This computes a matrix formalising 'local shape', i.e., aggregated
standardised variance/covariance in a Mahalanobis neighbourhood of the data
points. This can be used for finding clusters when used as one of the
covariance matrices in
Invariant Coordinate Selection (function `ics`

in package
`ICS`

), see Hennig's
discussion and rejoinder of Tyler et al. (2009).

```
localshape(xdata,proportion=0.1,mscatter="mcd",mcdalpha=0.8,
covstandard="det")
```

xdata

objects times variables data matrix.

proportion

proportion of points to be considered as neighbourhood.

mscatter

"mcd" or "cov"; specified minimum covariance determinant or classical covariance matrix to be used for Mahalanobis distance computation.

mcdalpha

if `mscatter="mcd"`

, this is the alpha parameter
to be used by the MCD covariance matrix, i.e. one minus the
asymptotic breakdown point, see `covMcd`

.

covstandard

one of "trace", "det" or "none", determining by what constant the pointwise neighbourhood covariance matrices are standardised. "det" makes the affine equivariant, as noted in the discussion rejoinder of Tyler et al. (2009).

The local shape matrix.

Tyler, D. E., Critchley, F., Duembgen, L., Oja, H. (2009)
Invariant coordinate selection (with discussion).
*Journal of the Royal Statistical Society, Series B*, 549-592.

# NOT RUN { options(digits=3) data(iris) localshape(iris[,-5],mscatter="cov") # }