R/dcem_star_cluster_mv.R In DCEM: Clustering Big Data using Expectation Maximization Star (EM*) Algorithm

Documented in dcem_star_cluster_mv

#The main EM routine.
require(mvtnorm)
require(matrixcalc)

#' dcem_star_cluster_mv (multivariate data): Part of DCEM package.
#'
#' Implements the EM* algorithm for multivariate data. This function is called
#' by the dcem_star_train routine.
#'
#' @param data (matrix): The dataset provided by the user.
#'
#' @param meu (matrix): The matrix containing the initial meu(s).
#'
#' @param sigma (list): A list containing the initial covariance matrices.
#'
#' @param prior (vector): A vector containing the initial priors.
#'
#' @param num_clusters (numeric): The number of clusters specified by the user. Default value is 2.
#'
#' @param iteration_count (numeric): The number of iterations for which the algorithm should run, if the
#' convergence is not achieved then the algorithm stops and exits. Default: 200.
#'
#' @param num_data (numeric): Number of rows in the dataset.
#'
#' @return
#'         A list of objects. This list contains parameters associated with the
#'         Gaussian(s) (posterior probabilities, meu, co-variance and priors)
#'
#'\enumerate{
#'         \item (1) Posterior Probabilities:  \strong{prob}
#'         A matrix of posterior-probabilities for the points in the dataset.
#'
#'         \item (2) Meu: \strong{meu}: A matrix of meu(s). Each row in
#'         the  matrix corresponds to one meu.
#'
#'         \item (3) Sigma: Co-variance matrices: \strong{sigma}: List of co-variance
#'         matrices.
#'
#'         \item (4) Priors: \strong{prior}: A vector of prior.
#'
#'         \item (5) Membership: \strong{membership}: A vector of cluster membership for data.
#'         }
#'
#' @usage
#' dcem_star_cluster_mv(data, meu, sigma, prior, num_clusters, iteration_count, num_data)
#'
#' @references
#' Using data to build a better EM: EM* for big data.
#'
#' Hasan Kurban, Mark Jenne, Mehmet M. Dalkilic
#' (2016) <https://doi.org/10.1007/s41060-017-0062-1>.
#'
#' @author Parichit Sharma \email{parishar@iu.edu}, Hasan Kurban, Mark Jenne, Mehmet Dalkilic
#'
#' This work is supported by NCI Grant 1R01CA213466-01.

dcem_star_cluster_mv <-
function(data,
meu,
sigma,
prior,
num_clusters,
iteration_count,
num_data)

{
counter <- 1

weights <- matrix(0,
nrow = num_clusters,
ncol = num_data,
byrow = TRUE)

# Create a list of heaps (one heap per cluster, heap is implemneted as a matrix)
heap_list <- rep(list(), num_clusters)
index_list <- c()

old_leaf_values <- c()

# Get machine tolerance
tolerance <- .Machine$double.eps # Intialization attempts init_attempt = 1 # Declare a datadrame to store the data membership values. membership = data.frame() # Expectation weights = expectation_mv(data, weights, meu, sigma, prior, num_clusters, tolerance) heap_index <- apply(weights, 2, which.max) # Checking for empty partitiion. while (init_attempt < 5){ if(length(unique(heap_index)) < num_clusters){ print(paste("Retrying on empty partition, attempt: ", init_attempt)) meu = meu_mv(data, num_clusters) # Expectation weights = expectation_mv(data, weights, meu, sigma, prior, num_clusters, tolerance) heap_index <- apply(weights, 2, which.max) init_attempt = init_attempt + 1 } # Break if none of the heap is empty else if (length(unique(heap_index)) == num_clusters){ #print("Empty partition fixed.") break } # Inform user if non-empty clusters could not be # found in 5 attempts. else if (init_attempt==5){ cat("The specified number of clusters:", num_clusters, "results in", num_clusters - length(unique(heap_index)), "empty clusters.", "\nThe data may have lesser modalities. Please retry or specify lesser number of clusters.\n") stop("Exiting...") } } # Normalize the probability weights data_prob <- apply(weights, 2, max) # Store the cluster membership for data in cluster_map cluster_map <- heap_index # Maximisation out = maximisation_mv(data, weights, meu, sigma, prior, num_clusters, num_data) meu = out$meu
sigma = out$sigma prior = out$prior

