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clustering_functions.R
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clustering_functions.R
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utils::globalVariables(c("x", "y")) # to avoid the following NOTE when package checking takes place --> plot_2d: no visible binding for global variables 'x', 'y'
#' tryCatch function to prevent armadillo errors
#'
#' @keywords internal
tryCatch_GMM <- function(data, gaussian_comps, dist_mode, seed_mode, km_iter, em_iter, verbose, var_floor, seed) {
Error = tryCatch(GMM_arma(data, gaussian_comps, dist_mode, seed_mode, km_iter, em_iter, verbose, var_floor, seed),
error = function(e) e)
if (inherits(Error, "error")) {
return(list(Error = Error, warning = "probable causes of error: 'warning: gmm_diag::learn(): number of vectors is less than number of gaussians' OR 'warning: gmm_diag::learn(): EM algorithm failed'"))}
else {
return(Error)
}
}
#' Gaussian Mixture Model clustering
#'
#' @param data matrix or data frame
#' @param gaussian_comps the number of gaussian mixture components
#' @param dist_mode the distance used during the seeding of initial means and k-means clustering. One of, \emph{eucl_dist}, \emph{maha_dist}.
#' @param seed_mode how the initial means are seeded prior to running k-means and/or EM algorithms. One of, \emph{static_subset}, \emph{random_subset}, \emph{static_spread}, \emph{random_spread}.
#' @param km_iter the number of iterations of the k-means algorithm
#' @param em_iter the number of iterations of the EM algorithm
#' @param verbose either TRUE or FALSE; enable or disable printing of progress during the k-means and EM algorithms
#' @param var_floor the variance floor (smallest allowed value) for the diagonal covariances
#' @param seed integer value for random number generator (RNG)
#' @return a list consisting of the centroids, covariance matrix ( where each row of the matrix represents a diagonal covariance matrix), weights and the log-likelihoods for each gaussian component. In case of Error it returns the error message and the possible causes.
#' @details
#' This function is an R implementation of the 'gmm_diag' class of the Armadillo library. The only exception is that user defined parameter settings are not supported, such as seed_mode = 'keep_existing'.
#' For probabilistic applications, better model parameters are typically learned with dist_mode set to maha_dist.
#' For vector quantisation applications, model parameters should be learned with dist_mode set to eucl_dist, and the number of EM iterations set to zero.
#' In general, a sufficient number of k-means and EM iterations is typically about 10.
#' The number of training samples should be much larger than the number of Gaussians.
#' Seeding the initial means with static_spread and random_spread can be much more time consuming than with static_subset and random_subset.
#' The k-means and EM algorithms will run faster on multi-core machines when OpenMP is enabled in your compiler (eg. -fopenmp in GCC)
#' @references
#' http://arma.sourceforge.net/docs.html
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = as.matrix(dietary_survey_IBS[, -ncol(dietary_survey_IBS)])
#'
#' dat = center_scale(dat)
#'
#' gmm = GMM(dat, 2, "maha_dist", "random_subset", 10, 10)
#'
GMM = function(data, gaussian_comps = 1, dist_mode = 'eucl_dist', seed_mode = 'random_subset', km_iter = 10, em_iter = 5, verbose = FALSE, var_floor = 1e-10, seed = 1) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if (gaussian_comps < 1) stop('the number of gaussian mixture components should be greater than 0')
if (!dist_mode %in% c('eucl_dist', 'maha_dist')) stop("available distance modes are 'eucl_dist' and 'maha_dist'")
if (!seed_mode %in% c('static_subset','random_subset','static_spread','random_spread')) stop("available seed modes are 'static_subset','random_subset','static_spread' and 'random_spread'")
if (km_iter < 0 ) stop('the km_iter parameter can not be negative')
if (em_iter < 0 ) stop('the em_iter parameter can not be negative')
if (!is.logical(verbose)) stop('the verbose parameter should be either TRUE or FALSE')
if (var_floor < 0 ) stop('the var_floor parameter can not be negative')
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values")
res = tryCatch_GMM(data, gaussian_comps, dist_mode, seed_mode, km_iter, em_iter, verbose, var_floor, seed)
if ('Error' %in% names(res)) {
return(res)
} else {
structure(list(call = match.call(),
centroids = res$centroids,
covariance_matrices = res$covariance_matrices,
weights = as.vector(res$weights),
Log_likelihood = res$Log_likelihood_raw),
class = c("GMMCluster", 'Gaussian Mixture Models'))
}
}
#' Prediction function for a Gaussian Mixture Model object
#'
#' @param data matrix or data frame
#' @param CENTROIDS matrix or data frame containing the centroids (means), stored as row vectors
#' @param COVARIANCE matrix or data frame containing the diagonal covariance matrices, stored as row vectors
#' @param WEIGHTS vector containing the weights
#' @return a list consisting of the log-likelihoods, cluster probabilities and cluster labels.
#' @author Lampros Mouselimis
#' @details
#' This function takes the centroids, covariance matrix and weights from a trained model and returns the log-likelihoods, cluster probabilities and cluster labels for new data.
