LPCM (version 0.44-5)

lpc: Local principal curves

Description

This is the main function which computes the actual local principal curve, i.e. a sequence of local centers of mass.

Usage

lpc(X, h, t0 = mean(h),  x0,  way = "two",  scaled = TRUE,
      weights=1, pen = 2, depth = 1, control=lpc.control())

Arguments

X

data matrix with $N$ rows (observations) and $d$ columns (variables).

h

bandwidth. May be either specified as a single number, then the same bandwidth is used in all dimensions, or as a d-dimensional bandwidth vector. The default setting is 10 percent of the range in each direction. If scaled =TRUE then

t0

scalar step length. Default setting is t0=h, if h is a scalar, and t0=mean(h), if h is a vector.

x0

specifies the choice of starting points. The default choice x0=1 will select one suitable starting point automatically (in form of a local density mode). The second built-in option x0=0 will use all local density mod

way

"one": go only in direction of the first local eigenvector, "back": go only in opposite direction, "two": go from starting point in both directions.

scaled

if TRUE, scales each variable by dividing through its range (see also the Notes section below).

weights

a vector of observation weights (can also be used to exclude individual observations from the computation by setting their weight to zero.)

pen

power used for angle penalization (see [1]). If set to 0, the angle penalization is switched off.

depth

maximum depth of branches ($\phi_{max}$ in [2]), restricted to the values 1,2 or 3 (The original LPC branch has depth 1. If, along this curve, a point features a high second local PC, this launches a new starting point, and the resulting br

control

Additional parameters steering particularly the starting-, boundary-, and convergence behavior of the fitted curve. See lpc.control.

Value

• A list of items:
• LPC
  The coordinates of the local centers of mass of the fitted principal curve.
• Parametrization
  Curve parameters and branch labels for each local center of mass.
• h
  The bandwidth used for the curve estimation.
• to
  The constant $t_0$ used for the curve estimation.
• starting.points
  The coordinates of the starting point(s) used.
• data
  The data frame used for curve estimation.
• scaled
  Logical.
• weights
  The vector of weights used for curve estimation.
• control
  The settings used in lpc.control()
• Misc
  Miscellannea.

References

[1] Einbeck, J., Tutz, G., & Evers, L. (2005). Local principal curves. Statistics and Computing 15, 301-313.

[2] Einbeck, J., Tutz, G., & Evers, L. (2005): Exploring Multivariate Data Structures with Local Principal Curves. In: Weihs, C. and Gaul, W. (Eds.): Classification - The Ubiquitous Challenge. Springer, Heidelberg, pages 256-263.

Examples

data(calspeedflow)
lpc1 <- lpc(calspeedflow[,3:4])
plot(lpc1)

data(mussels, package="dr")
 lpc2 <- lpc(mussels[,-3], x0=as.numeric(mussels[49,-3]),scaled=FALSE)
 plot(lpc2, curvecol=2)

data(gaia)
s <- sample(nrow(gaia),200)
gaia.pc <-  princomp(gaia[s,5:20])
lpc3 <- lpc(gaia.pc$scores[,c(2,1,3)],scaled=FALSE)
plot(lpc3, curvecol=2, type=c("curve","mass"))

# Simulated letter 'E' with branched LPC
ex<- c(rep(0,40), seq(0,1,length=20), seq(0,1,length=20), seq(0,1,length=20))
ey<- c(seq(0,2,length=40), rep(0,20), rep(1,20), rep(2,20))
sex<-rnorm(100,0,0.01); sey<-rnorm(100,0,0.01)
eex<-rnorm(100,0,0.1);  eey<-rnorm(100,0,0.1)
ex1<-ex+sex; ey1<-ey+sey
ex2<-ex+eex; ey2<-ey+eey
e1<-cbind(ex1,ey1); e2<-cbind(ex2,ey2)
lpc.e1 <- lpc(e1, h= c(0.1,0.1),  depth=2, scaled=FALSE)
plot(lpc.e1, type=c("curve","mass", "start"))