Refit neighborhood component analysis (NCA) model for regression
mdlrefit = refit(mdl,Name,Value)
mdl— Neighborhood component analysis model for regression
Neighborhood component analysis model or classification, specified
comma-separated pairs of
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
FitMethod— Method for fitting the model
Method for fitting the model, specified as the comma-separated
pair consisting of
'FitMethod' and one of the following.
'exact' — Performs 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 function
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
mdlrefit— Neighborhood component analysis model for regression
Neighborhood component analysis model or classification, returned as a
FeatureSelectionNCARegression object. You can either save the
results as a new model or update the existing model as
Load the sample data.
robotarm (pumadyn32nm) dataset is created using a robot arm simulator with 7168 training and 1024 test observations with 32 features , . This is a preprocessed version of the original data set. Data are preprocessed by subtracting off a linear regression fit followed by normalization of all features to unit variance.
Compute the generalization error without feature selection.
nca = fsrnca(Xtrain,ytrain,'FitMethod','none','Standardize',1); L = loss(nca,Xtest,ytest)
L = 0.9017
Now, refit the model and compute the prediction loss with feature selection, with = 0 (no regularization term) and compare to the previous loss value, to determine feature selection seems necessary for this problem. For the settings that you do not change,
refit uses the settings of the initial model
nca. For example, it uses the feature weights found in
nca as the initial feature weights.
nca2 = refit(nca,'FitMethod','exact','Lambda',0); L2 = loss(nca2,Xtest,ytest)
L2 = 0.1088
The decrease in the loss suggests that feature selection is necessary.
Plot the feature weights.
Tuning the regularization parameter usually improves the results. Suppose that, after tuning using cross-validation as in Tune Regularization Parameter in NCA for Regression, the best value found is 0.0035. Refit the
nca model using this value and stochastic gradient descent as the solver. Compute the prediction loss.
nca3 = refit(nca2,'FitMethod','exact','Lambda',0.0035,... 'Solver','sgd'); L3 = loss(nca3,Xtest,ytest)
L3 = 0.0573
Plot the feature weights.
After tuning the regularization parameter, the loss decreased even more and the software identified four of the features as relevant.
 Rasmussen, C. E., R. M. Neal, G. E. Hinton, D. van Camp, M. Revow, Z. Ghahramani, R. Kustra, and R. Tibshirani. The DELVE Manual, 1996, http://mlg.eng.cam.ac.uk/pub/pdf/RasNeaHinetal96.pdf