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = as.matrix(dietary_survey_IBS[, -ncol(dietary_survey_IBS)])
#'
#' dat = center_scale(dat)
#'
#' gmm = GMM(dat, 2, "maha_dist", "random_subset", 10, 10)
#'
#' # pr = predict_GMM(dat, gmm$centroids, gmm$covariance_matrices, gmm$weights)
#'
predict_GMM = function(data, CENTROIDS, COVARIANCE, WEIGHTS) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if ('data.frame' %in% class(CENTROIDS)) CENTROIDS = as.matrix(CENTROIDS)
if (!inherits(CENTROIDS, 'matrix')) stop('CENTROIDS should be either a matrix or a data frame')
if ('data.frame' %in% class(COVARIANCE)) COVARIANCE = as.matrix(COVARIANCE)
if (!inherits(COVARIANCE, 'matrix')) stop('COVARIANCE should be either a matrix or a data frame')
if (ncol(data) != ncol(CENTROIDS) || ncol(data) != ncol(COVARIANCE) || length(WEIGHTS) != nrow(CENTROIDS) || length(WEIGHTS) != nrow(COVARIANCE))
stop('the number of columns of the data, CENTROIDS and COVARIANCE should match and the number of rows of the CENTROIDS AND COVARIANCE should be equal to the length of the WEIGHTS vector')
if (!inherits(WEIGHTS, 'numeric') || !is.vector(WEIGHTS))
stop('WEIGHTS should be a numeric vector')
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values")
res = predict_MGausDPDF(data, CENTROIDS, COVARIANCE, WEIGHTS, eps = 1.0e-8)
# I've added 1 to the output cluster labels to account for the difference in indexing between R and C++
list(log_likelihood = res$Log_likelihood_raw,
cluster_proba = res$cluster_proba,
cluster_labels = as.vector(res$cluster_labels) + 1)
}
#' @rdname predict_GMM
#' @param object,newdata,... arguments for the `predict` generic
#' @export
predict.GMMCluster <- function(object, newdata, ...) {
predict_GMM(newdata, object$centroids, object$covariance_matrices, object$weights)$cluster_labels
}
#' @export
print.GMMCluster <- function(x, ...) {
cat("GMM Cluster\n",
"Call:", deparse(x$call), "\n",
"Data cols:", ncol(x$centroids), "\n",
"Centroids:", nrow(x$centroids), "\n")
}
#' tryCatch function to prevent armadillo errors in GMM_arma_AIC_BIC
#'
#' @keywords internal
tryCatch_optimal_clust_GMM <- function(data, max_clusters, dist_mode, seed_mode, km_iter, em_iter, verbose, var_floor, criterion, seed) {
Error = tryCatch(GMM_arma_AIC_BIC(data, max_clusters, dist_mode, seed_mode, km_iter, em_iter, verbose, var_floor, criterion, seed),
error = function(e) e)
if (inherits(Error, "error")) {
return(list(Error = Error, warning = "probable causes of error: 'warning: gmm_diag::learn(): number of vectors is less than number of gaussians' OR 'warning: gmm_diag::learn(): EM algorithm failed'"))}
else {
return(Error)
}
}
#' Optimal number of Clusters for the gaussian mixture models
#'
#' @param data matrix or data frame
#' @param max_clusters either a numeric value, a contiguous or non-continguous numeric vector specifying the cluster search space
#' @param criterion one of 'AIC' or 'BIC'
#' @param dist_mode the distance used during the seeding of initial means and k-means clustering. One of, \emph{eucl_dist}, \emph{maha_dist}.
#' @param seed_mode how the initial means are seeded prior to running k-means and/or EM algorithms. One of, \emph{static_subset}, \emph{random_subset}, \emph{static_spread}, \emph{random_spread}.
#' @param km_iter the number of iterations of the k-means algorithm
#' @param em_iter the number of iterations of the EM algorithm
#' @param verbose either TRUE or FALSE; enable or disable printing of progress during the k-means and EM algorithms
#' @param var_floor the variance floor (smallest allowed value) for the diagonal covariances
#' @param plot_data either TRUE or FALSE indicating whether the results of the function should be plotted
#' @param seed integer value for random number generator (RNG)
#' @return a vector with either the AIC or BIC for each iteration. In case of Error it returns the error message and the possible causes.
#' @author Lampros Mouselimis
#' @details
#' \strong{AIC} : the Akaike information criterion
#'
#' \strong{BIC} : the Bayesian information criterion
#'
#' In case that the \emph{max_clusters} parameter is a contiguous or non-contiguous vector then plotting is disabled. Therefore, plotting is enabled only if the \emph{max_clusters} parameter is of length 1.
#'
#' @importFrom grDevices dev.cur
#' @importFrom grDevices dev.off
#' @importFrom graphics plot
#' @importFrom graphics axis
#' @importFrom graphics abline
#' @importFrom graphics text
#'
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = dietary_survey_IBS[, -ncol(dietary_survey_IBS)]
#'
#' dat = center_scale(dat)
#'
#' opt_gmm = Optimal_Clusters_GMM(dat, 10, criterion = "AIC", plot_data = FALSE)
#'
#'
#' #----------------------------
#' # non-contiguous search space
#' #----------------------------
#'
#' search_space = c(2,5)
#'
#' opt_gmm = Optimal_Clusters_GMM(dat, search_space, criterion = "AIC", plot_data = FALSE)
#'
Optimal_Clusters_GMM = function(data, max_clusters, criterion = "AIC", dist_mode = 'eucl_dist', seed_mode = 'random_subset',
