R: K-Means Clustering

kmeans {mlpack} | R Documentation

## 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,
      labels_only = FALSE,
      max_iterations = NA,
      percentage = NA,
      refined_start = FALSE,
      samplings = NA,
      seed = NA,
      verbose = FALSE
    )

### 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).
`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 "FALSE" (logical).

### 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 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.

### 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).

### Author(s)

mlpack developers

### 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:

    ## Not run:
    output <- kmeans(input=data, clusters=10)
    assignments <- output$output
    centroids <- output$centroid

    ## End(Not run)

    # 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:

    ## Not run:
    output <- kmeans(input=data, initial_centroids=initial, clusters=10,
      max_iterations=500)
    final <- output$centroid

    ## End(Not run)

[Package mlpack version 3.4.2.1 Index]