| fgwc {naspaclust} | R Documentation |
Fuzzy Geographicaly Weighted Clustering
Description
Fuzzy clustering with addition of spatial configuration of membership matrix
Usage
fgwc(data, pop, distmat, algorithm = "classic", fgwc_param, opt_param)
Arguments
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 |
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 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
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
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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/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, https://doi.org/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 (2014).
Nature-Inspired Optimization Algorithms, Elsevier insights.
Elsevier Science.
ISBN 9780124167452.
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, https://doi.org/10.1007/978-3-642-32894-7_27.
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, https://doi.org/10.1007/978-3-642-04944-6_14.
See Also
fgwcuv, abcfgwc, fpafgwc,
gsafgwc, hhofgwc, ifafgwc, psofgwc, tlbofgwc
Examples
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)