R: Error of the spectral coarse graining (SCG) approximation

scg_eps {igraph} | R Documentation

## Error of the spectral coarse graining (SCG) approximation

### Description

`scg_eps` computes |v[i]-Pv[i]|, where v[i] is the ith eigenvector in `V` and P is the projector corresponding to the `mtype` argument.

### Usage

    scg_eps(
      V,
      groups,
      mtype = c("symmetric", "laplacian", "stochastic"),
      p = NULL,
      norm = c("row", "col")
    )

### Arguments

`V` | A numeric matrix of (eigen)vectors assumed normalized. The vectors are to be stored column-wise in `V`).
`groups` | A vector of `nrow(V)` integers labeling each group vertex in the partition.
`mtype` | The type of semi-projector used for the SCG. For now “symmetric”, “laplacian” and “stochastic” are available.
`p` | A probability vector of length `nrow(V)`. `p` is the stationary probability distribution of a Markov chain when `mtype` = “stochastic”. This parameter is ignored otherwise.
`norm` | Either “row” or “col”. If set to “row” the rows of the Laplacian matrix sum to zero and the rows of the stochastic matrix sum to one; otherwise it is the columns.

### Value

`scg_eps` returns with a numeric vector whose ith component is |v[i]-Pv[i]| (see Details).

### Author(s)

David Morton de Lachapelle, http://people.epfl.ch/david.morton.

### References

D. Morton de Lachapelle, D. Gfeller, and P. De Los Rios, Shrinking Matrices while Preserving their Eigenpairs with Application to the Spectral Coarse Graining of Graphs. Submitted to SIAM Journal on Matrix Analysis and Applications, 2008. http://people.epfl.ch/david.morton

### See Also

scg-method and `scg`.

### Examples

    v <- rexp(20)
    km <- kmeans(v,5)
    sum(km$withinss)
    scg_eps(cbind(v), km$cluster)^2

[Package igraph version 1.3.1 Index]