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### -*- mode: R ; delete-old-versions: never -*-
## This program is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with this program; if not, a copy is available at
## http://www.r-project.org/Licenses/
### From package 'Biobase' (has only rowMedians + rowQ) / 'matrixStats'
### MM: all type checking now in C
## --- TODO: implement hasNA=NA ==> do check maybe differently than = TRUE
## --> ../src/rowMedians.c + ../src/rowMedians_TYPE-template.h
colMedians <- function(x, na.rm=FALSE, hasNA=TRUE, keep.names=TRUE)
.Call(R_rowMedians, x, na.rm, hasNA, FALSE, keep.names)
rowMedians <- function(x, na.rm=FALSE, hasNA=TRUE, keep.names=TRUE)
.Call(R_rowMedians, x, na.rm, hasNA, TRUE, keep.names)
### Maria Anna di Palma, without consistency factor 15.11.2014
### Fixes by Valentin Todorov
### Martin Maechler: added mad() consistency factor, 27.11.2014
### new name, class; more compatible to 'covMcd'
covComed <- function (X, n.iter = 2, reweight = FALSE,
tolSolve = control$ tolSolve,# had 1e-10 hardwired {now 1e-14 default}
trace = control$ trace,
wgtFUN = control$ wgtFUN,
control = rrcov.control())
{
## ATTENTION ##
## Med(abs(X))^2=Med(X*X) only if the number of rows is odd
d <- dim(X <- as.matrix(X))
n <- d[1]
p <- d[2]
if(is.character(wgtFUN))
wgtFUN <- .wgtFUN.covComed[[wgtFUN]](p=p, n=n, control)
if(!is.function(wgtFUN))
stop("'wgtFUN' must be a function or a string specifying such a function")
madX <- apply(X, 2, mad)
I.mad <- 1/madX
rho <- I.mad * COM(X) * rep(I.mad, each = p)
## better than
## D <- diag(1/madX)
## rho <- D %*% COM(X) %*% t(D)
U <- svd(rho, p, nv = 0L)$u
## DD <- diag(madX)
## Q <- DD %*% U
## invQ <- solve(Q) ## == t(U) %*% D -- since U is orthogonal!
t.inv.Q <- I.mad * U # = t(solve(Q)) = t(t(U) * D) == t(D) U = D U
Z <- X %*% t.inv.Q ## much faster than for (i in 1:n) Z[i,] <- invQ %*% X[i,]
out <- comedian(rho, Z, X)
## Mahalanobis distance
for(it in seq_len(n.iter))# allow n.iter = 0
out <- comedian(out$S., out$Z, X)
mm <- colMedians(out$Z)
mx <- drop(out$Q %*% mm)
## MM: These are "raw" distances compared to covMcd()
mah <- mahalanobis(X, mx, out$S., tol = tolSolve)
## compute weights
weights <- wgtFUN(mah)
covW <- cov.wt(X, wt=weights)[c("cov", "center", "n.obs")]
covW$weights <-
if(reweight) { ## above 'mah' = 'raw.mah' .. ==> allow another reweighting as in covMcd()
covW$raw.weights <- weights
covW$mah <- mahalanobis(X, covW$center, covW$cov, tol = tolSolve)
wgtFUN(mah)
} else # no re-weighting
weights
structure(class = "comed",
c(list(Z = out$Z, raw.cov = out$S., raw.center = mx, raw.mah = mah,
wgtFUN=wgtFUN),
covW))
}
##' Martin Maechler's simple proposal for an *adaptive* cutoff
##' i.e., one which does *not* reject outliers in good samples asymptotically
.COM.adaptWgt.c <- function(n,p, eps = 0.2 / n^0.3) {
## default eps ==> 1-eps(n=100) ~= 0.95; 1-eps(n=10) ~= 0.90
## using upper tail:
1.4826 * qchisq(eps, p, lower.tail=FALSE) / qchisq(0.5, p)
}
## Default wgtFUN() constructors for covComed():
.wgtFUN.covComed <-
list("01.original" = function(p, ...) {
cMah <- .COM.adaptWgt.c(p=p, eps = 0.05)# 1 - eps = 0.95
function(d) as.numeric(d < median(d)*cMah) },
"01.flex" = function(p, n, control) { ## 'beta' instead of 0.95
stopifnot(is.1num(beta <- control$beta), 0 <= beta, beta <= 1)
cMah <- 1.4826 * qchisq(beta, p) / qchisq(0.5, p)
function(d) as.numeric(d < median(d)*cMah) },
"01.adaptive" = function(p, n, ...) { ## 'beta_n' instead of 0.975
cMah <- .COM.adaptWgt.c(n,p)
function(d) as.numeric(d < cMah) },
"sm1.flex" = function(p, n, control) { ## 'beta' / smooth weight
stopifnot(is.1num(beta <- control$beta), 0 <= beta, beta <= 1)
cMah <- 1.4826 * qchisq(beta, p) / qchisq(0.5, p)
function(d) smoothWgt(d / median(d), c=cMah, h = 1) },
"sm1.adaptive" = function(p, n, ...) {
cMah <- .COM.adaptWgt.c(n=n, p=p)
function(d) smoothWgt(d / median(d), c = cMah, h = 1) },
"sm2.adaptive" = function(p, n, ...) {
cMah <- .COM.adaptWgt.c(n=n, p=p)
function(d) smoothWgt(d / median(d), c = cMah, h = 2) }
)
comedian <- function (rho, Z, X)
{
p <- ncol(X)
U <- svd(rho, nv = 0L)$u
madX <- apply(X, 2, mad)
I.mad <- 1/madX
## D <- diag(madX)
## Q <- D %*% U
Q <- madX * U
## invQ <- solve(Q)
t.inv.Q <- I.mad * U # = t(solve(Q)) = t(t(U) * D) == t(D) U = D U
Z <- X %*% t.inv.Q ## for (i in 1:n) Z[i,] <- invQ %*% X[i,]
madZ <- apply(Z, 2, mad)
list(Q=Q, Z=Z, S. = tcrossprod(Q * rep(madZ, each=p))) ## better than
## S. = Q %*% diag(madZ)^2 %*% t(Q)
}
COM <- function(X)
{
## Comedian *with* consistency factor. Falk(1997) was without it.
stopifnot(is.1num(p <- ncol(X)), p >= 1)
med <- colMedians(X)
Y <- sweep(X, 2L, med, `-`)
COM <- matrix(0., p,p)
madY <- numeric(p)
for(i in 1:p) {
madY[i] <- madYi <- mad(Yi <- Y[,i])
for(j in seq_len(i-1)) { # j <= i ==> madY[j] "exists"
COM[j,i] <- COM[i,j] <- median(Yi * Y[,j]) / (madYi * madY[j])
## COM[i,j] <- median((Y[,i])*(Y[,j]))
## COM[i,j] <- (1.4826^2)*median((Y[,i])*(Y[,j]))
}
## j == i :
COM[i,i] <- median(Yi^2) / (madYi^2)
}
## return [ 1.4826 = formals(mad)$constant = consistency factor of mad()]
1.4826^2 * COM
}
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