km_iter = 10, em_iter = 5, verbose = FALSE, var_floor = 1e-10, plot_data = TRUE, seed = 1) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if (!inherits(max_clusters, c('numeric', 'integer'))) stop('max_clusters should be a numeric or integer vector')
if (length(max_clusters) == 1) {
if (plot_data && max_clusters < 2) stop('if plot_data is TRUE the max_clusters parameter should be at least 2')
}
if (!criterion %in% c("AIC", "BIC")) stop("supported criteria are 'AIC' or 'BIC'")
if (!dist_mode %in% c('eucl_dist', 'maha_dist')) stop("available distance modes are 'eucl_dist' and 'maha_dist'")
if (!seed_mode %in% c('static_subset','random_subset','static_spread','random_spread'))
stop("available seed modes are 'static_subset','random_subset','static_spread' and 'random_spread'")
if (km_iter < 0 ) stop('the km_iter parameter can not be negative')
if (em_iter < 0 ) stop('the em_iter parameter can not be negative')
if (!is.logical(verbose)) stop('the verbose parameter should be either TRUE or FALSE')
if (var_floor < 0 ) stop('the var_floor parameter can not be negative')
if (length(max_clusters) != 1) {
plot_data = FALSE # set "plot_data" to FALSE if the "max_clusters" parameter is not of length 1
if (ncol(data) < max(max_clusters) && verbose) { warning("the number of columns of the data should be larger than the maximum value of 'max_clusters'", call. = F); cat(" ", '\n') }
}
else {
if (ncol(data) < max_clusters && verbose) { warning("the number of columns of the data should be larger than 'max_clusters'", call. = F); cat(" ", '\n') }
}
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values")
if (length(max_clusters) == 1) {
pass_vector = 1:max_clusters}
else {
pass_vector = max_clusters
}
if (0 %in% pass_vector) {
stop("The 'max_clusters' vector can not include a 0 value !", call. = F)
}
gmm = tryCatch_optimal_clust_GMM(data, pass_vector, dist_mode, seed_mode, km_iter, em_iter, verbose, var_floor, criterion, seed)
if ('Error' %in% names(gmm)) {
return(gmm)
} else {
if (plot_data) {
if (grDevices::dev.cur() != 1) {
grDevices::dev.off() # reset par()
}
vec_out = as.vector(gmm)
tmp_VAL = as.vector(stats::na.omit(vec_out))
if (length(which(is.na(vec_out))) > 0) {
x_dis = (1:length(vec_out))[-which(is.na(vec_out))]
y_dis = vec_out[-which(is.na(vec_out))]}
else {
x_dis = 1:length(vec_out)
y_dis = vec_out
}
y_MAX = max(tmp_VAL)
graphics::plot(x = x_dis, y = y_dis, type = 'l', xlab = 'clusters', ylab = criterion, col = 'blue', lty = 3, axes = FALSE)
graphics::axis(1, at = seq(1, length(vec_out) , by = 1))
graphics::axis(2, at = seq(round(min(tmp_VAL) - round(summary(y_MAX)[['Max.']]) / 10), y_MAX + round(summary(y_MAX)[['Max.']]) / 10, by = round((summary(tmp_VAL)['Max.'] - summary(tmp_VAL)['Min.']) / 5)), las = 1, cex.axis = 0.8)
graphics::abline(h = seq(round(min(tmp_VAL) - round(summary(y_MAX)[['Max.']]) / 10), y_MAX + round(summary(y_MAX)[['Max.']]) / 10, by = round((summary(tmp_VAL)['Max.'] - summary(tmp_VAL)['Min.']) / 5)), v = seq(1, length(vec_out) , by = 1),
col = "gray", lty = 3)
graphics::text(x = 1:length(vec_out), y = vec_out, labels = round(vec_out, 1), cex = 0.8, font = 2)
}
res = as.vector(gmm)
class(res) = c("GMMCluster", 'Gaussian Mixture Models')
return(res)
}
}
#' tryCatch function to prevent armadillo errors in KMEANS_arma
#'
#' @keywords internal
tryCatch_KMEANS_arma <- function(data, clusters, n_iter, verbose, seed_mode, CENTROIDS, seed) {
Error = tryCatch(KMEANS_arma(data, clusters, n_iter, verbose, seed_mode, CENTROIDS, seed),
error = function(e) e)
if (inherits(Error, "error")) {
return(list(Error = Error, message = Error$message))}
else if (sum(dim(Error)) == 0) {
return("warning: kmeans(): number of vectors is less than number of means")}
else {
return(Error)
}
}
#' k-means using the Armadillo library
#'
#' @param data matrix or data frame
#' @param clusters the number of clusters
#' @param n_iter the number of clustering iterations (about 10 is typically sufficient)
#' @param seed_mode how the initial centroids are seeded. One of, \emph{keep_existing}, \emph{static_subset}, \emph{random_subset}, \emph{static_spread}, \emph{random_spread}.
#' @param verbose either TRUE or FALSE, indicating whether progress is printed during clustering
#' @param CENTROIDS a matrix of initial cluster centroids. The rows of the CENTROIDS matrix should be equal to the number of clusters and the columns should be equal to the columns of the data. CENTROIDS should be used in combination with seed_mode 'keep_existing'.
#' @param seed integer value for random number generator (RNG)
#' @return the centroids as a matrix. In case of Error it returns the error message, whereas in case of an empty centroids-matrix it returns a warning-message.
#' @details
#' This function is an R implementation of the 'kmeans' class of the Armadillo library.
#' It is faster than the KMeans_rcpp function but it lacks some features. For more info see the details section of the KMeans_rcpp function.
#' The number of columns should be larger than the number of clusters or CENTROIDS.
#' If the clustering fails, the means matrix is reset and a bool set to false is returned.
