err = cvshrink(obj)
[err,gamma]
= cvshrink(obj)
[err,gamma,delta]
= cvshrink(obj)
[err,gamma,delta,numpred]
= cvshrink(obj)
[err,...] = cvshrink(obj,Name,Value)
returns
a vector of crossvalidated classification error values for differing
values of the regularization parameter Gamma.err
= cvshrink(obj
)
[
also returns the vector
of Gamma values.err
,gamma
]
= cvshrink(obj
)
[
also returns the vector
of Delta values.err
,gamma
,delta
]
= cvshrink(obj
)
[
returns the vector
of number of nonzero predictors for each setting of the parameters
Gamma and Delta.err
,gamma
,delta
,numpred
]
= cvshrink(obj
)
[
cross
validates with additional options specified by one or more err
,...] = cvshrink(obj
,Name,Value
)Name,Value
pair
arguments.
Examine the err
and numpred
outputs
to see the tradeoff between crossvalidated error and number of predictors.
When you find a satisfactory point, set the corresponding gamma
and delta
properties
in the model using dot notation. For example, if (i,j)
is
the location of the satisfactory point, set
obj.Gamma = gamma(i); obj.Delta = delta(i,j);

Discriminant analysis classifier, produced using 
Specify optional commaseparated pairs of Name,Value
arguments.
Name
is the argument
name and Value
is the corresponding
value. Name
must appear
inside single quotes (' '
).
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN
.

Default: 

Vector of Gamma values for crossvalidation. Default: 

Number of Delta intervals for crossvalidation. For every value
of Gamma, Default: 

Number of Gamma intervals for crossvalidation. Default: 

Verbosity level, an integer from Default: 

Numeric vector or matrix of errors.


Vector of Gamma values used for regularization. See Gamma and Delta. 

Vector or matrix of Delta values used for regularization. See Gamma and Delta.


Numeric vector or matrix containing the number of predictors
in the model at various regularizations.

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
.