# mahalanofix: Mahalanobis distances from center of indexed points In fpc: Flexible Procedures for Clustering

## Description

Computes the vector of (classical or robust) Mahalanobis distances of all points of `x` to the center of the points indexed (or weighted) by `gv`. The latter also determine the covariance matrix.

Thought for use within `fixmahal`.

## Usage

 ```1 2 3 4 5``` ```mahalanofix(x, n = nrow(as.matrix(x)), p = ncol(as.matrix(x)), gv = rep(1, times = n), cmax = 1e+10, method = "ml") mahalanofuz(x, n = nrow(as.matrix(x)), p = ncol(as.matrix(x)), gv = rep(1, times=n), cmax = 1e+10) ```

## Arguments

 `x` a numerical data matrix, rows are points, columns are variables. `n` positive integer. Number of points. `p` positive integer. Number of variables. `gv` for `mahalanofix` a logical or 0-1 vector of length `n`. For `mahalanofuz` a numerical vector with values between 0 and 1. `cmax` positive number. used in `solvecov` if covariance matrix is singular. `method` `"ml"`, `"classical"`, `"mcd"` or `"mve"`. Method to compute the covariance matrix estimator. See `cov.rob`, `fixmahal`.

## Details

`solvecov` is used to invert the covariance matrix. The methods `"mcd"` and `"mve"` in `mahalanofix` do not work properly with point constellations with singular covariance matrices!

## Value

A list of the following components:

 `md` vector of Mahalanobis distances. `mg` mean of the points indexed by `gv`, weighted mean in `mahalanofuz`. `covg` covariance matrix of the points indexed by `gv`, weighted covariance matrix in `mahalanofuz`. `covinv` `covg` inverted by `solvecov`. `coll` logical. If `TRUE`, `covg` has been (numerically) singular.

## Note

Methods `"mcd"` and `"mve"` require library `lqs`.

## See Also

`fixmahal`, `solvecov`, `cov.rob`

## Examples

 ```1 2 3 4 5 6``` ``` x <- c(1,2,3,4,5,6,7,8,9,10) y <- c(1,2,3,8,7,6,5,8,9,10) mahalanofix(cbind(x,y),gv=c(0,0,0,1,1,1,1,1,0,0)) mahalanofix(cbind(x,y),gv=c(0,0,0,1,1,1,1,0,0,0)) mahalanofix(cbind(x,y),gv=c(0,0,0,1,1,1,1,1,0,0),method="mcd") mahalanofuz(cbind(x,y),gv=c(0,0,0.5,0.5,1,1,1,0.5,0.5,0)) ```

fpc documentation built on Dec. 7, 2020, 1:08 a.m.