#' The clustering will run faster on multi-core machines when OpenMP is enabled in your compiler (eg. -fopenmp in GCC)
#' @references
#' http://arma.sourceforge.net/docs.html
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = dietary_survey_IBS[, -ncol(dietary_survey_IBS)]
#'
#' dat = center_scale(dat)
#'
#' km = KMeans_arma(dat, clusters = 2, n_iter = 10, "random_subset")
#'
KMeans_arma = function(data, clusters, n_iter = 10, seed_mode = "random_subset", verbose = FALSE, CENTROIDS = NULL, seed = 1) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if (!is.numeric(clusters) || length(clusters) != 1 || clusters < 1) stop('clusters should be numeric and greater than 0')
if (n_iter < 0) stop('the n_iter parameter can not be negative')
if (!seed_mode %in% c('keep_existing','static_subset','random_subset','static_spread','random_spread'))
stop("available seed modes are 'keep_existing','static_subset','random_subset','static_spread' and 'random_spread'")
if ((seed_mode == 'keep_existing' && is.null(CENTROIDS)) || (seed_mode != 'keep_existing' && !is.null(CENTROIDS)))
stop('the keep_existing seed_mode should be used when CENTROIDS is not NULL')
if (!is.logical(verbose)) stop('the verbose parameter should be either TRUE or FALSE')
if (!is.null(CENTROIDS) && (!inherits(CENTROIDS, 'matrix') || nrow(CENTROIDS) != clusters || ncol(CENTROIDS) != ncol(data)))
stop('CENTROIDS should be a matrix with number of rows equal to the number of clusters and number of columns equal to the number of columns of the data')
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values")
res = tryCatch_KMEANS_arma(data, clusters, n_iter, verbose, seed_mode, CENTROIDS, seed)
if ('Error' %in% names(res) || is.character(res)) {
return(res)
} else {
## FIXME: this function currently returns centroids. It should probably
## return the same data structure as KMeans_cpp.
## return(structure(res, class = c("KMeansCluster", "k-means clustering")))
return (structure(res, class = "k-means clustering"))
}
}
#' k-means using RcppArmadillo
#'
#' @param data matrix or data frame
#' @param clusters the number of clusters
#' @param num_init number of times the algorithm will be run with different centroid seeds
#' @param max_iters the maximum number of clustering iterations
#' @param initializer the method of initialization. One of, \emph{optimal_init}, \emph{quantile_init}, \emph{kmeans++} and \emph{random}. See details for more information
#' @param fuzzy either TRUE or FALSE. If TRUE, then prediction probabilities will be calculated using the distance between observations and centroids
#' @param verbose either TRUE or FALSE, indicating whether progress is printed during clustering.
#' @param CENTROIDS a matrix of initial cluster centroids. The rows of the CENTROIDS matrix should be equal to the number of clusters and the columns should be equal to the columns of the data.
#' @param tol a float number. If, in case of an iteration (iteration > 1 and iteration < max_iters) 'tol' is greater than the squared norm of the centroids, then kmeans has converged
#' @param tol_optimal_init tolerance value for the 'optimal_init' initializer. The higher this value is, the far appart from each other the centroids are.
#' @param seed integer value for random number generator (RNG)
#' @return a list with the following attributes: clusters, fuzzy_clusters (if fuzzy = TRUE), centroids, total_SSE, best_initialization, WCSS_per_cluster, obs_per_cluster, between.SS_DIV_total.SS
#' @author Lampros Mouselimis
#' @details
#' This function has the following features in comparison to the KMeans_arma function:
#'
#' Besides optimal_init, quantile_init, random and kmeans++ initilizations one can specify the centroids using the CENTROIDS parameter.
#'
#' The running time and convergence of the algorithm can be adjusted using the num_init, max_iters and tol parameters.
#'
#' If num_init > 1 then KMeans_rcpp returns the attributes of the best initialization using as criterion the within-cluster-sum-of-squared-error.
#'
#'
#' ---------------initializers----------------------
#'
#' \strong{optimal_init} : this initializer adds rows of the data incrementally, while checking that they do not already exist in the centroid-matrix [ experimental ]
#'
#' \strong{quantile_init} : initialization of centroids by using the cummulative distance between observations and by removing potential duplicates [ experimental ]
#'
#' \strong{kmeans++} : kmeans++ initialization. Reference : http://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf AND http://stackoverflow.com/questions/5466323/how-exactly-does-k-means-work
#'
#' \strong{random} : random selection of data rows as initial centroids
#'
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = dietary_survey_IBS[, -ncol(dietary_survey_IBS)]
#'
#' dat = center_scale(dat)
#'
#' km = KMeans_rcpp(dat, clusters = 2, num_init = 5, max_iters = 100, initializer = 'kmeans++')
#'
KMeans_rcpp = function(data, clusters, num_init = 1, max_iters = 100, initializer = 'kmeans++', fuzzy = FALSE,
verbose = FALSE, CENTROIDS = NULL, tol = 1e-4, tol_optimal_init = 0.3, seed = 1) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if (!is.numeric(clusters) || length(clusters) != 1 || clusters < 1) stop('clusters should be numeric and greater than 0')
if (num_init < 1) stop('the num_init parameter should be greater than 0')
if (max_iters < 1) stop('the max_iters parameter should be greater than 0')
if (!initializer %in% c('kmeans++', 'random', 'optimal_init', 'quantile_init')) stop("available initializer methods are 'kmeans++', 'random', 'optimal_init' and 'quantile_init'")
if (!is.logical(fuzzy)) stop('the fuzzy parameter should be either TRUE or FALSE')
if (!is.logical(verbose)) stop('the verbose parameter should be either TRUE or FALSE')
if (!is.null(CENTROIDS) && (!inherits(CENTROIDS, 'matrix') || nrow(CENTROIDS) != clusters || ncol(CENTROIDS) != ncol(data)))
stop('CENTROIDS should be a matrix with number of rows equal to the number of clusters and number of columns equal to the number of columns of the data')
if (tol <= 0.0) stop('tol should be a float number greater than 0.0')
if (tol_optimal_init <= 0.0) stop('tol_optimal_init should be a float number greater than 0.0')
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values")
res = KMEANS_rcpp(data, clusters, num_init, max_iters, initializer, fuzzy, verbose, CENTROIDS, tol, eps = 1.0e-6, tol_optimal_init, seed)
if (fuzzy) {
return(structure(list(call = match.call(),
clusters = as.vector(res$clusters + 1),
fuzzy_clusters = res$fuzzy_clusters,
centroids = res$centers,
total_SSE = res$total_SSE,
best_initialization = res$best_initialization,
WCSS_per_cluster = res$WCSS_per_cluster,
obs_per_cluster = res$obs_per_cluster,
between.SS_DIV_total.SS = (res$total_SSE - sum(res$WCSS_per_cluster)) / res$total_SSE),
class = c("KMeansCluster", "k-means clustering")))
} else {
return(structure(list(call = match.call(),
clusters = as.vector(res$clusters + 1),
centroids = res$centers,
total_SSE = res$total_SSE,
best_initialization = res$best_initialization,
WCSS_per_cluster = res$WCSS_per_cluster,
obs_per_cluster = res$obs_per_cluster,
between.SS_DIV_total.SS = (res$total_SSE - sum(res$WCSS_per_cluster)) / res$total_SSE),
class = c("KMeansCluster", "k-means clustering")))
}
}
#' Prediction function for the k-means
#'
#' @param data matrix or data frame
#' @param CENTROIDS a matrix of initial cluster centroids. The rows of the CENTROIDS matrix should be equal to the number of clusters and the columns should be equal to the columns of the data.
