| Title: | Nature-Inspired Spatial Clustering |
|---|---|
| Description: | Implement and enhance the performance of spatial fuzzy clustering using Fuzzy Geographically Weighted Clustering with various optimization algorithms, mainly from Xin She Yang (2014) <ISBN:9780124167438> with book entitled Nature-Inspired Optimization Algorithms. The optimization algorithm is useful to tackle the disadvantages of clustering inconsistency when using the traditional approach. The distance measurements option is also provided in order to increase the quality of clustering results. The Fuzzy Geographically Weighted Clustering with nature inspired optimisation algorithm was firstly developed by Arie Wahyu Wijayanto and Ayu Purwarianti (2014) <doi:10.1109/CITSM.2014.7042178> using Artificial Bee Colony algorithm. |
| Authors: | Bahrul Ilmi Nasution [aut, cre], Robert Kurniawan [aut], Rezzy Eko Caraka [aut] |
| Maintainer: | Bahrul Ilmi Nasution <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2.1 |
| Built: | 2024-11-05 03:56:46 UTC |
| Source: | https://github.com/bmlmcmc/naspaclust |
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Artificial Bee Colony
abcfgwc( 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", nfood = 10, n.onlooker = 5, limit = 4, pso = F, abc.same = 10 )abcfgwc( 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", nfood = 10, n.onlooker = 5, limit = 4, pso = F, abc.same = 10 )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
nfood |
number of foods population. Can be defined as |
n.onlooker |
number of onlooker bees, Can be defined as |
limit |
number of turns to eliminate food with no solutions. Can be defined as |
pso |
whether to add PSO term in bee's movement. Either |
abc.same |
number of consecutive unchange to stop the iteration. Can be defined as |
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 Artificial Bee Colony (ABC) algorithm was developed by Karaboga and Basturk (2007) in order to get a more optimal solution of a certain complex function. FGWC using ABC has been implemented previously by Wijayanto and Purwarianti (2014) and Wijayanto et al. (2016).
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.
Karaboga D, Basturk B (2007).
“A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm.”
Journal of Global Optimization, 39(3), 459–471.
doi:10.1007/s10898-007-9149-x.
Mason GA, Jacobson RD (2007).
“Fuzzy Geographically Weighted Clustering.”
In Proceedings of the 9th International Conference on Geocomputation, 1-7.
Wijayanto AW, Purwarianti A (2014).
“Improvement design of fuzzy geo-demographic clustering using Artificial Bee Colony optimization.”
In 2014 International Conference on Cyber and IT Service Management (CITSM), 69–74.
ISBN 978-1-4799-7975-2.
Wijayanto AW, Purwarianti A, Son LH (2016).
“Fuzzy geographically weighted clustering using artificial bee colony: An efficient geo-demographic analysis algorithm and applications to the analysis of crime behavior in population.”
Applied Intelligence, 44(2), 377–398.
ISSN 0924-669X.
data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- abcfgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,nfood=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 ABC parameter abc_param <- c(vi.dist='normal',npar=5,pso=FALSE,same=15,n.onlooker=5,limit=5) ##FGWC with ABC optimization algorithm res2 <- fgwc(census2010,census2010pop,census2010dist,'abc',param_fgwc,abc_param)data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- abcfgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,nfood=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 ABC parameter abc_param <- c(vi.dist='normal',npar=5,pso=FALSE,same=15,n.onlooker=5,limit=5) ##FGWC with ABC optimization algorithm res2 <- fgwc(census2010,census2010pop,census2010dist,'abc',param_fgwc,abc_param)
A dataset containing the demographic characteristics of Indonesia on provincial level from BPS-Statistics Indonesia
census2010census2010
An object of class data.frame with 33 rows and 110 columns.
A data frame with 33 rows and 110 demographic characteristics.
The dataset was used in Wijayanto (2015), Wijayanto and Purwarianti (2014), Wijayanto and Purwarianti (2014) and Wijayanto et al. (2016).
The details of each variable can be seen in Wijayanto (2015),
Wijayanto AW (2015).
Improvement of fuzzy geo-demographic clustering using metaheuristic optimization on Indonesia population census.
Master's thesis, Insitut Teknologi Bandung.
