Feature selection for regression using neighborhood component analysis (NCA)
FeatureSelectionNCARegression contains the
data, fitting information, feature weights, and other model parameters
of a neighborhood component analysis (NCA) model.
fsrnca learns the feature weights using
a diagonal adaptation of NCA and returns an instance of
The function achieves feature selection by regularizing the feature
FeatureSelectionNCAClassification object using
FitMethod— Name of the fitting method used to fit this model
Name of the fitting method used to fit this model, stored as one of the following:
'exact' — Perform fitting
using all of the data.
'none' — No fitting. Use
this option to evaluate the generalization error of the NCA model
using the initial feature weights supplied in the call to
'average' — The software
divides the data into partitions (subsets), fits each partition using
exact method, and returns the average of the
feature weights. You can specify the number of partitions using the
InitialLearningRate— Initial learning rate
Initial learning rate for
'minibatch-lbfgs' solvers. The
learning rate decays over iterations starting at the value specified
control the automatic tuning of initial learning rate in the call
FeatureWeights— Feature weights
Feature weights, stored as a p-by-1 vector
of real scalar values, where p is the number of
'FitMethod' equal to
a p-by-m matrix, where m is
the number of partitions specified via the
pair argument in the call to
The absolute value of
a measure of the importance of predictor
close to 0, then this indicates that predictor
not influence the response in
|loss||Evaluate accuracy of learned feature weights on test data|
|predict||Predict responses using neighborhood component analysis (NCA) regression model|
|refit||Refit neighborhood component analysis (NCA) model for regression|
Load the sample data.
The first 15 columns contain the continuous predictor variables, whereas the 16th column contains the response variable, which is the price of a car. Define the variables for the neighborhood component analysis model.
Predictors = X(:,1:15); Y = X(:,16);
Fit a neighborhood component analysis (NCA) model for regression to detect the relevant features.
mdl = fsrnca(Predictors,Y);
The returned NCA model,
mdl, is a
FeatureSelectionNCARegression object. This object stores information about the training data, model, and optimization. You can access the object properties, such as the feature weights, using dot notation.
Plot the feature weights.
figure() plot(mdl.FeatureWeights,'ro') xlabel('Feature Index') ylabel('Feature Weight') grid on
The weights of the irrelevant features are zero. The
'Verbose',1 option in the call to
fsrnca displays the optimization information on the command line. You can also visualize the optimization process by plotting the objective function versus the iteration number.
figure() plot(mdl.FitInfo.Iteration,mdl.FitInfo.Objective,'ro-') grid on xlabel('Iteration Number') ylabel('Objective')
ModelParameters property is a
struct that contains more information about the model. You can access the fields of this property using dot notation. For example, see if the data was standardized or not.
ans = logical 0
0 means that the data was not standardized before fitting the NCA model. You can standardize the predictors when they are on very different scales using the
'Standardize',1 name-value pair argument in the call to
Value. To learn how value classes affect copy operations, see Copying Objects (MATLAB).