Number of nonzero linear coefficients in discriminant analysis classifier
Find the Number of Nonzero Coefficients in a Discriminant Analysis Classifier
Find the number of nonzero coefficients in a discriminant analysis classifier for various
Create a discriminant analysis classifier from the
load fisheriris obj = fitcdiscr(meas,species);
Find the number of nonzero coefficients in
ncoeffs = nLinearCoeffs(obj)
ncoeffs = 4
Find the number of nonzero coefficients for
delta = 1, 2, 4, and 8.
delta = [1 2 4 8]; ncoeffs = nLinearCoeffs(obj,delta)
ncoeffs = 4×1 4 4 3 0
DeltaPredictor property gives the values of
delta where the number of nonzero coefficients changes.
ncoeffs2 = nLinearCoeffs(obj,obj.DeltaPredictor)
ncoeffs2 = 4×1 4 3 1 2
ncoeffs — Number of nonzero coefficients in discriminant analysis model
Number of nonzero coefficients in discriminant analysis model
mdl, returned as a nonnegative integer.
If you call
nLinearCoeffs with a
ncoeffs is the number of
nonzero linear coefficients for threshold parameter
delta is a vector,
ncoeffs is a vector with
the same number of elements.
mdl is a quadratic discriminant model,
ncoeffs is the number of predictors in
Gamma and Delta
Regularization is the process of finding a small set of predictors
that yield an effective predictive model. For linear discriminant
analysis, there are two parameters, γ and δ,
that control regularization as follows.
you select appropriate values of the parameters.
Let Σ represent the covariance matrix of the data X, and let be the centered data (the data X minus the mean by class). Define
The regularized covariance matrix is
Whenever γ ≥
MinGamma, is nonsingular.
Let μk be the mean vector for those elements of X in class k, and let μ0 be the global mean vector (the mean of the rows of X). Let C be the correlation matrix of the data X, and let be the regularized correlation matrix:
where I is the identity matrix.
The linear term in the regularized discriminant analysis classifier for a data point x is
The parameter δ enters into this equation as a threshold on the final term in square brackets. Each component of the vector is set to zero if it is smaller in magnitude than the threshold δ. Therefore, for class k, if component j is thresholded to zero, component j of x does not enter into the evaluation of the posterior probability.
DeltaPredictor property is a vector related
to this threshold. When δ ≥
DeltaPredictor(i), all classes k have
Therefore, when δ ≥
DeltaPredictor(i), the regularized
classifier does not use predictor
Introduced in R2011b