Wijayanto AW, Purwarianti A (2014).
“Improvement of fuzzy geographically weighted clustering using particle swarm optimization.”
In 2014 International Conference on Information Technology Systems and Innovation (ICITSI), 7–12.
ISBN 978-1-4799-6527-4.
Wijayanto AW, Purwarianti A (2014).
“Improvement design of fuzzy geo-demographic clustering using Artificial Bee Colony optimization.”
In 2014 International Conference on Cyber and IT Service Management (CITSM), 69–74.
ISBN 978-1-4799-7975-2.
Wijayanto AW, Purwarianti A, Son LH (2016).
“Fuzzy geographically weighted clustering using artificial bee colony: An efficient geo-demographic analysis algorithm and applications to the analysis of crime behavior in population.”
Applied Intelligence, 44(2), 377–398.
ISSN 0924-669X.
A dataset containing the calculated distance between provinces in Indonesia.
census2010distcensus2010dist
An object of class matrix (inherits from array) with 33 rows and 33 columns.
A matrix with 33x33 rows.
The dataset was firstly used in Wijayanto (2015), Wijayanto and Purwarianti (2014), Wijayanto and Purwarianti (2014), and Wijayanto et al. (2016).
Wijayanto AW (2015).
Improvement of fuzzy geo-demographic clustering using metaheuristic optimization on Indonesia population census.
Master's thesis, Insitut Teknologi Bandung.
Wijayanto AW, Purwarianti A (2014).
“Improvement of fuzzy geographically weighted clustering using particle swarm optimization.”
In 2014 International Conference on Information Technology Systems and Innovation (ICITSI), 7–12.
ISBN 978-1-4799-6527-4.
Wijayanto AW, Purwarianti A (2014).
“Improvement design of fuzzy geo-demographic clustering using Artificial Bee Colony optimization.”
In 2014 International Conference on Cyber and IT Service Management (CITSM), 69–74.
ISBN 978-1-4799-7975-2.
Wijayanto AW, Purwarianti A, Son LH (2016).
“Fuzzy geographically weighted clustering using artificial bee colony: An efficient geo-demographic analysis algorithm and applications to the analysis of crime behavior in population.”
Applied Intelligence, 44(2), 377–398.
ISSN 0924-669X.
A dataset containing the 2010 population in Indonesia based on census result.
census2010popcensus2010pop
An object of class integer of length 33.
A vector with 33 elements.
The dataset was firstly used in Wijayanto (2015), Wijayanto and Purwarianti (2014), Wijayanto and Purwarianti (2014), and Wijayanto et al. (2016).
Wijayanto AW (2015).
Improvement of fuzzy geo-demographic clustering using metaheuristic optimization on Indonesia population census.
Master's thesis, Insitut Teknologi Bandung.
Wijayanto AW, Purwarianti A (2014).
“Improvement of fuzzy geographically weighted clustering using particle swarm optimization.”
In 2014 International Conference on Information Technology Systems and Innovation (ICITSI), 7–12.
ISBN 978-1-4799-6527-4.
Wijayanto AW, Purwarianti A (2014).
“Improvement design of fuzzy geo-demographic clustering using Artificial Bee Colony optimization.”
In 2014 International Conference on Cyber and IT Service Management (CITSM), 69–74.
ISBN 978-1-4799-7975-2.
Wijayanto AW, Purwarianti A, Son LH (2016).
“Fuzzy geographically weighted clustering using artificial bee colony: An efficient geo-demographic analysis algorithm and applications to the analysis of crime behavior in population.”
Applied Intelligence, 44(2), 377–398.
ISSN 0924-669X.
Fuzzy clustering with addition of spatial configuration of membership matrix
fgwc(data, pop, distmat, algorithm = "classic", fgwc_param, opt_param)fgwc(data, pop, distmat, algorithm = "classic", fgwc_param, opt_param)
data |
an object of data with d>1. Can be |
pop |
an n*1 vector contains population. |
distmat |
an n*n distance matrix between regions. |
algorithm |
algorithm used for FGWC |
fgwc_param |
a vector that consists of FGWC parameter (see |
opt_param |
a vector that consists of optimization algorithm parameter (see |
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 seven optimisation algorithms that currently provided in this package, mainly from the Yang (2014). The optimization algorithm uses the centroid as the parameter to be optimized. Here are the algorithm that can be used:
"classic" - The classical algorithm of FGWC based on Mason and Jacobson (2007) for centroid optimisation
and Runkler and Katz (2006) for membership optimization.
