Mallows: Fits a Mallows mixture model to ranking data
In YunlongJiao/kernrank: Kernel Methods for Rank Data

Description Usage Arguments Value Author(s) References See Also Examples

Fits the Mallows mixture model to total rankings, using EM algorithm, for clustering permutations.

Mallows(datas, G, weights = NULL, iter = 100, iterin = iter,
  tol = 0.001, logsumexp.trick = TRUE, seed = 47631439,
  key = c("copelandMallows", "bruteMallows", "bordaMallows", "kernelMallows",
  "kernelMallows_Exh", "kernelGaussian", "copelandMallows_Eqlam",
  "bruteMallows_Eqlam", "bordaMallows_Eqlam", "kernelMallows_Eqlam",
  "kernelMallows_Exh_Eqlam", "kernelGaussian_Eqlam"), exhkey = "_Exh",
  eqlamkey = "_Eqlam")

`datas`	Matrix of dimension `N x n` with sequences in rows.
`G`	Number of modes, 2 or greater.
`weights`	Numeric vector of length `N` denoting frequencies of each permutation observed. Each observation is observed once by default. Notably it must not contain 0 and should be of equal length with `nrow(datas)`.
`iter`	Maximum number of iterations for EM algorithm.
`iterin`	Maximum number of iterations for alternate optimization between centers and lambda. Effective only when performing kernel Mallows with exhaustive optimization.
`tol`	Stopping precision.
`logsumexp.trick`	Logical. Whether or not to use log-sum-exp trick to compute log-likelihood.
`seed`	Seed index for reproducible results when optimization is performed. Set to NULL to disable the action.
`key`	A character string defining the type of Mallows mixture model to perform: `copelandMallows` denotes original Mallows mixture model with cluster centers found by Copeland's method `bruteMallows` denotes original Mallows mixture model with cluster centers found by brute-force search for optimal Kemeny consensus (not applicable for large n) `bordaMallows` denotes original Mallows mixture model with cluster centers as Borda count `kernelMallows` denotes kernel version of Mallows mixture model with cluster centers as the barycenter in Euclidean space induced by Kendall embedding `kernelGaussian` denotes Gaussian mixture model in the Euclidean space induced by Kendall embedding
`exhkey`	DO NOT CHANGE. A character string. If it greps successfully in "`key`", an alternate optimization between centers and lambda. Effective only when performing "`kernelMallows`" with exhaustive optimization.
`eqlamkey`	DO NOT CHANGE. A character string. If it greps successfully in "`key`", the dispersion parameters (or lambda) are constrained to be equal for all clusters; otherwise no constraints on lambda.

List.

`key`	Character string indicating the type of Mallows mixture model performed
`R`	List of length "`G`" of cluster centers, each entry being a permutation of length "`n`" if original Mallows mixture model is performed, or a numeric vector of length `choose(n,2)` if kernel version is performed
`p`	Numeric vector of length "`G`" representing the proportion probability of each cluster
`lambda`	Numeric vector of length "`G`" representing the dispersion parameters of each cluster
`datas`	A copy of "`datas`" on which the Mallows mixture model is fitted, combined with "`weights`", fuzzy assignment membership probability "`z`", distances to centers in "`R`"
`min.like`	Numeric vector of length "`iter`" representing fitted likelihood values at each iteration

Yunlong Jiao

Thomas Brendan Murphy, Donal Martin. "Mixtures of distance-based models for ranking data." Computational Statistics & Data Analysis, vol. 41, no. 3, pp. 645-655, 2003. DOI:10.1016/S0167-9473(02)00165-2

Yunlong Jiao, Jean-Philippe Vert. "The Kendall and Mallows Kernels for Permutations." IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), vol. 40, no. 7, pp. 1755-1769, 2018. DOI:10.1109/TPAMI.2017.2719680

MallowsCV

datas <- do.call('rbind', combinat::permn(1:5))
G <- 3
weights <- runif(nrow(datas))

# Fit Mallows mixture model
model <- Mallows(datas, G, weights, key = 'bordaMallows')
str(model)