Optimal_Clusters_KMeans: Optimal number of Clusters for Kmeans or Mini-Batch-Kmeans

Description

Optimal number of Clusters for Kmeans or Mini-Batch-Kmeans

Usage

Optimal_Clusters_KMeans(
  data,
  max_clusters,
  criterion = "variance_explained",
  fK_threshold = 0.85,
  num_init = 1,
  max_iters = 200,
  initializer = "kmeans++",
  tol = 1e-04,
  plot_clusters = TRUE,
  verbose = FALSE,
  tol_optimal_init = 0.3,
  seed = 1,
  mini_batch_params = NULL
)

Value

a vector with the results for the specified criterion. If plot_clusters is TRUE then it plots also the results.

Arguments

data: matrix or data frame
max_clusters: either a numeric value, a contiguous or non-continguous numeric vector specifying the cluster search space
criterion: one of variance_explained, WCSSE, dissimilarity, silhouette, distortion_fK, AIC, BIC and Adjusted_Rsquared. See details for more information.
fK_threshold: a float number used in the 'distortion_fK' criterion
num_init: number of times the algorithm will be run with different centroid seeds
max_iters: the maximum number of clustering iterations
initializer: the method of initialization. One of, optimal_init, quantile_init, kmeans++ and random. See details for more information
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
plot_clusters: either TRUE or FALSE, indicating whether the results of the Optimal_Clusters_KMeans function should be plotted
verbose: either TRUE or FALSE, indicating whether progress is printed during clustering
tol_optimal_init: tolerance value for the 'optimal_init' initializer. The higher this value is, the far appart from each other the centroids are.
seed: integer value for random number generator (RNG)
mini_batch_params: either NULL or a list of the following parameters : batch_size, init_fraction, 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.

Author

Lampros Mouselimis

Details

---------------criteria--------------------------

variance_explained : the sum of the within-cluster-sum-of-squares-of-all-clusters divided by the total sum of squares

WCSSE : the sum of the within-cluster-sum-of-squares-of-all-clusters

dissimilarity : the average intra-cluster-dissimilarity of all clusters (the distance metric defaults to euclidean)

silhouette : the average silhouette width where first the average per cluster silhouette is computed and then the global average (the distance metric defaults to euclidean). To compute the silhouette width for each cluster separately see the 'silhouette_of_clusters()' function

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)

AIC : the Akaike information criterion

BIC : the Bayesian information criterion

Adjusted_Rsquared : the adjusted R^2 statistic

---------------initializers----------------------

optimal_init : this initializer adds rows of the data incrementally, while checking that they do not already exist in the centroid-matrix [ experimental ]

quantile_init : initialization of centroids by using the cummulative distance between observations and by removing potential duplicates [ experimental ]

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

random : random selection of data rows as initial centroids

If the 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 init_fraction parameter is the more close the results between Mini-Batch-Kmeans and Kmeans will be.

In case that the max_clusters parameter is a contiguous or non-contiguous vector then plotting is disabled. Therefore, plotting is enabled only if the max_clusters parameter is of length 1. Moreover, the distortion_fK criterion can't be computed if the max_clusters parameter is a contiguous or non-continguous vector ( the distortion_fK criterion requires consecutive clusters ). The same applies also to the Adjusted_Rsquared criterion which returns incorrect output.

References

https://www.ee.columbia.edu/~dpwe/papers/PhamDN05-kmeans.pdf

Examples

Run this code


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)

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