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Compute Average Membership Degree from soft memberships

Source: R/amd_score.R
amd_score.Rd

amd_score() defines Average Membership Degree (AMD) independently of the algorithm used to estimate the memberships. Rows represent observations, columns represent candidate configurations, entries are non-negative, and each row sums to one.

Usage

amd_score(membership, tolerance = sqrt(.Machine$double.eps))

Arguments

membership

Numeric matrix or data frame with observations in rows and configurations in columns.

tolerance

Non-negative numerical tolerance used to check membership bounds and row sums.

Value

One un-named numeric AMD value in the interval [0, 1 - 1 / c], where c is the number of membership columns.

Details

For a membership matrix with c columns, AMD is the mean of the largest membership in each row minus 1 / c. The term 1 / c is the value attained by a completely uniform membership vector. It is not a distribution-free expectation under random assignment.

A one-column membership matrix is mathematically valid and has AMD zero. Curves used to compare alternative numbers of configurations nevertheless begin at c = 2; see compute_amd_curve().

References

Mendoza, M. and Araújo, M. B. (2022). Biogeography of bird and mammal trophic structures. Ecography, 2022(5), e06289. doi:10.1111/ecog.06289

Examples

memberships <- rbind(
  c(0.90, 0.10),
  c(0.25, 0.75),
  c(0.50, 0.50)
)
amd_score(memberships)
#> [1] 0.2166667