funkmeans: Functional k-means clustering for parallel smooths
In vows: Voxelwise Semiparametrics

Description Usage Arguments Details Value Author(s) References See Also Examples

This function performs k-means clustering for curve estimates corresponding to each of a 3D grid of points. For example, when scatterplot smoothing is performed at each of a grid of brain voxels as in Reiss et al. (2014), this function can be used to cluster the obtained smooths.

1 2	funkmeans(fdobj, deriv = 1, lambda = 0, ncomp, centers, nstart = 10, store.fdobj = TRUE)

`fdobj`	a functional data object, of class `"fd"`, defining the set of curves being clustered.
`deriv`	which derivative of the curves should be clustered. If `0`, the curves themselves are clustered; if `1` (the default), their first derivatives are clustered, a natural way to assign curves of similar shape to the same cluster.
`lambda`	smoothing parameter for functional PCA as implemented by `pca.fd`.
`ncomp`	number of functional principal components.
`centers`	number of clusters.
`nstart`	number of randomly chosen sets of initial centers used by the `kmeans` function.
`store.fdobj`	logical: Should the input fd object be stored in the output? May wish to set to FALSE for large sets of smooths.

The functional clustering algorithm consists of performing (i) functional principal component analysis of the curve estimates or their derivatives, followed by (ii) k-means clustering of the functional PC scores (Tarpey and Kinateder, 2003).

An object of class "funkmeans", which is a list with elements:

`cluster, centers, withinss, tots, tot.withinss, betweenness, size`	see `kmeans`.
`basis,coef`	basis object and coefficient matrix defining the functional data object (see `fd`) for the curves that are clustered.
`fpca`	functional principal components object, output by `pca.fd`.
`R2`	proportion of variance explained by the k clusters.

Philip Reiss phil.reiss@nyumc.org, Lei Huang huangracer@gmail.com and Lan Huo

Alexander-Bloch, A. F., Reiss, P. T., Rapoport, J., McAdams, H., Giedd, J. N., Bullmore, E. T., and Gogtay, N. (2014). Abnormal cortical growth in schizophrenia targets normative modules of synchronized development. Biological Psychiatry, in press.

Reiss, P. T., Huang, L., Chen, Y.-H., Huo, L., Tarpey, T., and Mennes, M. (2014). Massively parallel nonparametric regression, with an application to developmental brain mapping. Journal of Computational and Graphical Statistics, Journal of Computational and Graphical Statistics, 23(1), 232–248.

Tarpey, T., and Kinateder, K. K. J. (2003). Clustering functional data. Journal of Classification, 20, 93–114.

funkmeans4d

data(test)
d4 = test$d4
x = test$x
semi.obj = semipar4d(d4, ~sf(x), -5:5, data.frame(x = x))
fdobj = extract.fd(semi.obj)
fkmobj = funkmeans4d(fdobj, d4, ncomp=6, centers=3)