optraShapes {Anthropometry} R Documentation

## Auxiliary optra subroutine of the Hartigan-Wong k-means for 3D shapes

### Description

The Hartigan-Wong version of the k-means algorithm uses two auxiliary algorithms: the optimal transfer stage (optra) and the quick transfer stage (qtran).

This function is the optra subroutine adapted to the shape analysis context. It is used within HartiganShapes. See Hartigan and Wong (1979) for details of the original k-means algorithm and Amaral et al. (2010) for details about its adaptation to shape analysis.

### Usage

optraShapes(array3D,n,c,numClust,ic1,ic2,nc,an1,an2,ncp,d,itran,live,indx)


### Arguments

 array3D Array with the 3D landmarks of the sample objects. n Number of sample objects. c Array of centroids. numClust Number of clusters. ic1 The cluster to each object belongs. ic2 This vector is used to remember the cluster which each object is most likely to be transferred to at each step. nc Number of objects in each cluster. an1 $an1(l) = nc(l) / (nc(l) - 1), l=1,...,numClust$. an2 $an2(l) = nc(l) / (nc(l) + 1), l=1,...,numClust$. ncp In the optimal transfer stage, ncp(l) stores the step at which cluster l is last updated, $l=1,...,numClust$. In the quick transfer stage, ncp(l) stores the step at which cluster l is last updated plus n, $l=1,...,numClust$. d Vector of distances from each object to every centroid. itran itran(l) = 1 if cluster l is updated in the quick-transfer stage (0 otherwise), $l=1,...,numClust$. live Vector that indicates whether a cluster is included in the live set or not. indx Number of steps since a transfer took place.

### Value

A list with the following elements: c,ic1,ic2,nc,an1,an2,ncp,d,itran,live,indx, updated after the optimal transfer stage.

### Note

This function belongs to HartiganShapes and it is not solely used. That is why there is no section of examples in this help page.

### Note

This function is based on the optra.m file available from https://github.com/johannesgerer/jburkardt-m/tree/master/asa136.

Guillermo Vinue

### References

Vinue, G., Simo, A., and Alemany, S., (2016). The k-means algorithm for 3D shapes with an application to apparel design, Advances in Data Analysis and Classification 10(1), 103–132.

Hartigan, J. A., and Wong, M. A., (1979). A K-Means Clustering Algorithm, Applied Statistics, 100–108.

Amaral, G. J. A., Dore, L. H., Lessa, R. P., and Stosic, B., (2010). k-Means Algorithm in Statistical Shape Analysis, Communications in Statistics - Simulation and Computation 39(5), 1016–1026.

Dryden, I. L., and Mardia, K. V., (1998). Statistical Shape Analysis, Wiley, Chichester.

HartiganShapes