"abc" - Optimization using artificial bee colony algorithm based on Karaboga and Basturk (2007)
(see also Wijayanto and Purwarianti 2014 and Wijayanto et al. 2016 for FGWC implementation).
"fpa" - Optimization using flower pollination algorithm based on (Yang 2012).
"gsa" - Optimization using gravitational search algorithm based on Rashedi et al. (2009) and
Li and Dong (2017) (see also Pamungkas and Pramana 2019 for FGWC implementation).
"hho" - Optimization using harris-hawk optimization with "heidari" (Heidari et al. 2019) (default).
and "bairathi" (Bairathi and Gopalani 2018).
"ifa" - Optimization using intelligent firefly algorithm based on Yang (2009),
as well as the intelligent improvement by Fateen and Bonilla-Petriciolet (2013) (see also Nasution et al. 2020 for FGWC implementation).
"pso" - Optimization using particle swarm optimization based on Runkler and Katz (2006) and
Bansal et al. (2011) for inertia option (see also Wijayanto and Purwarianti 2014; Putra and Kurniawan 2017; Abdussamad 2020 for FGWC implementation).
"tlbo" - Optimization using teaching - learning based optimization based on Rao et al. (2012) and
elitism improvement by Rao and Patel (2012).
Furthermore, there are 10 distance that can be used to calculate the membership (see cdist for details).
the default parameter of FGWC (in case you do not want to tune anything) is
c(kind='u',ncluster=2,m=2,distance='euclidean',order=2,alpha=0.7,a=1,b=1,max.iter=500,error=1e-5,randomN=1).
There is also a universal parameter to the optimization algorithm as well as the details. The default parameter
for the optimization algorithm is c(vi.dist='uniform',npar=10,par.no=2,par.dist='euclidean',par.order=2,pso=TRUE,same=10,type='sim.annealing',ei.distr='normal',vmax=0.7,wmax=0.9,wmin=0.4,chaos=4,x0='F',map=0.7,ind=1,skew=0,sca=1)
If you do not define a certain parameter, the parameter will be set to its default 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.
Abdussamad S (2020).
“Evaluation of Implementation Context Based Clustering In Fuzzy Geographically Weighted Clustering-Particle Swarm Optimization Algorithm.”
Jurnal EECCIS, 14(1), 10–15.
ISSN 2460-8122, https://jurnaleeccis.ub.ac.id/index.php/eeccis/article/view/609.
Bairathi D, Gopalani D (2018).
“A Novel Swarm Intelligence Based Optimization Method: Harris' Hawk Optimization.”
In Advances in Intelligent Systems and Computing, 832–842.
Springer International Publishing.
doi:10.1007/978-3-030-16660-1_81.
Bansal JC, Singh PK, Saraswat M, Verma A, Jadon SS, Abraham A (2011).
“Inertia Weight strategies in Particle Swarm Optimization.”
In 2011 Third World Congress on Nature and Biologically Inspired Computing.
doi:10.1109/nabic.2011.6089659.
Fateen SK, Bonilla-Petriciolet A (2013).
“Intelligent Firefly Algorithm for Global Optimization.”
Cuckoo Search and Firefly Algorithm: Theory and Applications, 516, 315-330.
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019).
“Harris hawks optimization: Algorithm and applications.”
Future Generation Computer Systems, 97, 849–872.
doi:10.1016/j.future.2019.02.028.
Karaboga D, Basturk B (2007).
“A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm.”
Journal of Global Optimization, 39(3), 459–471.
doi:10.1007/s10898-007-9149-x.
Li J, Dong N (2017).
“Gravitational Search Algorithm with a New Technique.”
In 2017 13th International Conference on Computational Intelligence and Security (CIS), 516-519.
doi:10.1109/CIS.2017.00120.
Mason GA, Jacobson RD (2007).
“Fuzzy Geographically Weighted Clustering.”
