Clustering by fitting a mixture model using EM with K
groups
and unconstrained covariance matrices for a matrix variate normal or
matrix variate t distribution (with specified degrees of freedom nu
).
matrixmixture( x, init = NULL, prior = NULL, K = length(prior), iter = 1000, model = "normal", method = NULL, row.mean = FALSE, col.mean = FALSE, tolerance = 0.1, nu = NULL, ..., verbose = 0, miniter = 5, convergence = TRUE )
x | data, \(p \times q \times n\) array |
---|---|
init | a list containing an array of |
prior | prior for the |
K | number of classes - provide either this or the prior. If this is provided, the prior will be of uniform distribution among the classes. |
iter | maximum number of iterations. |
model | whether to use the |
method | what method to use to fit the distribution. Currently no options. |
row.mean | By default, |
col.mean | By default, |
tolerance | convergence criterion, using Aitken acceleration of the log-likelihood by default. |
nu | degrees of freedom parameter. Can be a vector of length |
... | pass additional arguments to |
verbose | whether to print diagnostic output, by default |
miniter | minimum number of iterations |
convergence | By default, |
A list of class MixMatrixModel
containing the following
components:
prior
the prior probabilities used.
init
the initialization used.
K
the number of groups
N
the number of observations
centers
the group means.
U
the between-row covariance matrices
V
the between-column covariance matrix
posterior
the posterior probabilities for each observation
pi
the final proportions
nu
The degrees of freedom parameter if the t distribution was used.
convergence
whether the model converged
logLik
a vector of the log-likelihoods of each iteration ending in the final log-likelihood of the model
model
the model used
method
the method used
call
The (matched) function call.
Andrews, Jeffrey L., Paul D. McNicholas, and Sanjeena Subedi. 2011. "Model-Based Classification via Mixtures of Multivariate T-Distributions." Computational Statistics & Data Analysis 55 (1): 520–29. \doi{10.1016/j.csda.2010.05.019}. Fraley, Chris, and Adrian E Raftery. 2002. "Model-Based Clustering, Discriminant Analysis, and Density Estimation." Journal of the American Statistical Association 97 (458). Taylor & Francis: 611–31. \doi{10.1198/016214502760047131}. McLachlan, Geoffrey J, Sharon X Lee, and Suren I Rathnayake. 2019. "Finite Mixture Models." Annual Review of Statistics and Its Application 6. Annual Reviews: 355–78. \doi{10.1146/annurev-statistics-031017-100325}. Viroli, Cinzia. 2011. "Finite Mixtures of Matrix Normal Distributions for Classifying Three-Way Data." Statistics and Computing 21 (4): 511–22. \doi{10.1007/s11222-010-9188-x}.
set.seed(20180221) A <- rmatrixt(20,mean=matrix(0,nrow=3,ncol=4), df = 5) # 3x4 matrices with mean 0 B <- rmatrixt(20,mean=matrix(1,nrow=3,ncol=4), df = 5) # 3x4 matrices with mean 1 C <- array(c(A,B), dim=c(3,4,40)) # combine into one array prior <- c(.5,.5) # equal probability prior # create an intialization object, starts at the true parameters init = list(centers = array(c(rep(0,12),rep(1,12)), dim = c(3,4,2)), U = array(c(diag(3), diag(3)), dim = c(3,3,2))*20, V = array(c(diag(4), diag(4)), dim = c(4,4,2)) ) # fit model res<-matrixmixture(C, init = init, prior = prior, nu = 5, model = "t", tolerance = 1e-3, convergence = FALSE) print(res$centers) # the final centers #> , , 1 #> #> [,1] [,2] [,3] [,4] #> [1,] 0.117537755 0.05142832 0.03229732 -0.02163010 #> [2,] 0.005705083 -0.03489656 -0.03159498 -0.05027392 #> [3,] -0.041192795 -0.10381233 -0.07923590 -0.06302149 #> #> , , 2 #> #> [,1] [,2] [,3] [,4] #> [1,] 1.065892 1.0573621 0.8615166 1.0380062 #> [2,] 1.069079 0.9432203 1.0902007 0.9915732 #> [3,] 1.080176 1.0671593 0.9880986 0.7968937 #> print(res$pi) # the final mixing proportion #> [1] 0.4987695 0.5012305 plot(res) # the log likelihood by iteration logLik(res) # log likelihood of final result #> 'log Lik.' -414.8875 (df=54) BIC(res) # BIC of final result #> [1] 1028.975 predict(res, newdata = C[,,c(1,21)]) # predicted class membership #> $class #> [1] 1 2 #> #> $posterior #> [,1] [,2] #> [1,] 9.999883e-01 1.170306e-05 #> [2,] 6.703426e-07 9.999993e-01 #>