unfold computes a metric unfolding solution based on a rectangular matrix, that is,
reconstructs two sets of points from the distances between points of the first set and
the points of the second set.
uapply applies a function the two point sets that are reconstructed by
unfold(x,...) ## S4 method for signature 'matrix' unfold(x, ndims=NULL, squared=FALSE, tol=1e-7, method=c("Schoenemann", "CG"), ...) ## S4 method for signature 'formula' unfold(x,data=parent.frame(), ...) ## S4 method for signature 'unfolding' biplot(x, dimen=c(1,2), type=attr(x,"biplot_type"), xlim, ylim, tpos=c(4,2), tposdim=1, asp=1, lty=c(1,2), lwd=c(1,1), pch=c(1,3), cex=c(1,1), col=c("black","black"), contour.col="black", contour.lty=1, xlab=paste("Dimension ",dimen), ylab=paste("Dimension ",dimen), ...) ## S4 method for signature 'unfolding' plot(x, y=NULL ,dimen=1, discrete=attr(x,"plot_discrete"), use.rownames=discrete, xlab=paste("Dimension ",dimen), ...) uapply(x,FUN)
unfold.matrix: a rectangular matrix that contains distances or squared distances (if argument
unfold.formula: a formula which specifies the variables that form the columns of the matrix of distances. For
plot.unfolding: an object that contains an unfolding solution.
a data frame or an environment that contains variables specified in the formula given as first argument.
an optional integer value that specifies the dimensionality of the solution. If
NULLthe dimensionality is selected automatically based on a singular value decomposition of the matrix of squared distances.
a logical value; does the matrix
Dcontain squared distances?
a tolerance value for the convergence of the conjugate gradients method.
a method for the iterative computation of the unfolding solution.
a dummy argument for compatibility with default methods, ignored.
biplot: a two-element integer vector, for
plot: a single integer value, that specifies the dimension(s) of the unfolding solution to be plotted.
a character vector of length less then or equal to 2. Determines how each of the two point sets of the unfolding solutions are represented in the biplot. Valid choices are
the respective set of points are plotted as points in the biplot.
the points of the respective set are connected by lines.
the points of the respective set are plotted as points and connected by lines.
the points of the respective set are represented by the corresponding row names and, if argument
tposis present, by points.
contour lines are drawn of two-dimensional kernel density estimate for the respective set of points. This biplot type uses the function
a two-element integer vector; specifies the position of text labels relative to the points. For the meaning of these integer values see
an integer value; specifies which how elements of
tposare used. Labels of points with negative positions along coordinate axis
dimen[tposdim]are positioned according to
tpos, labels of other points are positioned according to
arguments passed to base graphics functions
colour and line type for contour lines, see
a logical vector of lenght 2; if
TRUE, the respective set of points are represented by spikes in theplot, otherwise the set is represented by a graph of a kernel density estimate.
logical; should row names used for annotation?
further arguments passed to
optimin case of
pointsin case of the plotting methods.
a function applied to the two sets of points that result from the unfolding.
unfold returns an object of class
"unfolding" with components
a numeric matrix representing the first set of points. Each row contains the coordinate of one point of the first set.
a numeric matrix representing the second set of points. Each row contains the coordinate of one point of the second set.
a numeric matrix that contains the fitted squared distances.
A stress value, denotes the “badness of fit”.
unfold first computes an unfolding solution according to Schoenemanns metric
unfolding algorithm that uses only linear algebra operations. This preliminary solution
is then refined by minimizing the stress using a conjugate-gradients method.
uapply applies a given function to the two sets of points recovered by an unfolding
solution. It applies the function to the components
B of an object of class
r <- seq(from=0,to=2*pi,length=24) a1 <- cos(r)*4 + 0.00001*rnorm(r) a2 <- sin(r)*4 + 0.00001*rnorm(r) b1 <- c(.5,-.5,-.5,.5)*3 + 5 b2 <- c(.5,.5,-.5,-.5)*3 + 1 D1 <- outer(b1,a1,"-") D2 <- outer(b2,a2,"-") Dsq <- D1^2+D2^2 Dsq.uf<-unfold(sqrt(Dsq),squared=FALSE) oldpar <- par(mfrow=c(1,2))
A <- cbind(a1,a2) B <- cbind(b1,b2) ltype <- c(rep(1,NROW(A)),rep(2,NROW(A))) orig <- rbind(A,B) unfolded <- rbind(Dsq.uf$A,Dsq.uf$B) xlim <- ylim <- range(orig)#*1.5 plot(A,type="b",pch=1, xlim=xlim,ylim=ylim, xlab="Dimension 1",ylab="Dimension 2",main=expression("Original data"),asp=1) lines(B,type="b",pch=3,lty=2) abline(h=0,v=0,lty=3) biplot(Dsq.uf,type="b", xlim=xlim,ylim=ylim, main=expression(paste(italic(unfold)," solution")),asp=1)