FuzzyClusteringSimilarity

Code for Dirichlet Random Models for Fuzzy Rand Adjustment

Summary

Adjusted Normalized Degree of Concordance (ANDC) is a similarity measure between two fuzzy (or hard) clusterings. The value is in (-inf, 1], with 1 representing identical clusterings, and 0 representing the clusterings have the same agreement as "random" clusterings. The selection of "random" is required by the user, and four models are provided.

Getting Started

This package is available from the julia general repository.

using Pkg
Pkg.add("FuzzyCLusteringSimilarity")

Then import the module.

using FuzzyClusteringSimilarity

You can run the unit tests to insure the package was properly installed.

Pkg.test("FuzzyClusteringSimilarity")

Documentation

andc(matrix1::AbstractMatrix, matrix2::AbstractMatrix, model::String, oneSided=True, p::Int=1, q::Int=1)

Calculate the adjusted normalized degree of concordance of matrix1 and matrix2 using model to adjust for chance agreement. Available models are '"fit", "sym", "flat", "perm" '.

ndc(matrix1::AbstractMatrix, matrix2::AbstractMatrix, p::Int=1, q::Int=1)

Calculate the normalized degree of concordance of matrix1 and matrix2.

endc(matrix1::AbstractMatrix, matrix2::AbstractMatrix, model::String, oneSided=True, p::Int=1, q::Int=1)

Calculate the expected normalized degree of concordance of random matrices. Models for generating random matrices based on matrix1 and matrix2 are '"fit", "sym", "flat", "perm" '.

massageMatrix(matrix::AbstractMatrix)

Massage a matrix to enable julia's multiple dispatch. Matrix is formated with points as columns and clusters and rows. If matrix is a hard clustering the type is converted to Bool.

References

E. Hullermeier, M. Rifqi, S. Henzgen and R. Senge, "Comparing Fuzzy Partitions: A Generalization of the Rand Index and Related Measures," in IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp. 546-556, June 2012. https://doi.org/10.1109/TFUZZ.2011.2179303

D’Ambrosio, A., Amodio, S., Iorio, C. et al. Adjusted Concordance Index: an Extensionl of the Adjusted Rand Index to Fuzzy Partitions. J Classif 38, 112–128 (2021). https://doi.org/10.1007/s00357-020-09367-0

Andrews, J.L., Browne, R. & Hvingelby, C.D. On Assessments of Agreement Between Fuzzy Partitions. J Classif 39, 326–342 (2022). https://doi.org/10.1007/s00357-021-09407-3