for (clus in 1:num_clusters) {

# Put the data in the matrix (data belonging to their own clusters)
ind <- which(heap_index == clus)
temp_matrix <- matrix(data_prob[ind])
temp_matrix <- cbind(temp_matrix, ind)

heap_list[[clus]] <- temp_matrix
#print(paste("heap: ", clus, "size: ", nrow(heap_list[[clus]])))

# Build the heap from matrices
temp_out <- build_heap(heap_list[[clus]])
heap_list[[clus]] <- split(temp_out, 1:nrow(temp_out))
}

# Seperate the leaf and non-leaf nodes
out = separate_data(heap_list, num_clusters)
heap_list <- out[[1]]
index_list <- unlist(out[[2]])

# Store the current leaf nodes for comparison with the new leaves
old_leaf_values <- c(old_leaf_values, index_list)

# Repeat till convergence threshold or iteration which-ever is earlier.
while (counter <= iteration_count) {

new_leaf_values <- c()

temp_weights <- matrix(0,
nrow = num_clusters,
ncol = length(index_list),
byrow = TRUE)

# Expectation only for leaf nodes (not for all data - save time and computation)
temp_weights = expectation_mv(data[index_list, ], temp_weights, meu, sigma, prior, num_clusters, tolerance)
# Update the weights for leaf nodes only
weights = update_weights(temp_weights, weights, index_list, num_clusters)

# Expectation
sum_weights <- colSums(weights)
weights <- sweep(weights, 2, sum_weights, '/')
weights[is.nan(weights)] <- tolerance
weights[weights <= 0.0] <- tolerance

# Maximisation
out = maximisation_mv(data, weights, meu, sigma, prior, num_clusters, num_data)
meu = out$meu sigma = out$sigma
prior = out\$prior

leaves_ind <- index_list

# Re-assign the leaf nodes based on their estimated probabilities
# Only leaf nodes are moved.
if (length(leaves_ind) == 1){
new_heap_assign_for_leaves <-which.max(temp_weights)
new_liklihood_for_leaves <- max(temp_weights)
}
else{
new_heap_assign_for_leaves <- unlist(apply(temp_weights, 2, which.max))
new_liklihood_for_leaves <- unlist(apply(temp_weights, 2, max))
}

# Insert into new heap
heap_list <- insert_nodes(heap_list, new_heap_assign_for_leaves, new_liklihood_for_leaves, leaves_ind, num_clusters)
#print(paste("Inserting done: ", length(leaves_ind)))

out = separate_data(heap_list, num_clusters)
heap_list <- out[[1]]
index_list <- out[[2]]

# Putting all leaf nodes together to re-assign later
new_leaf_values <- c(new_leaf_values, index_list)

# Check convergence (if old and new leaves are same across heaps)
if (round( (length(setdiff(old_leaf_values, new_leaf_values)) / length(new_leaf_values)), 4) <= 0.01) {
print(paste("Convergence at iteration", counter))
break
}

# Check iterations
else if (counter == iteration_count) {
print("Maximum iterations reached. Halting.")
break
}

# Put new leaves into the old leaves variable
old_leaf_values <- new_leaf_values
index_list <- new_leaf_values
counter <- counter + 1

}

# Assign clusters to data
membership = rbind(membership, apply(weights, 2, which.max))
colnames(membership) <- seq(1:num_data)

# Prepare the output list
output = list(
prob = weights,
'meu' = meu,
'sigma' = sigma,
'prior' = prior,
'count' = counter,
'membership' = membership
)
return(output)

}


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DCEM documentation built on Aug. 2, 2020, 9:07 a.m.