In Proceedings of the 9th International Conference on Geocomputation, 1-7.
Nasution BI, Kurniawan R, Siagian TH, Fudholi A (2020).
“Revisiting social vulnerability analysis in Indonesia: An optimized spatial fuzzy clustering approach.”
International Journal of Disaster Risk Reduction, 51, 101801.
doi:10.1016/j.ijdrr.2020.101801.
Pamungkas IH, Pramana S (2019).
“Improvement Method of Fuzzy Geographically Weighted Clustering using Gravitational Search Algorithm.”
Journal of Computer Science and Information, 11(1).
Putra FH, Kurniawan R (2017).
“Clustering for Disaster Areas Endemic Dengue Hemorrhagic Fever Based on Factors had Caused in East Java Using Fuzzy Geographically Weighted Clustering - Particle Swarm Optimization.”
Jurnal Aplikasi Statistika & Komputasi Statistik, 8(01), 27.
ISSN 2615-1367.
Rao RV, Patel V (2012).
“An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems.”
International Journal of Industrial Engineering Computations, 3(4), 535–560.
ISSN 19232926, doi:10.5267/j.ijiec.2012.03.007.
Rao RV, Savsani VJ, Balic J (2012).
“Teaching\- learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems.”
Engineering Optimization, 44(12), 1447–1462.
doi:10.1080/0305215x.2011.652103.
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009).
“GSA: A Gravitational Search Algorithm.”
Information Sciences, 179(13).
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.
Wijayanto AW, Purwarianti A (2014).
“Improvement design of fuzzy geo-demographic clustering using Artificial Bee Colony optimization.”
In 2014 International Conference on Cyber and IT Service Management (CITSM), 69–74.
ISBN 978-1-4799-7975-2.
Wijayanto AW, Purwarianti A (2014).
“Improvement of fuzzy geographically weighted clustering using particle swarm optimization.”
In 2014 International Conference on Information Technology Systems and Innovation (ICITSI), 7–12.
ISBN 978-1-4799-6527-4.
Wijayanto AW, Purwarianti A, Son LH (2016).
“Fuzzy geographically weighted clustering using artificial bee colony: An efficient geo-demographic analysis algorithm and applications to the analysis of crime behavior in population.”
Applied Intelligence, 44(2), 377–398.
ISSN 0924-669X.
Yang X (2009).
“Firefly Algorithms for Multimodal Optimization.”
In Stochastic Algorithms: Foundations and Applications, 169–178.
Springer Berlin Heidelberg.
doi:10.1007/978-3-642-04944-6_14.
Yang X (2012).
“Flower Pollination Algorithm for Global Optimization.”
In Unconventional Computation and Natural Computation, 240–249.
Springer Berlin Heidelberg.
doi:10.1007/978-3-642-32894-7_27.
Yang X (2014).
Nature-Inspired Optimization Algorithms, Elsevier insights.
Elsevier Science.
ISBN 9780124167452.
fgwcuv, abcfgwc, fpafgwc,
gsafgwc, hhofgwc, ifafgwc, psofgwc, tlbofgwc
data('census2010') data('census2010dist') data('census2010pop') # 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) ## FGWC with classical algorithm res1 <- fgwc(census2010,census2010pop,census2010dist,'classic',param_fgwc,1) ## tune the ABC parameter abc_param <- c(vi.dist='normal',npar=5,pso=FALSE,same=15,n.onlooker=5,limit=5) ## FGWC with ABC optimization algorithm res2 <- fgwc(census2010,census2010pop,census2010dist,'abc',param_fgwc,abc_param)data('census2010') data('census2010dist') data('census2010pop') # 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) ## FGWC with classical algorithm res1 <- fgwc(census2010,census2010pop,census2010dist,'classic',param_fgwc,1) ## tune the ABC parameter abc_param <- c(vi.dist='normal',npar=5,pso=FALSE,same=15,n.onlooker=5,limit=5) ## FGWC with ABC optimization algorithm res2 <- fgwc(census2010,census2010pop,census2010dist,'abc',param_fgwc,abc_param)
Fuzzy clustering with addition of spatial configuration of membership matrix
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 )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 )
data |
an object of data with d>1. Can be |
pop |
an n*1 vector contains population. |
distmat |
an n*n distance matrix between regions. |
kind |
use |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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. |
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.
