flagMean {MMOC}

Calculate the Flag mean of multiple subspaces

Description

Calculate the flag-mean of multiple subspaces. This method allows you to find the extrinsic mean of a finite set of subspaces. You can think of this as a median subspace. This method is also able to handle subspaces with different dimensions. See the references for more details

Usage

flagMean(LapList, k, laplacian = c("shift", "Ng", "sym", "rw"), plots = TRUE)

Arguments

LapList

A list of Laplacian matrices

k

A vector indicating how many eigenvectors to take from each Laplacian, i.e., the number of clusters in each view

laplacian

One of "shift", "Ng", "rw" or "sym". Should be the same type used to calculate your Laplacians

plots

Whether or not to plot the singular values from SVD

Details

Despite the complex linear algebra to achieve this result, the opperation is very simple. This function concatonates (cbind) the given subspaces and then performs singular value decomposition on the resulting matrix. This gives the 'median' subspace of the given set of subspaces. We would then cluster on the columns of the U matrix just as we do in standard spectral clustering

Value

The output from a singular value decomposition. See svd

References

https://www.semanticscholar.org/paper/Flag-Manifolds-for-the-Characterization-of-in-Large-Marrinan-Beveridge/7d306512b545df98243f87cb8173df83b4672b18 https://www.sciencedirect.com/science/article/pii/S0024379514001669?via%3Dihub

Examples

## Generating data with 2 and 3 distinct clusters
## Note that 'clustStruct' returns a list
n=120; k <- c(2,3)
dd <- clustStruct(n=n, p=30, k=k, noiseDat='random')

## Laplacians
L_list <- lapply(dd, kernelLaplacian, kernel="Spectrum", plots=FALSE, verbose=FALSE)

## Calculating the flag mean
fm <- flagMean(L_list, k=k, laplacian='shift')

## Knowing the true structure makes it much easier to know how
## many right singular vectors to grab. There are 4 distinct
## groups in these data from 'clustStruct'

trueGroups(n=n, k=k)

kmeans(fm$u[, 1:4], centers=4)