refit

Refit neighborhood component analysis (NCA) model for classification

Syntax

mdlrefit = refit(mdl,Name=Value)

Description

mdlrefit = refit(mdl,Name=Value) refits the model mdl, with modified parameters specified by one or more name-value arguments.

Examples

Refit NCA Model for Classification with Modified Settings

Generate checkerboard data using the generateCheckerBoardData.m function.

rng(2016,"twister"); % For reproducibility
pps = 1375;
[X,y] = generateCheckerBoardData(pps);
X = X + 2;

Plot the data.

plot(X(y==1,1),X(y==1,2),"x")
hold on
plot(X(y==-1,1),X(y==-1,2),"x")
hold off

[n,p] = size(X)

n = 
22000

p = 
2

Add irrelevant predictors to the data.

Q = 98;
Xrnd = unifrnd(0,4,n,Q);
Xobs = [X,Xrnd];

This piece of code creates 98 additional predictors, all uniformly distributed between 0 and 4.

Partition the data into training and test sets. To create stratified partitions, so that each partition has similar proportion of classes, use y instead of length(y) as the partitioning criteria.

cvp = cvpartition(y,"Holdout",2000);

cvpartition randomly chooses 2000 of the observations to add to the test set and the rest of the data to add to the training set. Create the training and validation sets using the assignments stored in the cvpartition object cvp.

Xtrain = Xobs(cvp.training(1),:);
ytrain = y(cvp.training(1),:);

Xval = Xobs(cvp.test(1),:);
yval = y(cvp.test(1),:);

Compute the misclassification error without feature selection.

nca = fscnca(Xtrain,ytrain,FitMethod="none",Standardize=true, ...
    Solver="lbfgs");
loss_nofs = loss(nca,Xval,yval)

loss_nofs = 
0.5165

The FitMethod="none" option uses the default weights (all 1s), which means all features are equally important.

This time, perform feature selection using neighborhood component analysis for classification, with $$\lambda =1/n$$.

w0 = rand(100,1);
n = length(ytrain)

n = 
20000

lambda = 1/n;
nca = refit(nca,InitialFeatureWeights=w0,FitMethod="exact", ...
    Lambda=lambda,Solver="sgd");

Plot the objective function value versus the iteration number.

plot(nca.FitInfo.Iteration,nca.FitInfo.Objective,"o")
hold on
plot(nca.FitInfo.Iteration,movmean(nca.FitInfo.Objective,10),".-")
hold off
xlabel("Iteration number")
ylabel("Objective value")

Compute the misclassification error with feature selection.

loss_withfs = loss(nca,Xval,yval)

loss_withfs = 
0.0115

Plot the selected features.

semilogx(nca.FeatureWeights,"o")
xlabel("Feature index")
ylabel("Feature weight")
grid on

Select features using the feature weights and a relative threshold.

tol = 0.15;
selidx = find(nca.FeatureWeights > tol*max(1,max(nca.FeatureWeights)))

selidx = 2×1

     1
     2

Feature selection improves the results and fscnca detects the correct two features as relevant.

Input Arguments

mdl — Neighborhood component analysis model for classification

FeatureSelectionNCAClassification object

Neighborhood component analysis model or classification, specified as a FeatureSelectionNCAClassification object.

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: refit(mdl,Lambda=0.01) refits the model mdl with a lambda value of 0.01.

Fitting Options

FitMethod — Method for fitting the model

mdl.FitMethod (default) | "exact" | "none" | "average"

Method for fitting the model, specified as 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 fscnca.

• "average" — The function divides the data into partitions (subsets), fits each partition using the exact method, and returns the average of the feature weights. You can specify the number of partitions using the NumPartitions name-value argument.

Example: FitMethod="none"

Lambda — Regularization parameter

mdl.Lambda (default) | nonnegative scalar value

Regularization parameter, specified as a nonnegative scalar value.

For n observations, the best Lambda value that minimizes the generalization error of the NCA model is expected to be a multiple of 1/n

Example: Lambda=0.01

Data Types: double | single

Solver — Solver type

mdl.Solver (default) | "lbfgs" | "sgd" | "minibatch-lbfgs"

Solver type for estimating feature weights, specified as one of the following.

• "lbfgs" — Limited memory BFGS (Broyden-Fletcher-Goldfarb-Shanno) algorithm (LBFGS algorithm)

• "sgd" — Stochastic gradient descent

• "minibatch-lbfgs" — Stochastic gradient descent with LBFGS algorithm applied to mini-batches

Example: Solver="minibatch-lbfgs"

InitialFeatureWeights — Initial feature weights

mdl.InitialFeatureWeights (default) | p-by-1 vector of real positive scalar values

Initial feature weights, specified as a p-by-1 vector of real positive scalar values.

Data Types: double | single

Verbose — Indicator for verbosity level

mdl.Verbose (default) | 0 | 1 | >1

Indicator for verbosity level for the convergence summary display, specified as one of the following.

• 0 — No convergence summary

• 1 — Convergence summary including iteration number, norm of the gradient, and objective function value.

• >1 — More convergence information depending on the fitting algorithm

  When using solver "minibatch-lbfgs" and verbosity level >1, the convergence information includes iteration log from intermediate mini-batch LBFGS fits.

Example: Verbose=2

Data Types: double | single

LBFGS or Mini-Batch LBFGS Options

GradientTolerance — Relative convergence tolerance

mdl.GradientTolerance (default) | positive real scalar value

Relative convergence tolerance on the gradient norm for solver lbfgs, specified as a positive real scalar value.

Example: GradientTolerance=0.00001

Data Types: double | single

SGD or Mini-Batch LBFGS Options

InitialLearningRate — Initial learning rate for solver sgd

mdl.InitialLearningRate (default) | positive real scalar value

Initial learning rate for solver sgd, specified as a positive scalar value.

When using solver type "sgd", the learning rate decays over iterations starting with the value specified for InitialLearningRate.

Example: InitialLearningRate=0.8

Data Types: double | single

PassLimit — Maximum number of passes for solver "sgd"

mdl.PassLimit (default) | positive integer value

Maximum number of passes for solver "sgd" (stochastic gradient descent), specified as a positive integer value. Every pass processes size(mdl.X,1) observations.

Example: PassLimit=10

Data Types: double | single

SGD or LBFGS or Mini-Batch LBFGS Options

IterationLimit — Maximum number of iterations

mdl.IterationLimit (default) | positive integer value

Maximum number of iterations, specified as a positive integer.

Example: IterationLimit=250

Data Types: double | single

Output Arguments

mdlrefit — Neighborhood component analysis model for classification

FeatureSelectionNCAClassification object

Neighborhood component analysis model for classification, returned as a FeatureSelectionNCAClassification object. You can either save the results as a new model or update the existing model as mdl = refit(mdl,Name=Value).

Version History

Introduced in R2016b