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.
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.
abcfgwc fpafgwc gsafgwc hhofgwc ifafgwc psofgwc tlbofgwc
data('census2010') data('census2010dist') data('census2010pop') res1 <- fgwcuv(census2010,census2010pop,census2010dist,'u',3,2,'euclidean',4)data('census2010') data('census2010dist') data('census2010pop') res1 <- fgwcuv(census2010,census2010pop,census2010dist,'u',3,2,'euclidean',4)
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Flower Pollination Algorithm
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 )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 )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
nflow |
number of flowers population. Can be defined as |
p |
switch probability between global and local pollination, Can be defined as |
gamma |
Step size scaling factor. Can be defined as |
lambda |
Levy flights index parameter between [0,2]. Can be defined as |
delta |
Levi flights shift. Can be defined as |
ei.distr |
distribution of random walk parameter. Can be defined as |
flow.same |
number of consecutive unchange to stop the iteration. Can be defined as |
r |
weight in logistic chaotic between [0,4]. Can be used when |
m.chaotic |
mapping parameter in kent chaotic between [0,1]. Can be used when |
skew |
Levy distribution skewness for random walk. Can be used when |
sca |
Levy distribution scale for random walk. Can be used when |
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.
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.
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)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)
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Gravitational Search Algorithm
gsafgwc( 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", npar = 10, par.no = 2, par.dist = "euclidean", par.order = 2, gsa.same = 10, G = 1, vmax = 0.7, new = F )gsafgwc( 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", npar = 10, par.no = 2, par.dist = "euclidean", par.order = 2, gsa.same = 10, G = 1, vmax = 0.7, new = F )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
npar |
number of particle. Can be defined as |
par.no |
The number of selected best particle. Can be defined as |
par.dist |
The distance between particles. Can be defined as |
par.order |
The minkowski order of the |
gsa.same |
number of consecutive unchange to stop the iteration. Can be defined as |
G |
initial gravitatioal constant, Can be defined as |
vmax |
maximum velocity to be tolerated. Can be defined as |
new |
Boolean that represents whether to use the new algorithm by Li and Dong (2017). Can be defined as |
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 Gravitational Search Algorithm was developed by Rashedi et al. (2009) and and the technique is also upgraded by Li and Dong (2017) in order to get a more optimal solution of a certain complex function. FGWC using GSA has been implemented previously by Pamungkas and Pramana (2019).
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.
Li J, Dong N (2017).
“Gravitational Search Algorithm with a New Technique.”
In 2017 13th International Conference on Computational Intelligence and Security (CIS), 516-519.
doi:10.1109/CIS.2017.00120.
Pamungkas IH, Pramana S (2019).
“Improvement Method of Fuzzy Geographically Weighted Clustering using Gravitational Search Algorithm.”
Journal of Computer Science and Information, 11(1).
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009).
“GSA: A Gravitational Search Algorithm.”
Information Sciences, 179(13).
data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- gsafgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,npar=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 GSA parameter gsa_param <- c(vi.dist='normal',npar=5,same=15,G=1,vmax=0.7,new=FALSE) ##FGWC with GSA res2 <- fgwc(census2010,census2010pop,census2010dist,'gsa',param_fgwc,gsa_param)data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- gsafgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,npar=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 GSA parameter gsa_param <- c(vi.dist='normal',npar=5,same=15,G=1,vmax=0.7,new=FALSE) ##FGWC with GSA res2 <- fgwc(census2010,census2010pop,census2010dist,'gsa',param_fgwc,gsa_param)
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Harris-Hawk Algorithm.
hhofgwc( 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", nhh = 10, hh.alg = "heidari", A = c(2, 1, 0.5), p = 0.5, hh.same = 10, levy.beta = 1.5, update.type = 5 )hhofgwc( 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", nhh = 10, hh.alg = "heidari", A = c(2, 1, 0.5), p = 0.5, hh.same = 10, levy.beta = 1.5, update.type = 5 )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
nhh |
number of harris-hawk eagles. Can be defined as |
hh.alg |
String between default is |
A |
a 3 vectors which represents initial energy and cut-off for exploitation and exploration. In |
p |
a real number between 0 and 1. The eagle's movement probability |
hh.same |
number of consecutive unchange to stop the iteration. Can be defined as |
levy.beta |
The skewness of levy flight. Can be defined as |
update.type |
An integer. The type of energy |
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 Harris-Hawk Optimization was developed by Bairathi and Gopalani (2018) and the technique is also upgraded by Heidari et al. (2019) by adding progressive rapid dives in order to get a more optimal solution of a certain complex function.