#' @param threads an integer specifying the number of cores to run in parallel
#' @return a vector (clusters)
#' @author Lampros Mouselimis
#' @details
#' This function takes the data and the output centroids and returns the clusters.
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = dietary_survey_IBS[, -ncol(dietary_survey_IBS)]
#'
#' dat = center_scale(dat)
#'
#' km = KMeans_rcpp(dat, clusters = 2, num_init = 5, max_iters = 100, initializer = 'kmeans++')
#'
#' pr = predict_KMeans(dat, km$centroids, threads = 1)
predict_KMeans = function(data, CENTROIDS, threads = 1) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if (!is.matrix(CENTROIDS)) stop("CENTROIDS should be a matrix")
if (ncol(data) != ncol(CENTROIDS))
stop('the number of columns of the data should match the number of columns of the CENTROIDS ')
if (threads < 1) stop('the number of threads should be greater or equal to 1')
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values", call. = F)
if (!is.null(class(CENTROIDS))) class(CENTROIDS) = NULL # set the class of the input 'CENTROIDS' to NULL otherwise the 'duplicated()' function might check it column-wise rather than row-wise
flag_dups = duplicated(CENTROIDS)
if (sum(flag_dups) > 0) stop("The 'CENTROIDS' input matrix includes duplicated rows!", call. = F)
as.vector(validate_centroids(data, CENTROIDS, threads)) + 1
}
#' @rdname predict_KMeans
#' @param object,newdata,... arguments for the `predict` generic
#' @export
predict.KMeansCluster <- function(object, newdata, threads = 1, ...) {
predict_KMeans(newdata, CENTROIDS = object$centroids, threads = threads)
}
#' @export
print.KMeansCluster <- function(x, ...) {
WSSE <- sum(x$WCSS_per_cluster)
BSSE <- x$total_SSE - WSSE
cat("KMeans Cluster\n",
"Call:", deparse(x$call), "\n",
"Data cols:", ncol(x$centroids), "\n",
"Centroids:", nrow(x$centroids), "\n",
"BSS/SS:", BSSE/x$total_SSE, "\n",
"SS:", x$total_SSE, "=", WSSE, "(WSS) +", BSSE, "(BSS)\n")
}
#' Optimal number of Clusters for Kmeans or Mini-Batch-Kmeans
#'
#' @param data matrix or data frame
#' @param max_clusters either a numeric value, a contiguous or non-continguous numeric vector specifying the cluster search space
#' @param criterion one of \emph{variance_explained}, \emph{WCSSE}, \emph{dissimilarity}, \emph{silhouette}, \emph{distortion_fK}, \emph{AIC}, \emph{BIC} and \emph{Adjusted_Rsquared}. See details for more information.
#' @param fK_threshold a float number used in the 'distortion_fK' criterion
#' @param num_init number of times the algorithm will be run with different centroid seeds
#' @param max_iters the maximum number of clustering iterations
#' @param initializer the method of initialization. One of, \emph{optimal_init}, \emph{quantile_init}, \emph{kmeans++} and \emph{random}. See details for more information
#' @param tol a float number. If, in case of an iteration (iteration > 1 and iteration < max_iters) 'tol' is greater than the squared norm of the centroids, then kmeans has converged
#' @param plot_clusters either TRUE or FALSE, indicating whether the results of the \emph{Optimal_Clusters_KMeans} function should be plotted
#' @param verbose either TRUE or FALSE, indicating whether progress is printed during clustering
#' @param tol_optimal_init tolerance value for the 'optimal_init' initializer. The higher this value is, the far appart from each other the centroids are.
#' @param seed integer value for random number generator (RNG)
#' @param mini_batch_params either NULL or a list of the following parameters : \emph{batch_size}, \emph{init_fraction}, \emph{early_stop_iter}. If not NULL then the optimal number of clusters will be found based on the Mini-Batch-Kmeans. See the details and examples sections for more information.
#' @return a vector with the results for the specified criterion. If plot_clusters is TRUE then it plots also the results.
