Rationale

Unlike local or exhaustive search algorithms, spectral clustering provides a global approximation that can rapidly identify candidate subsets with minimal internal association.

Overview of Steps

The algorithm follows these steps:

1. Similarity matrix from absolute correlations: \(S_{ij} = 1 - |r_{ij}|\)
2. Degree vector: \(D_i = \sum_j S_{ij}\)
3. Normalized Laplacian: \(L = I - D^{-1/2} S D^{-1/2}\)
4. Eigen decomposition of \(L\)
5. K-means clustering in the reduced eigenvector space
6. Validation of each cluster based on correlation threshold and forced variables

Basic Example

set.seed(1)
mat <- matrix(rnorm(100), ncol = 10)
colnames(mat) <- paste0("V", 1:10)
cmat <- cor(mat)

res <- MatSelect(cmat, threshold = 0.5, method = "spectral")
res

Customizing the Number of Clusters

You can pass an integer k to override the default number of clusters:

res <- MatSelect(cmat, threshold = 0.5, method = "spectral", k = 4)

Note that this method is still under testing and might change before release.