Revisiting Cluster Vulnerabilities towards Information and Communication Technologies in the Eastern Island of Indonesia Using Fuzzy C Means
Abstract
:1. Introduction
2. Methods
2.1. Clustering
 Euclidean distance:
 ${d}_{AB}$ = distance between cluster objects,
 p = many measurement variables,
 ${x}_{Aj}$ = observation of objectA; variablesj,
 ${x}_{Bj}$ = observation of objectB; variablesj.
 Manhattan distance:
 The Chebychev distance is the difference in the maximum absolute value of each variable:
 Pearson correlation distance:
 Eisen cosine correlation distance:
 Spearman correlation distance:
 Kendall correlation distance:
 ${n}_{c}$: total number of concordant pairs.
 ${n}_{d}$: total number of discordant pairs.
 $n$: size of $x$ and $y$.
2.2. Fuzzy C Means
2.3. Conventional Set (Crisp)
 $x$ is not a member of $A$, if ${U}_{A}\left(x\right)$ = 0
 $x$ member of A with low membership degree, if ${U}_{A}\left(x\right)\approx 0$
 $x$ member of A with high membership degree, if ${U}_{A}\left(x\right)\approx 1$
 $x$ member of A, if ${U}_{A}\left(x\right)=1$.
Algorithm 1 
Step 1: Determine the data to be $X$ clustered, in the form of a matrix of size $n\times p$ ($n=$ data sample size, p = variable for each data). ${X}_{ij}$ is the $i$th sample data $\left(i=1,2,\dots ,n\right)$ and the $j$th variable $\left(j=1,2,\dots ,p\right)$ 
Step 2: Determine: Number of clusters $=c$ Weighting power $=m$ Expected smallest error $=\xi $ Initial objective function $={P}_{o}=0$ 
Step 3: Generate random numbers ${\mu}_{ik},i=1,2,\dots ,n;k=1,2,3,\dots ,c$ 
Step 4: Calculate the $k$th cluster center $\left({v}_{kj}\right),$ with $k=1,2,\dots ,c;$ and $j=1,2,\dots ,p$ ${v}_{kj}=\frac{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mu}_{ik}\right)}^{m}{x}_{ij}}{{{\displaystyle \sum}}_{i=1}^{n}{\left({\mu}_{ik}\right)}^{m}}$ 
Step 5: Update fuzzy membership value ${\mu}_{ik}^{\left(t+1\right)}={\left[\frac{{\left[{{\displaystyle \sum}}_{j=1}^{p}{\left({x}_{ij}{v}_{kj}\right)}^{2}\right]}^{\frac{1}{m1}}}{{{\displaystyle \sum}}_{k=1}^{c}{\left[{{\displaystyle \sum}}_{j=1}^{p}{\left({x}_{ij}{v}_{kj}\right)}^{2}\right]}^{\frac{1}{m1}}}\right]}^{1}$ 
Step 6: Calculating the objective function in the $t$th iteration ${P}_{t}={\displaystyle {\displaystyle \sum}_{i1}^{n}}{\displaystyle {\displaystyle \sum}_{k=1}^{c}}{\left({\mu}_{ik}\right)}^{m}\left[{\displaystyle {\displaystyle \sum}_{j=1}^{p}}{\left({x}_{ij}{v}_{kj}\right)}^{2}\right]$ 
Step 7: Checking the stop condition (convergent) with condition below:

