fgwcuv {naspaclust}

Classical Fuzzy Geographicaly Weighted Clustering

Description

Fuzzy clustering with addition of spatial configuration of membership matrix

Usage

fgwcuv(
  data,
  pop,
  distmat,
  kind = NA,
  ncluster = 2,
  m = 2,
  distance = "euclidean",
  order = 2,
  alpha = 0.7,
  a = 1,
  b = 1,
  max.iter = 500,
  error = 1e-05,
  randomN = 0,
  uij = NA,
  vi = NA
)

Arguments

data

an object of data with d>1. Can be matrix or data.frame. If your data is univariate, bind it with 1 to get a 2 columns.

pop

an n*1 vector contains population.

distmat

an n*n distance matrix between regions.

kind

use 'u' if you want to use membership approach and 'v' for centroid approach.

ncluster

an integer. The number of clusters.

m

degree of fuzziness or fuzzifier. Default is 2.

distance

the distance metric between data and centroid, the default is euclidean, see cdist for details.

order

minkowski order. default is 2.

alpha

the old membership effect with [0,1], if alpha equals 1, it will be same as fuzzy C-Means, if 0, it equals to neighborhood effect.

a

spatial magnitude of distance. Default is 1.

b

spatial magnitude of population. Default is 1.

max.iter

maximum iteration. Default is 500.

error

error tolerance. Default is 1e-5.

randomN

random seed for initialisation (if uij or vi is NA). Default is 0.

uij

membership matrix initialisation.

vi

centroid matrix initialisation.

Details

Fuzzy Geographically Weighted Clustering (FGWC) was developed by Mason and Jacobson (2007) by adding neighborhood effects and population to configure the membership matrix in Fuzzy C-Means. There are two kinds of options in doing classical FGWC. The first is using "u" (Runkler and Katz 2006) (default) for membership optimization and "v" (Mason and Jacobson 2007) for centroid optimisation.

Value

an object of class "fgwc".
An "fgwc" object contains as follows:

• converg - the process convergence of objective function

• f_obj - objective function value

• membership - membership matrix

• centroid - centroid matrix

• validation - validation indices (there are partition coefficient (PC), classification entropy (CE), SC index (SC), separation index (SI), Xie and Beni's index (XB), IFV index (IFV), and Kwon index (Kwon))

• max.iter - Maximum iteration

• cluster - the cluster of the data

• finaldata - The final data (with the cluster)

• call - the syntax called previously

• time - computational time.

References

Mason GA, Jacobson RD (2007). “Fuzzy Geographically Weighted Clustering.” In Proceedings of the 9th International Conference on Geocomputation, 1–7.

Runkler TA, Katz C (2006). “Fuzzy Clustering by Particle Swarm Optimization.” In 2006 IEEE International Conference on Fuzzy Systems. doi: 10.1109/fuzzy.2006.1681773, https://doi.org/10.1109/fuzzy.2006.1681773.

See Also

abcfgwc fpafgwc gsafgwc hhofgwc ifafgwc psofgwc tlbofgwc

Examples

data('census2010')
data('census2010dist')
data('census2010pop')
res1 <- fgwcuv(census2010,census2010pop,census2010dist,'u',3,2,'euclidean',4)