ncoeffs = nLinearCoeffs(obj)
ncoeffs = nLinearCoeffs(obj,delta)
returns
the number of nonzero linear coefficients in the linear discriminant
model ncoeffs
= nLinearCoeffs(obj
)obj
.
returns
the number of nonzero linear coefficients for threshold parameter ncoeffs
= nLinearCoeffs(obj
,delta
)delta
.

Discriminant analysis classifier, produced using 

Scalar or vector value of the 

Nonnegative integer, the number of nonzero coefficients in the
discriminant analysis model If you call If 
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. cvshrink
helps
you select appropriate values of the parameters.
Let Σ represent the covariance matrix of the data X, and let $$\widehat{X}$$ be the centered data (the data X minus the mean by class). Define
$$D=\text{diag}\left({\widehat{X}}^{T}*\widehat{X}\right).$$
The regularized covariance matrix $$\tilde{\Sigma}$$ is
$$\tilde{\Sigma}=\left(1\gamma \right)\Sigma +\gamma D.$$
Whenever γ ≥ MinGamma
, $$\tilde{\Sigma}$$ is nonsingular.
Let μ_{k} be the mean vector for those elements of X in class k, and let μ_{0} be the global mean vector (the mean of the rows of X). Let C be the correlation matrix of the data X, and let $$\tilde{C}$$ be the regularized correlation matrix:
$$\tilde{C}=\left(1\gamma \right)C+\gamma I,$$
where I is the identity matrix.
The linear term in the regularized discriminant analysis classifier for a data point x is
$${\left(x{\mu}_{0}\right)}^{T}{\tilde{\Sigma}}^{1}\left({\mu}_{k}{\mu}_{0}\right)=\left[{\left(x{\mu}_{0}\right)}^{T}{D}^{1/2}\right]\left[{\tilde{C}}^{1}{D}^{1/2}\left({\mu}_{k}{\mu}_{0}\right)\right].$$
The parameter δ enters into this equation as a threshold on the final term in square brackets. Each component of the vector $$\left[{\tilde{C}}^{1}{D}^{1/2}\left({\mu}_{k}{\mu}_{0}\right)\right]$$ 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.
The DeltaPredictor
property is a vector related
to this threshold. When δ ≥ DeltaPredictor(i)
, all classes k have
$$\left{\tilde{C}}^{1}{D}^{1/2}\left({\mu}_{k}{\mu}_{0}\right)\right\le \delta .$$
Therefore, when δ ≥ DeltaPredictor(i)
, the regularized
classifier does not use predictor i
.