Uses a Mixture-of-experts algorithm to find cluster centers that are influenced by prediction covariates.
predkmeans(
X,
R,
K,
mu = NULL,
muStart = c("kmeans", "random"),
sigma2 = 0,
sigma2fixed = FALSE,
maxitEM = 100,
tol = 1e-05,
convEM = c("both", "mu", "gamma"),
nStarts = 1,
maxitMlogit = 500,
verbose = 0,
muRestart = 1000,
returnAll = FALSE,
...
)An n by p matrix or data frame of data to be clustered.
Covariates used for clustering. Required unless doing k-means
clustering (i.e. sigma2=0 and sigma2fixed=TRUE).
Number of clusters
starting values for cluster centers. If NULL (default),
then value is chosen according to muStart.
Character string indicating how initial value
of mu should be selected. Only used if mu=NULL. Possible
values are "random" or "kmeans" (default).
starting value of sigma2. If set to 0 and
sigma2fixed=TRUE, the standard k-means is done
instead of predictive k-means.
Logical indicating whether sigma2 should be held fixed. If FALSE, then sigma2 is estimated using Maximum Likelihood.
Maximum number of EM iterations for
finding the Mixture of Experts solution. If doing regular
k-means, this is passed as iter.max.
convergence criterion
controls the measure of convergence for the EM algorithm. Should be one of "mu", "gamma", or "both". Defaults to "both." The EM algorithm stops when the Frobenius norm of the change in mu, the change in gamma, or the change in mu and the change in gamma is less than 'tol'.
number of times to perform EM algorithm
Maximum number of iterations in the mlogit optimization (nested within EM algorithm)
numeric vector indicating how much output to produce
Gives max number of attempts at picking starting values. Only used when muStart='random'. If selected starting values for mu are constant within each cluster, then the starting values are re-selected up to muRestart times.
A list containing all nStarts solutions is
included in the output.
Additional arguments passed to mlogit
An object of class predkmeans, containing the following elements:
A list containing the results from the best-fitting solution to the Mixture of Experts problem:
Maximum-likelihood estimate of intercepts from normal mixture model. These are the cluster centers.
Maximum-likelihood estimates of the mixture coefficeints.
If sigma2fixed=FALSE, the maximum likelihood estimate of sigma2
Indicator of covergence.
Value of the log-likelihood.
Number of iterations.
A subset of output from mlogit.
Matrix of cluster centers
Vector of cluster labels assigned to observations
Number of clusters
Final value of sigma^2.
Mean within-cluster sum-of-squares
Logical indicator of whether sigma2 was held fixed
A thorough description of this method is provided in Keller et al. (2017). The algorithm for sovling the mixture of Experts model is based upon the approach presented by Jordan and Jacobs (1994).
If sigma2 is 0 and sigm2fixed is TRUE, then standard k-means clustering (using kmeans) is done instead.
Keller, J.P., Drton, M., Larson, T., Kaufman, J.D., Sandler, D.P., and Szpiro, A.A. (2017). Covariate-adaptive clustering of exposures for air pollution epidemiology cohorts. Annals of Applied Statistics, 11(1):93--113.
Jordan M. and Jacobs R. (1994). Hierarchical mixtures of experts and the EM algorithm. Neural computation 6(2), 181-214.
# NOT RUN {
n <- 200
r1 <- rnorm(n)
r2 <- rnorm(n)
u1 <- rbinom(n, size=1,prob=0)
cluster <- ifelse(r1<0, ifelse(u1, "A", "B"), ifelse(r2<0, "C", "D"))
mu1 <- c(A=2, B=2, C=-2, D=-2)
mu2 <- c(A=1, B=-1, C=-1, D=-1)
x1 <- rnorm(n, mu1[cluster], 4)
x2 <- rnorm(n, mu2[cluster], 4)
R <- model.matrix(~r1 + r2)
X <- cbind(x1, x2)
pkm <- predkmeans(X=cbind(x1, x2), R=R, K=4)
summary(pkm)
# }
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