plot.opt.TPO {pcaPP}

Tradeoff Curves for Sparse PCs

Description

Tradeoff curves of one or more sparse PCs for a series of lambdas, which contrast the loss of explained variance and the gain of sparseness.

Usage

## S3 method for class 'opt.TPO'
 plot(x, k, f.x = c ("l0", "pl0", "l1", "pl1", "lambda"),
                        f.y = c ("var", "pvar"), ...)
## S3 method for class 'opt.BIC'
 plot(x, k, f.x = c ("l0", "pl0", "l1", "pl1", "lambda"),
                        f.y = c ("var", "pvar"), ...)

Arguments

x

An opt.TPO or opt.BIC object.

k

This function plots the tradeoff curve of the k-th component for opt.TPO-objects, or the first k components for opt.BIC-objects.

f.x, f.y

A string, specifying which information shall be plotted on the x and y - axis. See the details section for more information.

...

Further arguments passed to or from other functions.

Details

The argument f.x can obtain the following values:

• "l0": l0 - sparseness, which corresponds to the number of zero loadings of the considered component(s).

• "pl0": l0 - sparseness in percent (l0 - sparseness ranges from 0 to p-1 for each component).

• "l1": l1 - sparseness, which corresponds to the negative sum of absolute loadings of the considered component(s).
  (The exact value displayed for a single component is sqrt (p) - S, with S as the the absolute sum of loadings.)
  As this value is a part of the objective function which selects the candidate directions within the sPCAgrid function, this option is provided here.

• "pl1" The "l1 - sparseness" in percent (l1 - sparseness ranges from 0 to sqrt (p-1) for each component).

• "lambda": The lambda used for computing a particular model.

The argument f.y can obtain the following values:

• "var": The (cumulated) explained variance of the considered component(s). The value shown here is calculated using the variance estimator specified via the method argument of function sPCAgrid.

• "pvar": The (cumulated) explained variance of the considered component(s) in percent. The 100%-level is assumed as the sum of variances of all columns of argument x.
  Again the same variance estimator is used as specified via the method argument of function sPCAgrid.
  

The subtitle summarizes the result of the applied criterion for selecting a value of lambda:

• The name of the applied method (TPO/BIC).

• The selected value of lambda for the k-th component (opt.TPO) or all computed components (opt.BIC).

• The empirical cumulated variance (ECV) of the first k components in percent.

• The obtained l0-sparseness of the first k components.

This function operates on the return object of function opt.TPO or opt.BIC. The model (lambda) selected by the minimization of the corresponding criterion is highlighted by a dashed vertical line.

The component the argument k refers to, corresponds to the $pc.noord item of argument x. For more info on the order of sparse PCs see the details section of opt.TPO.

Author(s)

Heinrich Fritz, Peter Filzmoser <[e-mail]>

References

C. Croux, P. Filzmoser, H. Fritz (2011). Robust Sparse Principal Component Analysis Based on Projection-Pursuit, ?? To appear.

See Also

sPCAgrid, princomp

Examples

  set.seed (0)
                      ##  generate test data
  x <- data.Zou (n = 250)

  k.max <- 3          ##  max number of considered sparse PCs

                      ##  arguments for the sPCAgrid algorithm
  maxiter <- 25       ##    the maximum number of iterations
  method <- "sd"      ##    using classical estimations

                      ##  Optimizing the TPO criterion
  oTPO <- opt.TPO (x, k.max = k.max, method = method, maxiter = maxiter)

                      ##  Optimizing the BIC criterion
  oBIC <- opt.BIC (x, k.max = k.max, method = method, maxiter = maxiter)

          ##  Tradeoff Curves: Explained Variance vs. sparseness
  par (mfrow = c (2, k.max))
  for (i in 1:k.max)        plot (oTPO, k = i)
  for (i in 1:k.max)        plot (oBIC, k = i)

          ##  Explained Variance vs. lambda
  par (mfrow = c (2, k.max))
  for (i in 1:k.max)        plot (oTPO, k = i, f.x = "lambda")
  for (i in 1:k.max)        plot (oBIC, k = i, f.x = "lambda")