#' @author Lampros Mouselimis
#' @details
#' ---------------criteria--------------------------
#'
#' \strong{variance_explained} : the sum of the within-cluster-sum-of-squares-of-all-clusters divided by the total sum of squares
#'
#' \strong{WCSSE} : the sum of the within-cluster-sum-of-squares-of-all-clusters
#'
#' \strong{dissimilarity} : the average intra-cluster-dissimilarity of all clusters (the distance metric defaults to euclidean)
#'
#' \strong{silhouette} : the average silhouette width of all clusters (the distance metric defaults to euclidean)
#'
#' \strong{distortion_fK} : this criterion is based on the following paper, 'Selection of K in K-means clustering' (https://www.ee.columbia.edu/~dpwe/papers/PhamDN05-kmeans.pdf)
#'
#' \strong{AIC} : the Akaike information criterion
#'
#' \strong{BIC} : the Bayesian information criterion
#'
#' \strong{Adjusted_Rsquared} : the adjusted R^2 statistic
#'
#'
#' ---------------initializers----------------------
#'
#' \strong{optimal_init} : this initializer adds rows of the data incrementally, while checking that they do not already exist in the centroid-matrix [ experimental ]
#'
#' \strong{quantile_init} : initialization of centroids by using the cummulative distance between observations and by removing potential duplicates [ experimental ]
#'
#' \strong{kmeans++} : kmeans++ initialization. Reference : http://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf AND http://stackoverflow.com/questions/5466323/how-exactly-does-k-means-work
#'
#' \strong{random} : random selection of data rows as initial centroids
#'
#'
#' If the \emph{mini_batch_params} parameter is not NULL then the optimal number of clusters will be found based on the Mini-batch-Kmeans algorithm, otherwise based on the Kmeans. The higher the \emph{init_fraction}
#' parameter is the more close the results between Mini-Batch-Kmeans and Kmeans will be.
#'
#' In case that the \emph{max_clusters} parameter is a contiguous or non-contiguous vector then plotting is disabled. Therefore, plotting is enabled only if the \emph{max_clusters} parameter is of length 1.
#' Moreover, the \emph{distortion_fK} criterion can't be computed if the \emph{max_clusters} parameter is a contiguous or non-continguous vector ( the \emph{distortion_fK} criterion requires consecutive clusters ).
#' The same applies also to the \emph{Adjusted_Rsquared} criterion which returns incorrect output.
#'
#' @references
#'
#' https://core.ac.uk/download/pdf/205410925.pdf
#'
#' @importFrom utils txtProgressBar
#' @importFrom utils setTxtProgressBar
#' @importFrom graphics par
#' @importFrom graphics mtext
#' @importFrom stats na.omit
#'
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = dietary_survey_IBS[, -ncol(dietary_survey_IBS)]
#'
#' dat = center_scale(dat)
#'
#'
#' #-------
#' # kmeans
#' #-------
#'
#' opt_km = Optimal_Clusters_KMeans(dat, max_clusters = 10, criterion = "distortion_fK",
#'
#' plot_clusters = FALSE)
#'
#' #------------------
#' # mini-batch-kmeans
#' #------------------
#'
#'
#' params_mbkm = list(batch_size = 10, init_fraction = 0.3, early_stop_iter = 10)
#'
#' opt_mbkm = Optimal_Clusters_KMeans(dat, max_clusters = 10, criterion = "distortion_fK",
#'
#' plot_clusters = FALSE, mini_batch_params = params_mbkm)
#'
#'
#' #----------------------------
#' # non-contiguous search space
#' #----------------------------
#'
#' search_space = c(2,5)
#'
#' opt_km = Optimal_Clusters_KMeans(dat, max_clusters = search_space,
#'
#' criterion = "variance_explained",
#'
#' plot_clusters = FALSE)
#'
Optimal_Clusters_KMeans = function(data, max_clusters, criterion = "variance_explained", fK_threshold = 0.85, num_init = 1, max_iters = 200,
initializer = 'kmeans++', tol = 1e-4, plot_clusters = TRUE, verbose = FALSE, tol_optimal_init = 0.3,
seed = 1, mini_batch_params = NULL) {
if ('data.frame' %in% class(data)) data = as.matrix(data)
if (!inherits(data, 'matrix')) stop('data should be either a matrix or a data frame')
if (!inherits(max_clusters, c('numeric', 'integer'))) stop('max_clusters should be a numeric or integer vector')
if (length(max_clusters) == 1) {
if (max_clusters < 1) {
stop('In case that max_clusters is of length 1 it should be greater than 0')
}
}
if (!criterion %in% c('variance_explained', 'WCSSE', 'dissimilarity', 'silhouette', 'distortion_fK', 'AIC', 'BIC', 'Adjusted_Rsquared'))
stop("available criteria are 'variance_explained', 'WCSSE', 'dissimilarity', 'silhouette', 'distortion_fK', 'AIC', 'BIC' and 'Adjusted_Rsquared'")
if (num_init < 1) stop('the num_init parameter should be greater than 0')
if (max_iters < 1) stop('the max_iters parameter should be greater than 0')
if (!initializer %in% c('kmeans++', 'random', 'optimal_init', 'quantile_init'))
stop("available initializer methods are 'kmeans++', 'random', 'quantile_init' and 'optimal_init'")
if (tol <= 0.0) stop('tol should be a float number greater than 0.0')