Step 8: Finish 
3. Results and Discussion
3.1. Bibliography towards Information and Communication Technologies Vulnerability
3.2. Initial Diagnostic
3.3. Spatial Fuzzy C Means Clustering
3.4. Future Work toward ICT Expansion Based on an Existing Plan
4. Conclusions
Author Contributions
Funding
Ethical Statement
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Variable  Description  Source 

use_cellph  % of population who use cell phones  SUSENAS 
have_cellph  % of population who own a cell phone  
use_pc  % of population who use a PC  
acc_int  % of population who access the internet  
saving  % of population who have savings  
edu  % of population who recent graduation in junior high and below  
course  % of working population who attended training  SAKERNAS 
no_empl_14  % of population who own a micro business  
digitech1  % of population who use computers to work  
digitech2  % of population who use smartphones to work  
digitech3  % of population who use other digital technologies to work  
jobint_use1  % of population who use the internet for communication  
jobint_use2  % of population who use the internet for promotion  
jobint_use3  % of population who use the internet to sell via email/social media  
jobint_use4  % of population who use the internet to sell via ecommerce 
Variable  Min  1st Qu.  Median  Mean  3rd Qu.  Max 

use_cellph  24.03  82.87  90.62  87.99  97.74  100 
have_cellph  0  70.80  81.86  79.30  90.24  100 
use_pc  0  4.86  13.61  15.75  23.06  62.60 
acc_int  0  15.15  25.58  26.60  35.66  77.42 
saving  3.49  24.05  33.21  35.48  46.05  85.00 
edu  0  33.46  47.97  49.80  65.48  100 
course  0  82.33  89.82  87.55  96.80  100 
no_empl_14  0  76.92  84.04  80.59  91.22  100 
digitech1  0  2.90  8.49  12.70  17.97  100 
digitech2  0  23.54  34.76  38.22  53.33  100 
digitech3  0  11.20  19.94  24.08  35.15  100 
jobint_use1  0  9.20  18.34  23.44  35.52  100 
jobint_use2  0  0  8.90  11.24  17.07  100 
jobint_use3  0  0  7.61  10.84  17.28  49.92 
jobint_use4  0  0  0  2.98  3.51  32.47 
n Cluster  Fuzzy Silhouette Index (SI)  Partitiony Entropy (PE)  Partition Coefficient (PC)  Modified Partition Coefficient (MPC) 

2  0.5264  0.5699  0.6135  0.2270 
3  0.2175  0.9653  0.4158  0.1238 
4  0.1321  1.2527  0.3151  0.0868 
5  0.1345  1.4750  0.2535  0.0669 
6  0.0859  1.6544  0.2125  0.0550 
Centroid  Cluster 1  Cluster 2 

use_cellph  86.4039  90.5869 
have_cellph  76.8411  83.2404 
use_pc  11.4294  21.9411 
acc_int  21.3440  34.3597 
saving  29.5173  43.5743 
edu  40.9851  61.5661 
course  90.3803  83.4344 
no_empl_14  83.3196  77.6748 
digitech1  7.2430  20.4872 
digitech2  28.6493  52.2365 
digitech3  17.6596  33.2556 
jobint_use1  14.7200  36.5879 
jobint_use2  7.0391  17.2886 
jobint_use3  6.7720  17.2540 
jobint_use4  1.6964  5.0362 
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Anggoro, F.; Caraka, R.E.; Prasetyo, F.A.; Ramadhani, M.; Gio, P.U.; Chen, R.C.; Pardamean, B. Revisiting Cluster Vulnerabilities towards Information and Communication Technologies in the Eastern Island of Indonesia Using Fuzzy C Means. Sustainability 2022, 14, 3428. https://doi.org/10.3390/su14063428
Anggoro F, Caraka RE, Prasetyo FA, Ramadhani M, Gio PU, Chen RC, Pardamean B. Revisiting Cluster Vulnerabilities towards Information and Communication Technologies in the Eastern Island of Indonesia Using Fuzzy C Means. Sustainability. 2022; 14(6):3428. https://doi.org/10.3390/su14063428
Chicago/Turabian StyleAnggoro, Faisal, Rezzy Eko Caraka, Fajar Agung Prasetyo, Muthia Ramadhani, Prana Ugiana Gio, RungChing Chen, and Bens Pardamean. 2022. "Revisiting Cluster Vulnerabilities towards Information and Communication Technologies in the Eastern Island of Indonesia Using Fuzzy C Means" Sustainability 14, no. 6: 3428. https://doi.org/10.3390/su14063428