Eigenvalue gap diagnostic

eigengap() plots the smallest eigenvalues of the symmetric normalized Laplacian of S. A pronounced gap after the k-th eigenvalue suggests k well-separated clusters.

Usage

eigengap(sim, k_max = 30)

Arguments

sim

An outrank_sim object from outrank_similarity().

k_max

Number of smallest eigenvalues to show.

Value

Invisibly, a data frame with the eigenvalue index, the eigenvalue, and the gap to the next one.

Examples

m <- matrix(0.1, 6, 6) + diag(0.9, 6)
m[1:3, 1:3] <- 0.9; m[4:6, 4:6] <- 0.9; diag(m) <- 1
dimnames(m) <- list(1:6, 1:6)
crit <- criterion(m, "similarity", indifference = 0.3, similarity = 0.95)
tr <- as_traces(
  data.frame(case = as.character(1:6), act = "x",
             ts = as.POSIXct("2020-01-01")),
  "case", "act", "ts"
)
eigengap(outrank_similarity(tr, crit), k_max = 5)