if (!is.logical(plot_clusters)) stop('the plot_clusters parameter should be either TRUE or FALSE')
if (!is.logical(verbose)) stop('the verbose parameter should be either TRUE or FALSE')
if (tol_optimal_init <= 0.0) stop('tol_optimal_init should be a float number greater than 0.0')
if (!is.null(mini_batch_params)) {
if (!all(names(mini_batch_params) %in% c("batch_size", "init_fraction", "early_stop_iter"))) {
stop("The 'mini_batch_params' parameter should be of type list and valid inputs to the 'mini_batch_params' are: 'batch_size', 'init_fraction' and 'early_stop_iter'!", call. = F)
}
if (criterion == "variance_explained") {
stop("The 'variance_explained' criterion is not supported in case of mini-batch-kmeans (when 'mini_batch_params' is not NULL)!", call. = F)
}
}
if (length(max_clusters) != 1) plot_clusters = FALSE # set "plot_clusters" to FALSE if the "max_clusters" parameter is not of length 1
flag_non_finite = check_NaN_Inf(data)
if (!flag_non_finite) stop("the data includes NaN's or +/- Inf values")
LEN_CLUST = ITER_CLUST = NA
if (length(max_clusters) == 1) {
LEN_CLUST = max_clusters
ITER_CLUST = 1:max_clusters}
else {
LEN_CLUST = length(max_clusters)
ITER_CLUST = max_clusters
}
vec_out = rep(NA, LEN_CLUST)
if (verbose) { cat("", '\n'); pb = utils::txtProgressBar(min = 1, max = LEN_CLUST, style = 3); cat("", '\n') }
COUNT = 1
for (i in ITER_CLUST) {
if (is.null(mini_batch_params)) {
km = KMEANS_rcpp(data, i, num_init, max_iters, initializer, FALSE, FALSE, NULL, tol, 1.0e-6, tol_optimal_init, seed)
}
else {
km = MiniBatchKmeans(data, i, mini_batch_params[["batch_size"]], num_init, max_iters, mini_batch_params[["init_fraction"]], initializer,
mini_batch_params[["early_stop_iter"]], FALSE, NULL, tol, tol_optimal_init, seed)
tmp_cent = km$centroids
km["centroids"] = NULL
km[["centers"]] = tmp_cent # rename the mini-batch-kmeans centroids-name to match the one of the kmeans algorithm
if (criterion %in% c("dissimilarity", "silhouette", "BIC")) { # in these cases call also the 'predict_MBatchKMeans' function to receive the clusters
km_preds = predict_MBatchKMeans(data, tmp_cent, FALSE)
km[["clusters"]] = as.vector(km_preds)
}
}
if (criterion == "variance_explained") {
vec_out[COUNT] = sum(stats::na.omit(as.vector(km$WCSS_per_cluster))) / km$total_SSE
}
if (criterion == "WCSSE") {
vec_out[COUNT] = sum(stats::na.omit(as.vector(km$WCSS_per_cluster)))
}
if (criterion == "dissimilarity") {
eval_km = evaluation_rcpp(data, as.vector(km$clusters), FALSE)
tmp_dis = mean(stats::na.omit(unlist(lapply(eval_km$INTRA_cluster_dissimilarity, mean))))
vec_out[COUNT] = tmp_dis
}
if (criterion == "silhouette") {
if (i == 1) {
vec_out[COUNT] = 0.0}
else {
eval_km = evaluation_rcpp(data, as.vector(km$clusters), TRUE)
tmp_silh = mean(stats::na.omit(unlist(lapply(eval_km$silhouette, mean))))
vec_out[COUNT] = tmp_silh
}
}
if (criterion == "distortion_fK") {
vec_out[COUNT] = sum(stats::na.omit(as.vector(km$WCSS_per_cluster)))
}
if (criterion == "AIC") { # http://stackoverflow.com/questions/15839774/how-to-calculate-bic-for-k-means-clustering-in-r
m = ncol(km$centers)
k = nrow(km$centers)
D = sum(stats::na.omit(km$WCSS_per_cluster))
vec_out[COUNT] = D + 2.0 * m * k
}
if (criterion == "BIC") { # http://stackoverflow.com/questions/15839774/how-to-calculate-bic-for-k-means-clustering-in-r
m = ncol(km$centers)
k = nrow(km$centers)
n = length(km$clusters)
D = sum(stats::na.omit(km$WCSS_per_cluster))
vec_out[COUNT] = D + log(n) * m * k
}
if (criterion == 'Adjusted_Rsquared') {
vec_out[COUNT] = sum(stats::na.omit(km$WCSS_per_cluster))
}
if (verbose) { utils::setTxtProgressBar(pb, COUNT) }
COUNT = COUNT + 1
}
if (verbose) { close(pb); cat("", '\n') }
if (criterion == 'Adjusted_Rsquared') { # http://sherrytowers.com/2013/10/24/k-means-clustering/
if (length(max_clusters) != 1) {
vec_out = "The 'Adjusted_Rsquared' criterion doesn't return the correct output if the 'max_clusters' parameter is greater than 1"
}
else {
vec_out = 1.0 - (vec_out * (nrow(data) - 1)) / (vec_out[1] * (nrow(data) - ITER_CLUST))
}
}
if (criterion %in% c('variance_explained', 'WCSSE', 'dissimilarity', 'silhouette', 'AIC', 'BIC', 'Adjusted_Rsquared')) {
if (plot_clusters) {
tmp_VAL = as.vector(stats::na.omit(vec_out))
if (length(which(is.na(vec_out))) > 0) {
x_dis = (1:length(vec_out))[-which(is.na(vec_out))]
y_dis = vec_out[-which(is.na(vec_out))]}
else {
x_dis = 1:length(vec_out)
y_dis = vec_out
}
y_MAX = max(tmp_VAL)
graphics::plot(x = x_dis, y = y_dis, type = 'l', xlab = 'clusters', ylab = criterion, col = 'blue', lty = 3, axes = FALSE)
graphics::axis(1, at = seq(1, length(vec_out) , by = 1))
if (criterion == 'silhouette') {
graphics::axis(2, at = seq(0, y_MAX + 0.05, by = 0.05 ), las = 1, cex.axis = 0.8)
graphics::abline(h = seq(0.0, max(as.vector(stats::na.omit(vec_out))), 0.05), v = seq(1, length(vec_out) , by = 1), col = "gray", lty = 3)}
else {
tmp_summary = round(summary(y_MAX)[['Max.']])
