mlpack (version 4.6.0)

kmeans: K-Means Clustering

Description

An implementation of several strategies for efficient k-means clustering. Given a dataset and a value of k, this computes and returns a k-means clustering on that data.

Usage

kmeans(
  clusters,
  input,
  algorithm = NA,
  allow_empty_clusters = FALSE,
  in_place = FALSE,
  initial_centroids = NA,
  kill_empty_clusters = FALSE,
  kmeans_plus_plus = FALSE,
  labels_only = FALSE,
  max_iterations = NA,
  percentage = NA,
  refined_start = FALSE,
  samplings = NA,
  seed = NA,
  verbose = getOption("mlpack.verbose", FALSE)
)

Value

A list with several components:

centroid

If specified, the centroids of each cluster will be written to the given file (numeric matrix).

output

Matrix to store output labels or labeled data to (numeric matrix).

Arguments

clusters

Number of clusters to find (0 autodetects from initial centroids) (integer).

input

Input dataset to perform clustering on (numeric matrix).

algorithm

Algorithm to use for the Lloyd iteration ('naive', 'pelleg-moore', 'elkan', 'hamerly', 'dualtree', or 'dualtree-covertree'). Default value "naive" (character).

allow_empty_clusters

Allow empty clusters to be persist. Default value "FALSE" (logical).

in_place

If specified, a column containing the learned cluster assignments will be added to the input dataset file. In this case, --output_file is overridden. (Do not use in Python.. Default value "FALSE" (logical).

initial_centroids

Start with the specified initial centroids (numeric matrix).

kill_empty_clusters

Remove empty clusters when they occur. Default value "FALSE" (logical).

kmeans_plus_plus

Use the k-means++ initialization strategy to choose initial points. Default value "FALSE" (logical).

labels_only

Only output labels into output file. Default value "FALSE" (logical).

max_iterations

Maximum number of iterations before k-means terminates. Default value "1000" (integer).

percentage

Percentage of dataset to use for each refined start sampling (use when --refined_start is specified). Default value "0.02" (numeric).

refined_start

Use the refined initial point strategy by Bradley and Fayyad to choose initial points. Default value "FALSE" (logical).

samplings

Number of samplings to perform for refined start (use when --refined_start is specified). Default value "100" (integer).

seed

Random seed. If 0, 'std::time(NULL)' is used. Default value "0" (integer).

verbose

Display informational messages and the full list of parameters and timers at the end of execution. Default value "getOption("mlpack.verbose", FALSE)" (logical).

Author

mlpack developers

Details

This program performs K-Means clustering on the given dataset. It can return the learned cluster assignments, and the centroids of the clusters. Empty clusters are not allowed by default; when a cluster becomes empty, the point furthest from the centroid of the cluster with maximum variance is taken to fill that cluster.

Optionally, the strategy to choose initial centroids can be specified. The k-means++ algorithm can be used to choose initial centroids with the "kmeans_plus_plus" parameter. The Bradley and Fayyad approach ("Refining initial points for k-means clustering", 1998) can be used to select initial points by specifying the "refined_start" parameter. This approach works by taking random samplings of the dataset; to specify the number of samplings, the "samplings" parameter is used, and to specify the percentage of the dataset to be used in each sample, the "percentage" parameter is used (it should be a value between 0.0 and 1.0).

There are several options available for the algorithm used for each Lloyd iteration, specified with the "algorithm" option. The standard O(kN) approach can be used ('naive'). Other options include the Pelleg-Moore tree-based algorithm ('pelleg-moore'), Elkan's triangle-inequality based algorithm ('elkan'), Hamerly's modification to Elkan's algorithm ('hamerly'), the dual-tree k-means algorithm ('dualtree'), and the dual-tree k-means algorithm using the cover tree ('dualtree-covertree').

The behavior for when an empty cluster is encountered can be modified with the "allow_empty_clusters" option. When this option is specified and there is a cluster owning no points at the end of an iteration, that cluster's centroid will simply remain in its position from the previous iteration. If the "kill_empty_clusters" option is specified, then when a cluster owns no points at the end of an iteration, the cluster centroid is simply filled with DBL_MAX, killing it and effectively reducing k for the rest of the computation. Note that the default option when neither empty cluster option is specified can be time-consuming to calculate; therefore, specifying either of these parameters will often accelerate runtime.

Initial clustering assignments may be specified using the "initial_centroids" parameter, and the maximum number of iterations may be specified with the "max_iterations" parameter.

Examples

# As an example, to use Hamerly's algorithm to perform k-means clustering
# with k=10 on the dataset "data", saving the centroids to "centroids" and
# the assignments for each point to "assignments", the following command
# could be used:

if (FALSE) {
output <- kmeans(input=data, clusters=10)
assignments <- output$output
centroids <- output$centroid
}

# To run k-means on that same dataset with initial centroids specified in
# "initial" with a maximum of 500 iterations, storing the output centroids in
# "final" the following command may be used:

if (FALSE) {
output <- kmeans(input=data, initial_centroids=initial, clusters=10,
  max_iterations=500)
final <- output$centroid
}