WH_adaptive_fcmeans: Fuzzy c-means with adaptive distances for histogram-valued...

In Airpino/HistDAWass: Histogram-Valued Data Analysis

Fuzzy c-means with adaptive distances for histogram-valued data

Description

Fuzzy c-means of a dataset of histogram-valued data using different adaptive distances based on the L2 Wasserstein metric.

Usage

WH_adaptive_fcmeans(
  x,
  k = 5,
  schema,
  m = 1.6,
  rep,
  simplify = FALSE,
  qua = 10,
  standardize = FALSE,
  init.weights = "EQUAL",
  weight.sys = "PROD",
  theta = 2,
  verbose = FALSE
)

Arguments

x	A MatH object (a matrix of distributionH).
k	An integer, the number of groups.
schema	An integer. 1=one weight per variable, 2=two weights per variables (one for each component: the mean and the variability component), 3=one weight per variable and per cluster, 4= two weights per variable and per cluster.
m	A number grater than 0, a fuzziness coefficient (default m=1.6).
rep	An integer, maximum number of repetitions of the algorithm (default rep=5).
simplify	A logic value (default is FALSE), if TRUE histograms are recomputed in order to speed-up the algorithm.
qua	An integer, if simplify=TRUE is the number of quantiles used for recodify the histograms.
standardize	A logic value (default is FALSE). If TRUE, histogram-valued data are standardized, variable by variable, using the Wassertein based standard deviation. Use if one wants to have variables with std equal to one.
init.weights	A string. (default='EQUAL'). EQUAL, all variables or components have the same weight; 'RANDOM', a random assignment is done.
weight.sys	A string. (default='PROD') PROD, Weights product is equal to one. SUM, the weights sum up to one.
theta	A number. (default=2) A parameter for the system of weights summing up to one.
verbose	A logic value (default is FALSE). If TRUE some details are provided.

Value

The results of the fuzzy c-means of the set of Histogram-valued data x into k cluster.

solution	A list.Returns the best solution among the repetitions, i.e. the ona having the minimum sum of squares deviation.
solution$membership	A matrix. The membership degree of each unit to each cluster.
solution$IDX	A vector. The crisp assignement to a cluster.
solution$cardinality	A vector. The cardinality of each final cluster (after the crisp assignement).
solution$Crit	A number. The criterion (Sum od square deviation from the prototypes) value at the end of the run.
quality	A number. The percentage of Sum of square deviation explained by the model. (The higher the better)

Examples

results <- WH_adaptive_fcmeans(
  x = BLOOD, k = 2, schema = 4, m = 1.5, rep = 3, simplify = TRUE,
  qua = 10, standardize = TRUE, init.weights = "EQUAL", weight.sys = "PROD"
)

Airpino/HistDAWass documentation built on Jan. 30, 2024, 7:53 p.m.