loss

Load the robotarm data set.

load robotarm.mat

The robotarm data set was created using a robot arm simulator with 7168 training observations and 1024 test observations with 32 features [1][2]. The data set used in this example is a preprocessed version of the original data set. The data was preprocessed by subtracting values given by a linear regression fit from the original data, followed by normalization of all features to unit variance.

Perform NCA feature selection for regression with the default regularization parameter value λ.

rng(1,"twister");   % For reproducibility
nca = fsrnca(Xtrain,ytrain);

Calculate the loss for the model using the test set as a measure of the performance.

l = loss(nca,Xtest,ytest)

l = 
0.0844

By default, the function calculates the mean squared error.

Select features using feature weights and a relative threshold.

fw = nca.FeatureWeights;
tol = 0.001;
threshold = max(fw)*tol;
vars = fw>threshold;

Create new training and test sets for the predictor data using only the selected features.

Xtrain2 = Xtrain(:,vars);
Xtest2 = Xtest(:,vars);

Update the NCA model using the new training set. Calculate the loss for the new model using the new test set.

nca2 = fsrnca(Xtrain2,ytrain);
l2 = loss(nca2,Xtest2,ytest)

l2 = 
0.0845

Calculate the difference in the loss for the original model and the loss for the updated model.

abs(l-l2)

ans = 
1.0549e-04

The small difference in the loss values indicates that the updated model trained with a subset of the original model features, performs similarly to the original model.