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.
Bairathi D, Gopalani D (2018).
“A Novel Swarm Intelligence Based Optimization Method: Harris' Hawk Optimization.”
In Advances in Intelligent Systems and Computing, 832–842.
Springer International Publishing.
doi:10.1007/978-3-030-16660-1_81.
Heidari AA, Mirjalili S, Faris H, Aljarah I, Mafarja M, Chen H (2019).
“Harris hawks optimization: Algorithm and applications.”
Future Generation Computer Systems, 97, 849–872.
doi:10.1016/j.future.2019.02.028.
Mason GA, Jacobson RD (2007).
“Fuzzy Geographically Weighted Clustering.”
In Proceedings of the 9th International Conference on Geocomputation, 1-7.
data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- hhofgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,nhh=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 HHO parameter hho_param <- c(vi.dist='normal',npar=5,same=15,algo='bairathi',a1=3,a2=1,a3=0.4) ##FGWC with HHO res2 <- fgwc(census2010,census2010pop,census2010dist,'hho',param_fgwc,hho_param)data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- hhofgwc(census2010,census2010pop,census2010dist,3,2,'euclidean',4,nhh=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 HHO parameter hho_param <- c(vi.dist='normal',npar=5,same=15,algo='bairathi',a1=3,a2=1,a3=0.4) ##FGWC with HHO res2 <- fgwc(census2010,census2010pop,census2010dist,'hho',param_fgwc,hho_param)
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using (Intelligent) Firefly Algorithm.
ifafgwc( 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", ei.distr = "normal", fa.same = 10, nfly = 10, ffly.no = 2, ffly.dist = "euclidean", ffly.order = 2, gamma = 1, ffly.beta = 1, ffly.alpha = 1, r.chaotic = 4, m.chaotic = 0.7, ind.levy = 1, skew.levy = 0, scale.levy = 1, ffly.alpha.type = 4 )ifafgwc( 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", ei.distr = "normal", fa.same = 10, nfly = 10, ffly.no = 2, ffly.dist = "euclidean", ffly.order = 2, gamma = 1, ffly.beta = 1, ffly.alpha = 1, r.chaotic = 4, m.chaotic = 0.7, ind.levy = 1, skew.levy = 0, scale.levy = 1, ffly.alpha.type = 4 )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
ei.distr |
distribution of random walk parameter. Can be defined as |
fa.same |
number of consecutive unchange to stop the iteration. Can be defined as |
nfly |
number of fireflies. Can be defined as |
ffly.no |
The number of selected best fireflies for intelligent firefly algorithm. Can be defined as |
ffly.dist |
The distance between fireflies. Can be defined as |
ffly.order |
The minkowski order of the |
gamma |
distance scaling factor. Can be defined as |
ffly.beta |
Attractiveness constant. Can be defined as |
ffly.alpha |
Randomisation constant. Can be defined as |
r.chaotic |
weight in logistic chaotic between [0,4]. Can be used when |
m.chaotic |
mapping parameter in kent chaotic between [0,1]. Can be used when |
ind.levy |
Levy distribution index for random walk. Can be used when |
skew.levy |
Levy distribution skewness for random walk. Can be used when |
scale.levy |
Levy distribution scale for random walk. Can be used when |
ffly.alpha.type |
An integer. The type of |
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 Firefly Algorithm was developed by Yang (2009) and the technique is also upgraded by Fateen and Bonilla-Petriciolet (2013) by adding the intelligent phase (choosing the best firefly based on the intensity) in order to get a more optimal solution of a certain complex function. FGWC using IFA has been implemented previously by Nasution et al. (2020).
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.
Fateen SK, Bonilla-Petriciolet A (2013).
