R/nlda.R

In aberHRML/FIEmspro: Flow In-jection Electrospray Mass Spectrometry Processing: \\ data processing, classification modelling and variable selection in metabolite fingerprinting

#' Linear Discriminant Analysis for High Dimensional Problems
#' 
#' Linear discriminant analysis for high dimensional problems. See details for
#' implementation.
#' 
#' A critical issue of applying linear discriminant analysis (LDA) is both the
#' singularity and instability of the within-class scatter matrix. In practice,
#' there are often a large number of features available, but the total number
#' of training patterns is limited and commonly less than the dimension of the
#' feature space. To tackle this issue, \code{nlda} combines principal
#' components analysis (PCA) and linear discriminant analysis (LDA) for the
#' classification problem.  Because the determination of the optimal number of
#' principal components representative for a dataset is not trivial and the
#' number of dimensions varies from one comparison to another introducing a
#' bias to the estimation of the separability measure, we have opted for a 2
#' steps procedure proposed in Thomaz, C. E. and Gillies, D. F. (2004): the
#' number of principal components to retain is equal to the rank of the
#' covariance matrix (usually number of training samples minus one) and the
#' within-class scatter matrix is replaced by a version where the less reliable
#' eigenvalues have been replaced. In addition to the proportion of explained
#' variance in each projection, the eigenvalue is a useful diagnostic quantity
#' (output \code{stats}).
#' 
#' @aliases nlda nlda.default nlda.formula print.nlda summary.nlda
#' print.summary.nlda
#' @usage nlda(dat, \dots{})
#' \method{nldadefault}(dat,cl,prior=NULL,scale=FALSE,comprank = FALSE,
#' \dots{})
#' 
#' \method{nldaformula}(formula, data = NULL, \dots{}, subset, na.action =
#' na.omit)
#' @param formula A formula of the form \code{groups ~ x1 + x2 + \dots{}} That
#' is, the response is the grouping factor and the right hand side specifies
#' the (non-factor) discriminators.
#' @param data Data frame from which variables specified in \code{formula} are
#' preferentially to be taken.
#' @param dat A matrix or data frame containing the explanatory variables if no
#' formula is given as the principal argument.
#' @param cl A factor specifying the class for each observation if no formula
#' principal argument is given.
#' @param prior The prior probabilities of class membership. If unspecified,
#' the class proportions for the training set are used. If present, the
#' probabilities should be specified in the order of the factor levels.
#' @param scale A logical value indicating whether or not PCA is scaled.
#' @param comprank A computation rank.
#' @param \dots Arguments passed to or from other methods.
#' @param subset An index vector specifying the cases to be used in the
#' training sample.
#' @param na.action A function to specify the action to be taken if \code{NA}s
#' are found. The default action is \code{na.omit}, which leads to rejection of
#' cases with missing values on any required variable. An alternative is
#' \code{na.fail}, which causes an error if \code{NA} cases are found.
#' @return An object of class \code{nlda} containing the following components:
#' \item{stats}{ The statistics based on the training data.  } \item{Tw}{ The
#' proportion of trace.  } \item{rankmat}{ The rank used for LDA.  }
#' \item{means}{ The means of training data.  } \item{loadings}{ A matrix of
#' the coefficients of linear discriminants.  } \item{x}{ The rotated data on
#' discriminant variables.  } \item{xmeans}{ The group means obtained from
#' training.  } \item{pred}{ The predicted class labels of training data.  }
#' \item{cl}{ The observed class labels of training data.  } \item{prior}{ The
#' prior probabilities used.  } \item{conf}{ The confusion matrix based on
#' training data.  } \item{acc}{ The accuracy rate of training data.  }
#' \item{lev}{ The levels of class.  } \item{call}{ The (matched) function
#' call.  }
#' @note This function may be given either a formula and optional data frame,
#' or a matrix and grouping factor as the first two arguments.
#' @author David Enot \email{dle@@aber.ac.uk} and Wanchang Lin
#' \email{wll@@aber.ac.uk}.
#' @seealso \code{\link{predict.nlda}}, \code{\link{plot.nlda}},
#' \code{\link{hca.nlda}}
#' @references Venables, W. N. and Ripley, B. D. (2002) \emph{Modern Applied
#' Statistics with S.} Fourth edition.  Springer.
#' 
#' Ripley, B. D. (1996) \emph{Pattern Recognition and Neural Networks}.
#' Cambridge University Press.
#' 
#' Thomaz, C. E. and Gillies, D. F. (2004) A Maximum Uncertainty LDA-based
#' approach for Limited Sample Size problems with application to Face
#' Recognition. \emph{Technical Report}.  Department of Computing, Imperial
#' College London.
#' 
#' Yang, J. and Yang J.-Y. (2003) Why can LDA be performed in PCA transformed
#' space? \emph{Pattern Recognition}, vol.36, 563 - 566.
#' @keywords classif
#' @examples
#' 
#' ## load abr1
#' data(abr1)
#' cl   <- factor(abr1$fact$class)
#' dat <- preproc(abr1$pos , y=cl, method=c("log10","TICnorm"),add=1)[,110:500]  
#' 
#' ## define random training and test datasets
#' idx <- sample(1:nrow(dat), round((2/3)*nrow(dat)), replace=FALSE) 
#' train.dat  <- dat[idx,]
#' train.t    <- cl[idx]
#' test.dat   <- dat[-idx,]        
#' test.t     <- cl[-idx] 
#' 
#' ## build nlda on the training data
#' model    <- nlda(train.dat,train.t)
#' ## print summary
#' summary(model)
#' 
#' ## map samples on the first 2 DFs
#' plot(model,dimen=c(1,2),main = "Training data",abbrev = TRUE)
#' ## map samples on all the DFs
#' plot(model,main = "Training data",abbrev = TRUE)
#' 
#' ## predict test sample membership
#' pred.te  <- predict(model, test.dat)$class
#' ## confusion matrix and error rates
#' table(test.t,pred.te)
#' 
#' 
nlda <- function (dat, ...) UseMethod ("nlda")