Fuzzy Geographicaly Weighted Clustering with Artificial Bee Colony Optimization

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Artificial Bee Colony

Usage

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
)

Arguments

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 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).

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

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.

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.

See Also

fpafgwc gsafgwc

Examples

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) 

Indonesia 2010 Provincial Census data

Description

A dataset containing the demographic characteristics of Indonesia on provincial level from BPS-Statistics Indonesia

Usage

census2010

Format

An object of class data.frame with 33 rows and 110 columns.

Details

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),

References

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.

Indonesia Provincial Matrix Distance

Description

A dataset containing the calculated distance between provinces in Indonesia.

Usage

census2010dist

Format

An object of class matrix (inherits from array) with 33 rows and 33 columns.

Details

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).

References

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.

Indonesia 2010 Population

Description

A dataset containing the 2010 population in Indonesia based on census result.

Usage

census2010pop

Format

An object of class integer of length 33.

Details

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).

References

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 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

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 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

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) 

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

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)

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

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)

Fuzzy Geographicaly Weighted Clustering with Gravitational Search Algorithm

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Gravitational Search Algorithm

Usage

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
)

Arguments

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 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).

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

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.

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).

See Also

fpafgwc gsafgwc

Examples

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 Geographicaly Weighted Clustering with Harris-Hawk Optimization

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Harris-Hawk Algorithm.

Usage

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
)

Arguments

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 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.

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

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.

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.

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

See Also

fpafgwc gsafgwc

Examples

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 Geographicaly Weighted Clustering with (Intelligent) Firefly Algorithm

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using (Intelligent) Firefly Algorithm.

Usage

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
)

Arguments

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 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).

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

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, https://doi.org/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, https://doi.org/10.1007/978-3-642-04944-6_14.

See Also

fpafgwc gsafgwc

Examples

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 Geographicaly Weighted Clustering with Particle Swarm Optimization

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Particle Swarm Algorithm.

Usage

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
)

Arguments

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 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).

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

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.

Kennedy J, Eberhart R (1995). “Particle swarm optimization.” In Proceedings of ICNN'95 - International Conference on Neural Networks, volume 4, 1942–1948. doi: 10.1109/ICNN.1995.488968, https://doi.org/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.

See Also

fpafgwc gsafgwc

Examples

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 Geographicaly Weighted Clustering with Teaching - Learning Based Optimization

Description

Fuzzy clustering with addition of spatial configuration of membership matrix with centroid optimization using Teaching - Learning Based Algorithm.

Usage

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
)

Arguments

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 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.

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.

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.

See Also

fpafgwc gsafgwc

Examples

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)