“Intelligent Firefly Algorithm for Global Optimization.”
Cuckoo Search and Firefly Algorithm: Theory and Applications, 516, 315-330.
Mason GA, Jacobson RD (2007).
“Fuzzy Geographically Weighted Clustering.”
In Proceedings of the 9th International Conference on Geocomputation, 1-7.
Nasution BI, Kurniawan R, Siagian TH, Fudholi A (2020).
“Revisiting social vulnerability analysis in Indonesia: An optimized spatial fuzzy clustering approach.”
International Journal of Disaster Risk Reduction, 51, 101801.
doi:10.1016/j.ijdrr.2020.101801.
Yang X (2009).
“Firefly Algorithms for Multimodal Optimization.”
In Stochastic Algorithms: Foundations and Applications, 169–178.
Springer Berlin Heidelberg.
doi:10.1007/978-3-642-04944-6_14.
data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- ifafgwc(census2010,census2010pop,census2010dist,3,2,'minkowski',4,nfly=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 IFA parameter ifa_param <- c(vi.dist='uniform', ei.distr='logchaotic', fa.same=10, npar=15, par.no=3, par.dist='minkowski', par.order=4, gamma=1, beta=1.5, alpha=1, chaos=4,update_type=4) ##FGWC with IFA res2 <- fgwc(census2010,census2010pop,census2010dist,'ifa',param_fgwc,ifa_param)data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- ifafgwc(census2010,census2010pop,census2010dist,3,2,'minkowski',4,nfly=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 IFA parameter ifa_param <- c(vi.dist='uniform', ei.distr='logchaotic', fa.same=10, npar=15, par.no=3, par.dist='minkowski', par.order=4, gamma=1, beta=1.5, alpha=1, chaos=4,update_type=4) ##FGWC with IFA res2 <- fgwc(census2010,census2010pop,census2010dist,'ifa',param_fgwc,ifa_param)
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Particle Swarm Algorithm.
psofgwc( 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", npar = 10, vmax = 0.7, pso.same = 10, c1 = 0.49, c2 = 0.49, w.inert = "sim.annealing", wmax = 0.9, wmin = 0.4, map = 0.4 )psofgwc( 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", npar = 10, vmax = 0.7, pso.same = 10, c1 = 0.49, c2 = 0.49, w.inert = "sim.annealing", wmax = 0.9, wmin = 0.4, map = 0.4 )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
npar |
number of particles. Can be defined as |
vmax |
maximum velocity to be tolerated. Can be defined as |
pso.same |
number of consecutive unchange to stop the iteration. Can be defined as |
c1 |
Cognitive scaling parameters. Can be defined as |
c2 |
Social scaling parameters. Can be defined as |
w.inert |
The inertia weight update method between |
wmax |
Maximum inertia weight. Can be defined as |
wmin |
Minimum inertia weight. Can be defined as |
map |
Chaotic mapping parameter. Userful when |
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 Particle Swarm Optimization was developed by Kennedy and Eberhart (1995) in order to get a more optimal solution of a certain complex function. PSO was also improved by Bansal et al. (2011) by modifying the inertia weight. FGWC using PSO has been implemented previously by some studies (Wijayanto and Purwarianti 2014; Putra and Kurniawan 2017; Abdussamad 2020).
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.
Abdussamad S (2020).
“Evaluation of Implementation Context Based Clustering In Fuzzy Geographically Weighted Clustering-Particle Swarm Optimization Algorithm.”
Jurnal EECCIS, 14(1), 10–15.
ISSN 2460-8122, https://jurnaleeccis.ub.ac.id/index.php/eeccis/article/view/609.
Bansal JC, Singh PK, Saraswat M, Verma A, Jadon SS, Abraham A (2011).
“Inertia Weight strategies in Particle Swarm Optimization.”
In 2011 Third World Congress on Nature and Biologically Inspired Computing.
doi:10.1109/nabic.2011.6089659.
Kennedy J, Eberhart R (1995).
“Particle swarm optimization.”
In Proceedings of ICNN'95 - International Conference on Neural Networks, volume 4, 1942-1948 vol.4.
doi:10.1109/ICNN.1995.488968.
Mason GA, Jacobson RD (2007).
