fpafgwc {naspaclust}

Fuzzy Geographicaly Weighted Clustering with Flower Pollination Algorithm

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Flower Pollination Algorithm

Usage

fpafgwc(
  data,
  pop = NA,
  distmat = NA,
  ncluster = 2,
  m = 2,
  distance = "euclidean",
  order = 2,
  alpha = 0.7,
  a = 1,
  b = 1,
  error = 1e-05,
  max.iter = 100,
  randomN = 0,
  vi.dist = "uniform",
  nflow = 10,
  p = 0.8,
  gamma = 1,
  lambda = 1.5,
  delta = 0,
  ei.distr = "normal",
  flow.same = 10,
  r = 4,
  m.chaotic = 0.7,
  skew = 0,
  sca = 1
)

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.

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.

error

error tolerance. Default is 1e-5.

max.iter

maximum iteration. Default is 500.

randomN

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

vi.dist

a string of centroid population distribution between "uniform" (default) and "normal". Can be defined as vi.dist= in opt_param.

nflow

number of flowers population. Can be defined as npar= in opt_param. Default is 10.

p

switch probability between global and local pollination, Can be defined as p in opt_param. default is 0.8.

gamma

Step size scaling factor. Can be defined as gamma in opt_param. Default is 1.

lambda

Levy flights index parameter between [0,2]. Can be defined as lambda in opt_param. Default is 1.5.

delta

Levi flights shift. Can be defined as delta in opt_param. Default is 0.

ei.distr

distribution of random walk parameter. Can be defined as ei.distr in opt_param.

flow.same

number of consecutive unchange to stop the iteration. Can be defined as same= in opt_param.

r

weight in logistic chaotic between [0,4]. Can be used when ei.distr='logchaotic'. Can be defined as chaos in opt_param.

m.chaotic

mapping parameter in kent chaotic between [0,1]. Can be used when ei.distr='kentchaotic'. Can be defined as map in opt_param.

skew

Levy distribution skewness for random walk. Can be used when ei.distr='levy'. Can be defined as skew in opt_param.

sca

Levy distribution scale for random walk. Can be used when ei.distr='levy'. Can be defined as sca in opt_param.

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. Furthermore, the Flower Pollination Algorithm was developed by Yang (2012) in order to get a more optimal solution of a certain complex function.

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.

See Also

fpafgwc gsafgwc

Examples

data('census2010')
data('census2010dist')
data('census2010pop')
# First way
res1 <- fpafgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,nflow=10)
# Second way
# initiate parameter
param_fgwc <- c(kind='v',ncluster=3,m=2,distance='minkowski',order=3,
               alpha=0.5,a=1.2,b=1.2,max.iter=1000,error=1e-6,randomN=10)
## tune the FPA parameter
fpa_param <- c(vi.dist='normal',npar=5,same=15,p=0.7,
               gamma=1.2,lambda=1.5,ei.distr='logchaotic',chaos=3) 
##FGWC with FPA
res2 <- fgwc(census2010,census2010pop,census2010dist,'fpa',param_fgwc,fpa_param)