# Auxiliary parameters for controlling local principal curves.

### Description

This function bundles parameters controlling mainly the starting-, convergence-, boundary-,
and stopping-behaviour of the local principal curve. It will be used
only inside the `lpc()`

function argument.

### Usage

1 2 3 4 | ```
lpc.control(iter =100, cross=TRUE,
boundary = 0.005, convergence.at = 0.00001,
mult=NULL, ms.h=NULL, ms.sub=30,
pruning.thresh=0.0, rho0=0.4)
``` |

### Arguments

`iter` |
Maximum number of iterations on either side of the starting point within each branch. |

`cross` |
Logical parameter. If |

`boundary` |
This boundary correction [2] reduces the bandwidth adaptively once the relative difference of parameter values between two centers of mass falls below the given threshold. This measure delays convergence and enables the curve to proceed further into the end points. If set to 0, this boundary correction is switched off. |

`convergence.at` |
This forces the curve to stop if the
relative difference of parameter values between two centers of mass
falls below the given threshold. If set to 0, then the curve will
always stop after exactly |

`mult` |
numerical value which enforeces a fixed number of starting points. If the
number given here is larger than the number of starting points
provided at |

`ms.h` |
sets the bandwidth (vector) for the initial mean shift procedure
which finds the local density modes, and, hence, the starting points
for the LPC. If unspecified, the bandwidth |

`ms.sub` |
proportion of data points (default=30) which are used to initialize mean shift trajectories for the mode finding. In fact, we use
trajectories. |

`pruning.thresh` |
Prunes branches corresponding to higher-depth starting points if their density estimate falls below this threshold. Typically, a value between 0.0 and 1.0. The setting 0.0 means no pruning. |

`rho0` |
A numerical value which steers the birth process of higher-depth starting points. Usually, between 0.3 and 0.4 (see reference [1]). |

### Value

A list of the nine specified imput parameters, which can be read by the
`control`

argument of the `lpc`

function.

### Author(s)

JE

### References

[1] 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.

[2] Einbeck, J. and Zayed, M. (2011). Some asymptotics for localized principal components and curves. Working paper, Durham University. Unpublished.

### Examples

1 2 3 4 | ```
data(calspeedflow)
fit1 <- lpc(calspeedflow[,c(3,4)], x0=c(50,60),scaled=TRUE,
control=lpc.control(iter=20, boundary=0))
plot(fit1, type=c("curve","start","mass"))
``` |