“Fuzzy Geographically Weighted Clustering.”
In Proceedings of the 9th International Conference on Geocomputation, 1-7.
Putra FH, Kurniawan R (2017).
“Clustering for Disaster Areas Endemic Dengue Hemorrhagic Fever Based on Factors had Caused in East Java Using Fuzzy Geographically Weighted Clustering - Particle Swarm Optimization.”
Jurnal Aplikasi Statistika & Komputasi Statistik, 8(01), 27.
ISSN 2615-1367.
Wijayanto AW, Purwarianti A (2014).
“Improvement of fuzzy geographically weighted clustering using particle swarm optimization.”
In 2014 International Conference on Information Technology Systems and Innovation (ICITSI), 7–12.
ISBN 978-1-4799-6527-4.
data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- psofgwc(census2010,census2010pop,census2010dist,3,2,'minkowski',4,npar=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 PSO parameter pso_param <- c(vi.dist='uniform',npar=15, vmax=0.8, pso.same=10, c1=0.7, c2=0.6, type='chaotic', wmax=0.8,wmin=0.3,map=0.3) ##FGWC with PSO res2 <- fgwc(census2010,census2010pop,census2010dist,'pso',param_fgwc,pso_param)data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- psofgwc(census2010,census2010pop,census2010dist,3,2,'minkowski',4,npar=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 PSO parameter pso_param <- c(vi.dist='uniform',npar=15, vmax=0.8, pso.same=10, c1=0.7, c2=0.6, type='chaotic', wmax=0.8,wmin=0.3,map=0.3) ##FGWC with PSO res2 <- fgwc(census2010,census2010pop,census2010dist,'pso',param_fgwc,pso_param)
Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Teaching - Learning Based Algorithm.
tlbofgwc( 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", nstud = 10, tlbo.same = 10, nselection = 10, elitism = F, n.elite = 2 )tlbofgwc( 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", nstud = 10, tlbo.same = 10, nselection = 10, elitism = F, n.elite = 2 )
data |
an object of data with d>1. Can be |
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 |
order |
minkowski order. default is 2. |
alpha |
the old membership effect with [0,1], if |
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 |
nstud |
number of students. Can be defined as |
tlbo.same |
number of consecutive unchange to stop the iteration. Can be defined as |
nselection |
number of teachers based on selected students. Can be defined as |
elitism |
wheter to use elitism algorithm or not. Either |
n.elite |
Number of elitist students. Can be defined as |
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 Teaching - Learning Based Optimization was developed by Rao et al. (2012) and Developed by Rao and Patel (2012) by adding the elitism algorithm in order to get a more optimal solution of a certain complex function.
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.
Mason GA, Jacobson RD (2007).
“Fuzzy Geographically Weighted Clustering.”
In Proceedings of the 9th International Conference on Geocomputation, 1-7.
Rao RV, Patel V (2012).
“An elitist teaching-learning-based optimization algorithm for solving complex constrained optimization problems.”
International Journal of Industrial Engineering Computations, 3(4), 535–560.
ISSN 19232926, doi:10.5267/j.ijiec.2012.03.007.
Rao RV, Savsani VJ, Balic J (2012).
“Teaching\- learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems.”
Engineering Optimization, 44(12), 1447–1462.
doi:10.1080/0305215x.2011.652103.
data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- tlbofgwc(census2010,census2010pop,census2010dist,3,2,'minkowski',4,nstud=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 TLBO parameter tlbo_param <- c(vi.dist="uniform",nstud=10, tlbo.same=10, nselection=10,elitism=FALSE,n.elite=2) ##FGWC with TLBO res2 <- fgwc(census2010,census2010pop,census2010dist,'tlbo',param_fgwc,tlbo_param)data('census2010') data('census2010dist') data('census2010pop') # First way res1 <- tlbofgwc(census2010,census2010pop,census2010dist,3,2,'minkowski',4,nstud=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 TLBO parameter tlbo_param <- c(vi.dist="uniform",nstud=10, tlbo.same=10, nselection=10,elitism=FALSE,n.elite=2) ##FGWC with TLBO res2 <- fgwc(census2010,census2010pop,census2010dist,'tlbo',param_fgwc,tlbo_param)