R/PcaLocantore.R

In armstrtw/rrcov: Scalable Robust Estimators with High Breakdown Point

setClass("PcaLocantore", representation(delta = "numeric",
                                    quan = "numeric"),
                                contains="PcaRobust")

setMethod("getQuan", "PcaLocantore", function(obj) obj@n.obs)

##  The S3 version
PcaLocantore <- function (x, ...)
    UseMethod("PcaLocantore")

PcaLocantore.formula <- function (formula, data = NULL, subset, na.action, ...)
{
    cl <- match.call()

    mt <- terms(formula, data = data)
    if (attr(mt, "response") > 0)
        stop("response not allowed in formula")
    mf <- match.call(expand.dots = FALSE)
    mf$... <- NULL
    mf[[1]] <- as.name("model.frame")
    mf <- eval.parent(mf)
    ## this is not a `standard' model-fitting function,
    ## so no need to consider contrasts or levels
    if (.check_vars_numeric(mf))
        stop("PCA applies only to numerical variables")

    na.act <- attr(mf, "na.action")
    mt <- attr(mf, "terms")
    attr(mt, "intercept") <- 0
    x <- model.matrix(mt, mf)

    res <- PcaLocantore.default(x, ...)

    ## fix up call to refer to the generic, but leave arg name as `formula'
    cl[[1]] <- as.name("PcaLocantore")
    res@call <- cl

#    if (!is.null(na.act)) {
#        res$na.action <- na.act
#        if (!is.null(sc <- res$x))
#            res$x <- napredict(na.act, sc)
#    }

    res
}

PcaLocantore.default <- function(x, k=0, kmax=ncol(x), delta = 0.001, na.action = na.fail, scale=FALSE, signflip=TRUE, trace=FALSE, ...)
{

    cl <- match.call()

    if(missing(x)){
        stop("You have to provide at least some data")
    }
    y <- data <- x <- as.matrix(x)
    n <- nrow(y)
    p <- ncol(y)

    ##
    ## verify and set the input parameters: k and kmax
    ##
    kmax <- max(min(floor(kmax), rankMM(x)),1)
    if((k <- floor(k)) < 0)
        k <- 0
    else if(k > kmax) {
        warning(paste("The number of principal components k = ", k, " is larger then kmax = ", kmax, "; k is set to ", kmax,".", sep=""))
        k <- kmax
    }
    if(k != 0)
        k <- min(k, ncol(data))
    else {
        k <- min(kmax, ncol(data))
        if(trace)
            cat("The number of principal components is defined by the algorithm. It is set to ", k,".\n", sep="")
    }
######################################################################

    ## VT::15.06.2010: introduce 'scale' parameter (instead of 'corr' in this case)
    ##  return the scale in the value object
    ##
    sc = vector('numeric', p) + 1
    if(scale == TRUE)
    {
        sc = apply(data, 2, "mad")
        for(i in 1:p) {
            data[, i] = data[, i]/sc[i]
        }
    }

    spa = spatial.median(data, delta)
    mu = spa$mu
    ep = spa$ep
    tt = matrix(mu, n, p, byrow=TRUE)
    data = data-tt
    for(i in 1:n)
    {
        z = sqrt(sum((data[i,  ])^2))
        y[i,  ] = 0 * data[i,  ]
        if(z > ep)
        {
            y[i,  ] = (data[i,  ]  )/z
        }
    }

    ##out = princomp(y, scores = TRUE, cor = FALSE, na.action=na.action, subset = TRUE)
    ## no scaling - we have already scaled with MAD
    out = PcaClassic(y, k=k, kmax=kmax, scale=FALSE, signflip=signflip, ...)

    k <- out@k
    scores = data %*% out@loadings
    sdev = apply(scores, 2, "mad")
    names2 = names(sdev)
    orsdev = order(sdev)
    orsdev = rev(orsdev)
    sdev  = sdev[orsdev]
    scores  = scores[,orsdev, drop=FALSE]
    loadings = out@loadings[,orsdev, drop=FALSE]

    names(sdev)=names2
    dimnames(scores)[[2]]=names2
    dimnames(loadings)[[2]]=names2

    scale       <- sc
    center      <- as.vector(mu)
    scores      <- scores[, 1:k, drop=FALSE]
    loadings    <- loadings[, 1:k, drop=FALSE]
    eigenvalues <- (sdev^2)[1:k]

######################################################################
    names(eigenvalues) <- NULL
    if(is.list(dimnames(data)))
    {
        ##dimnames(scores)[[1]] <- dimnames(data)[[1]]
        rownames(scores) <- rownames(data)
    }
    dimnames(scores)[[2]] <- as.list(paste("PC", seq_len(ncol(scores)), sep = ""))
    dimnames(loadings) <- list(colnames(data), paste("PC", seq_len(ncol(loadings)), sep = ""))

    ## fix up call to refer to the generic, but leave arg name as <formula>
    cl[[1]] <- as.name("PcaLocantore")
    res <- new("PcaLocantore", call=cl,
                            loadings=loadings,
                            eigenvalues=eigenvalues,
                            center=center,
                            scale=scale,
                            scores=scores,
                            k=k,
                            n.obs=n)

    ## Compute distances and flags
    res <- rrcov:::.distances(x, p, res)
    return(res)
}

## computes the spatial median
spatial.median <- function(x, delta)
{
    dime = dim(x)
    n=dime[1]
    p=dime[2]
    delta1=delta*sqrt(p)
    mu0=apply(x,2,median)
    h=delta1+1
    tt=0
    while(h>delta1)
    {
        tt=tt+1
        TT=matrix(mu0,n,p,byrow=TRUE)
        U=(x-TT)^2
        w=sqrt(apply(U,1,sum))
        w0=median(w)
        ep=delta*w0

        z=(w<=ep)
        w[z]=ep
        w[!z]=1/w[!z]
        w=w/sum(w)
        x1=x
        for(i in 1:n)
            x1[i,]=w[i]*x[i,]
        mu=apply(x1,2,sum)
        h=sqrt(sum((mu-mu0)^2))
        mu0=mu
    }
    out=list(mu=mu0,ep=ep)
    out
}