out_max_summary = ifelse(tmp_summary == 0, 1, tmp_summary)
graphics::axis(2, at = seq(0, y_MAX + out_max_summary / 10, by = out_max_summary / 10), las = 1, cex.axis = 0.8)
graphics::abline(h = seq(0.0, max(as.vector(stats::na.omit(vec_out))), out_max_summary / 10), v = seq(1, length(vec_out) , by = 1), col = "gray", lty = 3)
}
if (criterion %in% c("variance_explained", "Adjusted_Rsquared", "dissimilarity", "silhouette")) {
graphics::text(x = 1:length(vec_out), y = vec_out, labels = round(vec_out, 2), cex = 0.8, font = 2) }
else {
graphics::text(x = 1:length(vec_out), y = vec_out, labels = round(vec_out, 1), cex = 0.8, font = 2)
}
}
}
else { # "distortion_fK"
if (length(max_clusters) != 1) {
fK_vec = "The 'distortion_fK' criterion can not be computed if the length of the 'max_clusters' parameter is greater than 1. See the details for more information!"
}
else {
f_K = opt_clust_fK(vec_out, ncol(data), fK_threshold)
fK_vec = as.vector(f_K$fK_evaluation)
}
if (plot_clusters) {
if (length(which(is.na(fK_vec))) > 0) {
x_fk = (1:length(fK_vec))[-which(is.na(fK_vec))]
y_fk = fK_vec[-which(is.na(fK_vec))]}
else {
x_fk = 1:length(fK_vec)
y_fk = fK_vec
}
graphics::par(oma = c(0, 2, 0, 0))
graphics::plot(y_fk, type = 'l', xlab = 'clusters', ylab = 'f(K)', col = 'green', axes = FALSE)
graphics::axis(1, at = x_fk)
graphics::axis(2, at = seq(0, max(y_fk) + 0.1, by = round(summary(y_fk)[['Max.']]) / 10), las = 1, cex.axis = 0.8)
graphics::abline(h = seq(0.0, max(y_fk), round(summary(y_fk)[['Max.']]) / 10), v = seq(1, length(y_fk) , by = 1), col = "gray", lty = 3)
graphics::abline(h = fK_threshold, col = 'blue', lty = 3)
graphics::mtext("threshold", side = 2, line = 2, at = fK_threshold, las = 1, cex = 0.9)
graphics::text(x = x_fk, y = y_fk, labels = round(y_fk,2), cex = 0.8, font = 2)
}
}
if (criterion %in% c('variance_explained', 'WCSSE', 'dissimilarity', 'silhouette', 'AIC', 'BIC', 'Adjusted_Rsquared')) {
return(vec_out)
} else {
return(fK_vec) # "distortion_fK"
}
}
#' Mini-batch-k-means using RcppArmadillo
#'
#' @param data matrix or data frame
#' @param clusters the number of clusters
#' @param batch_size the size of the mini batches
#' @param num_init number of times the algorithm will be run with different centroid seeds
#' @param max_iters the maximum number of clustering iterations
#' @param init_fraction percentage of data to use for the initialization centroids (applies if initializer is \emph{kmeans++} or \emph{optimal_init}). Should be a float number between 0.0 and 1.0.
#' @param initializer the method of initialization. One of, \emph{optimal_init}, \emph{quantile_init}, \emph{kmeans++} and \emph{random}. See details for more information
#' @param early_stop_iter continue that many iterations after calculation of the best within-cluster-sum-of-squared-error
#' @param verbose either TRUE or FALSE, indicating whether progress is printed during clustering
#' @param CENTROIDS a matrix of initial cluster centroids. The rows of the CENTROIDS matrix should be equal to the number of clusters and the columns should be equal to the columns of the data
#' @param tol a float number. If, in case of an iteration (iteration > 1 and iteration < max_iters) 'tol' is greater than the squared norm of the centroids, then kmeans has converged
#' @param tol_optimal_init tolerance value for the 'optimal_init' initializer. The higher this value is, the far appart from each other the centroids are.
#' @param seed integer value for random number generator (RNG)
#' @return a list with the following attributes: centroids, WCSS_per_cluster, best_initialization, iters_per_initialization
#' @author Lampros Mouselimis
#' @details
#' This function performs k-means clustering using mini batches.
#'
#' ---------------initializers----------------------
#'
#' \strong{optimal_init} : this initializer adds rows of the data incrementally, while checking that they do not already exist in the centroid-matrix [ experimental ]
#'
#' \strong{quantile_init} : initialization of centroids by using the cummulative distance between observations and by removing potential duplicates [ experimental ]
#'
#' \strong{kmeans++} : kmeans++ initialization. Reference : http://theory.stanford.edu/~sergei/papers/kMeansPP-soda.pdf AND http://stackoverflow.com/questions/5466323/how-exactly-does-k-means-work
#'
#' \strong{random} : random selection of data rows as initial centroids
#'
#' @references
#' http://www.eecs.tufts.edu/~dsculley/papers/fastkmeans.pdf, https://github.com/siddharth-agrawal/Mini-Batch-K-Means
#' @export
#' @examples
#'
#' data(dietary_survey_IBS)
#'
#' dat = dietary_survey_IBS[, -ncol(dietary_survey_IBS)]
#'
#' dat = center_scale(dat)
#'
#' MbatchKm = MiniBatchKmeans(dat, clusters = 2, batch_size = 20, num_init = 5, early_stop_iter = 10)
#'
MiniBatchKmeans = function(data, clusters, batch_size = 10, num_init = 1, max_iters = 100, init_fraction = 1.0, initializer = 'kmeans++',
early_stop_iter = 10, verbose = FALSE, CENTROIDS = NULL, tol = 1e-4, tol_optimal_init = 0.3, seed = 1) {