the clusters of directions or orientations: one cluster id per element, counted from zero, and the centre of every cluster

Syntax

cId, center = calcCluster(v)

Directions by CLASSIX.

cId, center = calcCluster(ori)

Orientations by the modes of their density.

cId, center = calcCluster(ori, method='classix', radius=0.1, minPoints=15)

Orientations by CLASSIX.

cId, center = calcCluster(ori, method='odf', halfwidth=3*degree, numCluster=5)

The five largest modes.

cId, center = calcCluster(ori, method='hierarchical', maxAngle=15*degree)

Merged until the centres are 15 degree apart.

cId, center = calcCluster(v, method='hierarchical', numCluster=5)

Merged until five clusters are left.

Description

The method decides how the clusters are found:

‘classix’, the default for directions: sorts the points along their first principal axis, groups them within a radius and merges groups whose centres are close. Orientations are clustered on their embedding, which respects the symmetry, antipodal directions on a form that identifies v with -v.
‘odf’, the default for orientations: computes the kernel density and follows every orientation uphill to its mode. The largest modes are the centres.
‘hierarchical’: merges the closest pair of centres until numCluster clusters are left or the closest centres are more than maxAngle apart. More than 1000 orientations are first binned on a grid of the given resolution.

The density method leaves some orientations without a cluster: those further from their centre than twice the mean angle of the cluster and those whose mode is not among the centres get NaN in cId. Elements that are NaN themselves get NaN in cId with every method, the others are clustered without them; no elements give no clusters. The centres of ‘odf’ are the modes of the density, those of the other methods the (weighted) means of the clusters. cId has the shape of the input.

Input

`v`	vector3d, the directions
`ori`	orientation, the orientations

Keywords

keyword	default	description
`method`	`None`	‘classix’ (default for directions), ‘odf’ (default for orientations, the modes of the density) or ‘hierarchical’; may also be given positionally
`radius`	`None`	the radius of the CLASSIX groups, in the scaled coordinates; by default estimated from the distance to the tenth nearest neighbour
`minPoints`	`None`	the smallest cluster of CLASSIX, smaller ones are dissolved into the nearest larger one; by default one percent of the points
`mergeScale`	`1.5`	CLASSIX merges groups whose centres are closer than mergeScale times the radius
`numCluster`	`None`	the number of clusters of the hierarchical method (2 if neither it nor maxAngle is given), or the number of modes the density method keeps (at most 20)
`maxAngle`	`None`	the hierarchical method stops when the closest centres are further apart
`halfwidth`	`5*degree`	the halfwidth of the kernel of the density method
`weights`	`None`	a weight per element, for the density and the hierarchical method
`resolution`	`2.5*degree`	the grid the hierarchical method bins more than 1000 orientations on
`verbose`	`False`	report the progress of calcComponents (the density method)

Output

`cId`	ndarray of ints, the cluster of every element counted from zero, a float array with NaN for the elements that are NaN and the orientations the density method leaves out
`center`	vector3d or orientation, the centre of every cluster

References

X. Chen, S. Guettel, Fast and explainable clustering based on sorting, arXiv:2202.01456 (2022)

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/orientation.calcCluster_py.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.

orientation.calcCluster