mvr.rd

偏最小二乘算法代码及相关说明,在机器学习,实时数值仿真中用得较多

%% $Id: mvr.Rd 132 2007-08-24 09:21:05Z bhm $
\encoding{latin1}
\name{mvr}
\alias{mvr}
\alias{pcr}
\alias{plsr}
\title{Partial Least Squares and Principal Component Regression}
\description{
  Functions to perform partial least squares regression (PLSR) or
  principal component regression (PCR), with a formula interface.
  Cross-validation can be used.  Prediction, model extraction, plot,
  print and summary methods exist.
}
%% FIXME: Maybe use a \synopsis section, and show typical uses in \usage:
\usage{
mvr(formula, ncomp, data, subset, na.action,
    method = pls.options()$mvralg,
    scale = FALSE, validation = c("none", "CV", "LOO"),
    model = TRUE, x = FALSE, y = FALSE, \dots)
plsr(\dots, method = pls.options()$plsralg)
pcr(\dots, method = pls.options()$pcralg)
}
\arguments{
  \item{formula}{a model formula.  Most of the \code{lm} formula
    constructs are supported.  See below.}
  \item{ncomp}{the number of components to include in the model (see below).}
  \item{data}{an optional data frame with the data to fit the model from.}
  \item{subset}{an optional vector specifying a subset of observations
    to be used in the fitting process.}
  \item{na.action}{a function which indicates what should happen when
    the data contain missing values.}
  \item{method}{the multivariate regression method to be used.  If
    \code{"model.frame"}, the model frame is returned.}
  \item{scale}{numeric vector, or logical.  If numeric vector, \eqn{X}
    is scaled by dividing each variable with the corresponding element
    of \code{scale}.  If \code{scale} is \code{TRUE}, \eqn{X} is scaled
    by dividing each variable by its sample standard deviation.  If
    cross-validation is selected, scaling by the standard deviation is
    done for every segment.}
  \item{validation}{character.  What kind of (internal) validation to
    use.  See below.}
  \item{model}{a logical.  If \code{TRUE}, the model frame is returned.}
  \item{x}{a logical.  If \code{TRUE}, the model matrix is returned.}
  \item{y}{a logical.  If \code{TRUE}, the response is returned.}
  \item{\dots}{additional arguments, passed to the underlying fit
    functions, and \code{mvrCv}.}
}
\details{
  The functions fit PLSR or PCR models with 1, \eqn{\ldots},
  \code{ncomp} number of components.  Multi-response models are fully
  supported.

  The type of model to fit is specified with the \code{method}
  argument. Four PLSR algorithms are available: the kernel algorithm
  (\code{"kernelpls"}), the wide kernel algorithm (\code{"widekernelpls"}),
  SIMPLS (\code{"simpls"}) and the classical
  orthogonal scores algorithm (\code{"oscorespls"}).  One PCR algorithm
  is available: using the singular value decomposition (\code{"svdpc"}).
  If \code{method} is \code{"model.frame"}, the model frame is returned.
  The functions \code{pcr} and \code{plsr} are wrappers for \code{mvr},
  with different values for \code{method}.

  The \code{formula} argument should be a symbolic formula of the form
  \code{response ~ terms}, where \code{response} is the name of the
  response vector or matrix (for multi-response models) and \code{terms}
  is the name of one or more predictor matrices, usually separated by
  \code{+}, e.g., \code{water ~ FTIR} or \code{y ~ X + Z}.  See
  \code{\link{lm}} for a detailed description.  The named
  variables should exist in the supplied \code{data} data frame or in
  the global environment.  Note: Do not use \code{mvr(mydata$y ~
    mydata$X, \ldots)}, instead use \code{mvr(y ~ X, data = mydata,
    \ldots)}.  Otherwise, \code{\link{predict.mvr}} will not work properly.
  The chapter \samp{Statistical models in R} of the manual \samp{An
    Introduction to R} distributed with \R is a good reference on
  formulas in \R.

  The number of components to fit is specified with the argument
  \code{ncomp}.  It this is not supplied, the maximal number of
  components is used (taking account of any cross-validation).

  If \code{validation = "CV"}, cross-validation is performed.  The number and
  type of cross-validation segments are specified with the arguments
  \code{segments} and \code{segment.type}.  See \code{\link{mvrCv}} for
  details.  If \code{validation = "LOO"}, leave-one-out cross-validation
  is performed.  It is an error to specify the segments when
  \code{validation = "LOO"} is specified.

  Note that the cross-validation is optimised for speed, and some
  generality has been sacrificed.  Especially, the model matrix is
  calculated only once for the complete cross-validation, so models like
  \code{y ~ msc(X)} will not be properly cross-validated.  However,
  scaling requested by \code{scale = TRUE} is properly cross-validated.
  For proper cross-validation of models where the model matrix must be
  updated/regenerated for each segment, use the separate function
  \code{\link{crossval}}.
}
\value{
  If \code{method = "model.frame"}, the model frame is returned.
  Otherwise, an object of class \code{mvr} is returned.
  The object contains all components returned by the underlying fit
  function.  In addition, it contains the following components:
  \item{validation}{if validation was requested, the results of the
    cross-validation.  See \code{\link{mvrCv}} for details.}
  \item{na.action}{if observations with missing values were removed,
    \code{na.action} contains a vector with their indices.  The
    class of this vector is used by functions like \code{fitted} to
    decide how to treat the observations.}
  \item{ncomp}{the number of components of the model.}
  \item{method}{the method used to fit the model.  See the argument
    \code{method} for possible values.}
  \item{scale}{if scaling was requested (with \code{scale}), the
    scaling used.}
  \item{call}{the function call.}
  \item{terms}{the model terms.}
  \item{model}{if \code{model = TRUE}, the model frame.}
  \item{x}{if \code{x = TRUE}, the model matrix.}
  \item{y}{if \code{y = TRUE}, the model response.}
}
\references{
  Martens, H., N鎠, T. (1989) \emph{Multivariate calibration.}
  Chichester: Wiley.
}
\author{Ron Wehrens and Bj鴕n-Helge Mevik}
\seealso{
  \code{\link{kernelpls.fit}},
  \code{\link{widekernelpls.fit}},
  \code{\link{simpls.fit}},
  \code{\link{oscorespls.fit}},
  \code{\link{svdpc.fit}},
  \code{\link{mvrCv}},
  \code{\link{crossval}},
  \code{\link[stats]{loadings}},
  \code{\link{scores}},
  \code{\link{loading.weights}},
  \code{\link{coef.mvr}},
  \code{\link{predict.mvr}},
  \code{\link{R2}},
  \code{\link{MSEP}},
  \code{\link{RMSEP}},
  \code{\link{plot.mvr}}}
\examples{
data(yarn)
## Default methods:
yarn.pcr <- pcr(density ~ NIR, 6, data = yarn, validation = "CV")
yarn.pls <- plsr(density ~ NIR, 6, data = yarn, validation = "CV")

## Alternative methods:
yarn.oscorespls <- mvr(density ~ NIR, 6, data = yarn, validation = "CV",
                      method = "oscorespls")
yarn.simpls <- mvr(density ~ NIR, 6, data = yarn, validation = "CV",
                  method = "simpls")

data(oliveoil)
sens.pcr <- pcr(sensory ~ chemical, ncomp = 4, scale = TRUE, data = oliveoil)
sens.pls <- plsr(sensory ~ chemical, ncomp = 4, scale = TRUE, data = oliveoil)
}
\keyword{regression}
\keyword{multivariate}