examines all features for the
feature selection process. If you specify features to include using this argument,
`sequentialfs`

always includes the features in the candidate
feature sets. A `true`

entry in a logical vector or an index value in
a vector of positive integers indicates that the output argument
`tf`

must include the corresponding feature.

**Example: **`"KeepIn",[1 0 0 0]`

**Data Types: **`logical`

`KeepOut`

— Features to exclude

`[]`

(default) | logical vector | vector of positive integers

Features to exclude, specified as `[]`

, a logical vector, or a
vector of positive integers.

By default, `sequentialfs`

examines all features for the
feature selection process. If you specify features to exclude using this argument,
`sequentialfs`

excludes the features from the candidate feature
sets. A `true`

entry in a logical vector or an index value in a
vector of positive integers indicates that the output argument `tf`

must exclude the corresponding feature.

**Example: **`"KeepOut",[0 0 0 1]`

**Data Types: **`logical`

`NFeatures`

— Number of features to select

`[]`

(default) | positive integer

Number of features to select, specified as `[]`

or a positive
integer.

By default, `sequentialfs`

stops iterations when the function
satisfies one of the stopping criteria (`MaxIter`

or
`TolFun`

) specified by the `Options`

name-value
argument. If you specify the `NFeatures`

name-value argument as a
positive integer, `sequentialfs`

stops iterations after selecting
the specified number of features. This argument overrides other iteration
options.

**Example: **`"NFeatures",2`

**Data Types: **`single`

| `double`

`NullModel`

— Flag to include null model

`false`

or `0`

(default) | `true`

or `1`

Flag to include the null model (model containing no features), specified as a
logical `1`

(`true`

) or `0`

(`false`

).

If you specify `true`

, the `sequentialfs`

function includes the null model as a valid option for the output
`tf`

and computes the criterion value for the empty input data.
Therefore, the `fun`

function must be able to accept empty matrices
as input argument values.

**Example: **`"NullModel",true`

**Data Types: **`logical`

`Options`

— Options for iterations and parallel computation

`statset("sequentialfs")`

(default) | structure returned by `statset`

Options for the iterations and parallel computation, specified as a structure
returned by `statset`

.

This table lists the option fields and their values.

Field Name | Field Value | Default Value |
---|---|---|

`Display` | Level of display, specified as `"off"` — Display no information.`"final"` — Display the final information.`"iter"` — Display information at each iteration.
| `"off"` |

`MaxIter` | Maximum number of iterations allowed, specified as a positive integer | `Inf` |

`TolFun` | Termination tolerance on the criterion value, specified as a positive scalar | `1e-6` if `Direction` is
`"forward"` ; `0` if
`Direction` is `"backward"` |

`TolTypeFun` | Type of the termination tolerance for the criterion value, specified as
`"abs"` (absolute tolerance) or `"rel"`
(relative tolerance) | `"rel"` |

`UseParallel` | Flag to run in parallel, specified as logical `1`
(`true` ) or `0`
(`false` ) | `false` |

`UseSubstreams` | Flag to run computations in a reproducible manner, specified as
logical To compute
reproducibly, set | `false` |

`Streams` | Random number streams, specified as a | MATLAB^{®} default random number stream |

To compute in parallel, you need Parallel Computing Toolbox™.

**Example: **`"Options",statset("Display","iter")`

**Data Types: **`struct`

## Output Arguments

`tf`

— Selected features

logical vector

Selected features, returned as a logical vector. A `true`

(logical
`1`

) entry indicates that the corresponding feature is
selected.

`history`

— History of feature selection process

structure

History of the feature selection process, returned as a structure array including
the `In`

and `Crit`

fields.

`In`

is a logical matrix in which row`i`

indicates the features selected at iteration`i`

.`Crit`

is a vector containing the criterion values computed at each iteration.

## More About

### Feature Selection

Feature selection reduces the dimensionality of data by selecting only a subset of measured features (predictor variables) to create a model. Feature selection algorithms search for a subset of predictors that optimally models measured responses, subject to constraints such as required or excluded features and the size of the subset.

You can categorize feature selection algorithms into three types:

Filter type — The filter type feature selection algorithm measures feature importance based on the characteristics of the features, such as feature variance and feature relevance to the response. You select important features as part of a data preprocessing step and then train a model using the selected features. Therefore, filter type feature selection is uncorrelated to the training algorithm.

Wrapper type — The wrapper type feature selection algorithm starts training using a subset of features and then adds or removes a feature using a selection criterion. The selection criterion directly measures the change in model performance that results from adding or removing a feature. The algorithm repeats training and improving a model until its stopping criteria are satisfied.

Embedded type — The embedded type feature selection algorithm learns feature importance as part of the model learning process. Once you train a model, you obtain the importance of the features in the trained model. This type of algorithm selects features that work well with a particular learning process.

For more details, see Introduction to Feature Selection.

## Algorithms

`sequentialfs`

sequentially selects features in `X`

by performing these steps:

Define a random nonstratified partition for 10-fold cross-validation on

`n`

observations, where`n`

is the number of observations in`X`

.Initialize the selected feature set

`S`

as an empty set.For each feature

*x*in_{i}`X`

, compute the cross-validated criterion value using the`fun`

function.Add the feature with the smallest criterion value to

`S`

.For each feature

*x*in_{i}`X\S`

, define a candidate feature set`C`

_{i}as`S`

∪{*x*}. Compute the cross-validated criterion value using_{i}`fun`

for`C`

_{i}.Among the candidate sets (

`C`

_{i}s), select the set that reduces the criterion value the most, compared to the criterion value for`S`

. Add the feature corresponding to the selected candidate set to`S`

.Repeat steps 5 and 6 until adding a feature does not decrease the criterion value by greater than the termination tolerance value.

To customize the feature selection process, use the name-value arguments of
`sequentialfs`

.

You can specify cross-validation options by using the

`CV`

and`MCReps`

name-value arguments.For wrapper type feature selection, specify the arguments to cross-validate the criterion value for each candidate feature set. You can define the

`fun`

function to train a model and return a criterion value for the trained model. For an example, see Forward Feature Selection.For filter type feature selection, which does not involve cross-validation, specify

`CV`

as`"none"`

and use the`fun`

function to measure characteristics of the input data, such as correlation. For an example, see Filter Type Feature Selection.

To perform backward feature selection, or recursive feature elimination (RFE), specify the

`Direction`

name-value argument as`"backward"`

.`sequentialfs`

initializes the selected feature set`S`

as a set with all features, and then removes one feature at a time from the set.You can specify which features to always include or exclude, the number of features in the final selected feature set, and whether to consider a model with no features as a valid option. For details, see the

`KeepIn`

,`KeepOut`

,`NFeatures`

, and`NullModel`

name-value arguments.Use the

`Options`

name-value argument to specify options for the iterations and parallel computation. For example,`Options,statset("TolFun",1e-2)`

sets the iteration termination tolerance on the criterion value to`1e-2`

.

## Extended Capabilities

### Automatic Parallel Support

Accelerate code by automatically running computation in parallel using Parallel Computing Toolbox™.

To run in parallel, specify the `Options`

name-value argument in the call to
this function and set the `UseParallel`

field of the
options structure to `true`

using
`statset`

:

`Options=statset(UseParallel=true)`

For more information about parallel computing, see Run MATLAB Functions with Automatic Parallel Support (Parallel Computing Toolbox).

## Version History

**Introduced in R2008a**

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