Sequential feature selection
inmodel = sequentialfs(fun,X,y)
inmodel = sequentialfs(fun,X,Y,Z,...)
[inmodel,history] = sequentialfs(fun,X,...)
[] = sequentialfs(...,param1
,val1
,param2
,val2
,...)
inmodel = sequentialfs(fun,X,y)
selects
a subset of features from the data matrix X
that
best predict the data in y
by sequentially selecting
features until there is no improvement in prediction. Rows of X
correspond
to observations; columns correspond to variables or features. y
is
a column vector of response values or class labels for each observation
in X
. X
and y
must
have the same number of rows. fun
is a function
handle to a function that defines the criterion used to select features
and to determine when to stop. The output inmodel
is
a logical vector indicating which features are finally chosen.
Starting from an empty feature set, sequentialfs
creates
candidate feature subsets by sequentially adding each of the features
not yet selected. For each candidate feature subset, sequentialfs
performs
10fold crossvalidation by repeatedly calling fun
with
different training subsets of X
and y
, XTRAIN
and ytrain
,
and test subsets of X
and y
, XTEST
and ytest
,
as follows:
criterion = fun(XTRAIN,ytrain,XTEST,ytest)
XTRAIN
and ytrain
contain
the same subset of rows of X
and Y
,
while XTEST
and ytest
contain
the complementary subset of rows. XTRAIN
and XTEST
contain
the data taken from the columns of X
that correspond
to the current candidate feature set.
Each time it is called, fun
must return a
scalar value criterion
. Typically, fun
uses XTRAIN
and ytrain
to
train or fit a model, then predicts values for XTEST
using
that model, and finally returns some measure of distance, or loss,
of those predicted values from ytest
. In the crossvalidation
calculation for a given candidate feature set, sequentialfs
sums
the values returned by fun
and divides that sum
by the total number of test observations. It then uses that mean value
to evaluate each candidate feature subset.
Typical loss measures include sum of squared errors for regression
models (sequentialfs
computes the meansquared
error in this case), and the number of misclassified observations
for classification models (sequentialfs
computes
the misclassification rate in this case).
Note:

After computing the mean criterion
values
for each candidate feature subset, sequentialfs
chooses
the candidate feature subset that minimizes the mean criterion value.
This process continues until adding more features does not decrease
the criterion.
inmodel = sequentialfs(fun,X,Y,Z,...)
allows
any number of input variables X
, Y
, Z
,
... . sequentialfs
chooses features (columns)
only from X
, but otherwise imposes no interpretation
on X
, Y
, Z
,
... . All data inputs, whether column vectors or matrices, must have
the same number of rows. sequentialfs
calls fun
with
training and test subsets of X
, Y
, Z
,
... as follows:
criterion = fun(XTRAIN,YTRAIN,ZTRAIN,..., XTEST,YTEST,ZTEST,...)
sequentialfs
creates XTRAIN
, YTRAIN
, ZTRAIN
,
... , XTEST
, YTEST
, ZTEST
,
... by selecting subsets of the rows of X
, Y
, Z
,
... . fun
must return a scalar value criterion
,
but may compute that value in any way. Elements of the logical vector inmodel
correspond
to columns of X
and indicate which features are
finally chosen.
[inmodel,history] = sequentialfs(fun,X,...)
returns
information on which feature is chosen at each step. history
is
a scalar structure with the following fields:
Crit
— A vector containing
the criterion values computed at each step.
In
— A logical matrix in
which row i
indicates the features selected at
step i
.
[] = sequentialfs(...,
specifies
optional parameter name/value pairs from the following table.param1
,val1
,param2
,val2
,...)
Parameter  Value 

'cv'  The validation method used to compute the criterion for each candidate feature subset.
The default value is Socalled wrapper methods use a function 
'mcreps'  A positive integer indicating the number of MonteCarlo
repetitions for crossvalidation. The default value is 
'direction'  The direction of the sequential search. The default is 
'keepin'  A logical vector or a vector of column numbers specifying features that must be included. The default is empty. 
'keepout'  A logical vector or a vector of column numbers specifying features that must be excluded. The default is empty. 
'nfeatures'  The number of features at which 
'nullmodel'  A logical value, indicating whether or not the null model
(containing no features from 
'options'  Options structure for the iterative sequential search
algorithm, as created by

Perform sequential feature selection for classification of noisy features:
load fisheriris; X = randn(150,10); X(:,[1 3 5 7 ])= meas; y = species; c = cvpartition(y,'k',10); opts = statset('display','iter'); fun = @(XT,yT,Xt,yt)... (sum(~strcmp(yt,classify(Xt,XT,yT,'quadratic')))); [fs,history] = sequentialfs(fun,X,y,'cv',c,'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 0.0266667 Final columns included: 5 7 fs = 0 0 0 0 1 0 1 0 0 0 history = In: [2x10 logical] Crit: [0.0400 0.0267] history.In ans = 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1 0 0 0