sus ainabili y
A icle
Challenge o Planning by Using Clus e
Me hodology: The Case S udy o he Alga e Region
Da id Bien enido-Hue as 1,* , Fá ima Fa inha 2, Miguel JoséOli ei a 2, Elisa M. J. Sil a 2
and Rui Lança 2
1Depa men o Building Cons uc ion II, Uni e si y o Se ille, A . Reina Me cedes 4A, 41012 Se ille, Spain
2Uni e si y o Alga e, Ins i u e o Enginee ing, Campus da Penha, 8005-139 Fa o, Po ugal;
[email p o ec ed] (F.F.); [email p o ec ed] (M.J.O.); [email p o ec ed] (E.M.J.S.); [email p o ec ed] (R.L.)
*Co espondence: [email p o ec ed]
Recei ed: 31 Janua y 2020; Accep ed: 17 Feb ua y 2020; Published: 18 Feb ua y 2020


Abs ac :
This s udy analyses he mos app op ia e me hodology o make simila i y classi ica ions
among he ci ies o he Alga e (Po ugal) acco ding o 105 sus ainabili y indica o s moni o ed wi h
he Obse a o y o Sus ainabili y o he Alga e Region o Tou ism (OBSERVE). The me hodology
used o es ablish he simila i ies was he clus e analysis wi h 4 di e en app oaches which educed
he dimensions o he da a se : o al app oach, pilla app oach, subjec a ea app oach, and indica o
app oach. By combining he app oaches, a o al o 620 di e en clus e analyses we e pe o med. The
esul s e lec ed ha he da a analysis app oaches wi h less dimensions we e hose ha pe o med he
bes g oups among ci ies. In his sense, he app oaches wi h a high numbe o indica o s (e.g., he o al
o he pilla app oach) we e cha ac e ised by misclassi ying ci ies in mo e han 30% o he indica o s.
Thus, he mos accep able clus e analysis app oach was ha wi h a low numbe o indica o s.
Th ough his app oach, i was possible o make co ec g oups o he sus ainabili y le el o he ci ies o
he Alga e. These esul s p o ided an app op ia e me hodology o he decision-making ega ding
he sus ainabili y o a egion and could be ex apola ed o o he egions o assess sus ainabili y o
en i onmen al indica o s.
Keywo ds:
clus e analysis; sus ainabili y indica o s; he Alga e egion; OBSERVE pla o m;
sus ainable ou ism
1. In oduc ion
1.1. Tou ism and Sus ainabili y Indica o s
The sus ainable de elopmen o socie ies is an impo an issue belonging o he go e nmen al
policy o achie e a mo e sus ainable de elopmen . In his ega d, one o he ac i i ies o he ci ies which
signi ican ly in luences hei sus ainabili y le el is hei ou is ac i i y [
1
–
3
]. This ac i i y simila ly
in luences as o he ac i i ies do, such as u ban, ag icul u al o ma i ime [
4
–
6
], due o he impac o he
ou is ac i i y o ci ies in hei social, economic and en i onmen al dimensions. A posi i e and clea
aspec o such ac i i ies is he imp o emen o employabili y in a egion by gene a ing job posi ions,
al hough some nega i e aspec s such as he al e a ion o li es yles, damage in he he i age o he
al e a ion o ecosys ems could be a sign o he unsus ainable impac o he ac i i y in a egion [
7
]. In
addi ion, ou is ac i i ies a ec he sus ainabili y o o he sec o s, such as in as uc u es [
8
]. Wi hou
an adequa e con ol, he expansion o he ou ism ma ke will inc ease he p essu e on he ecosys ems
on which he li elihood o local communi ies depends [
7
]. The e o e, ou is o e s in egions o
ci ies should be managed in a b oade sus ainabili y con ex [
9
], also gua an eeing he economic
ad ancemen o such ac i i ies [
10
]. Imp o ing he sus ainabili y usually also leads o an imp o emen
o compe i i eness [11,12].
Sus ainabili y 2020,12, 1536; doi:10.3390/su12041536 www.mdpi.com/jou nal/sus ainabili y
Sus ainabili y 2020,12, 1536 2 o 16
The e o e, i is necessa y o con ol he sus ainabili y o he ou is ac i i y o a egion, hus
making possible o gua an ee ha he ou is o e could con ibu e o he economy o he egion
wi hou a ec ing i s inhabi an s. Fo his pu pose, he moni o ing o sus ainabili y indica o s allows
he e olu ion o a egion o be de e mined and, in his way, app op ia e policies o be es ablished
owa ds a mo e sus ainable ou ism [
13
,
14
]. Sus ainabili y indica o s a e unde s ood as hose ools
con ibu ing o he analysis and assessmen o he in o ma ion so ha manage s could make igh
decisions [
15
]. As gene al c i e ion, sus ainabili y indica o s should be quan i a i e o be assessed [
16
].
Howe e , he e a e no de ined c i e ia abou which such indica o s should be, hus a ying among
di e en esea ch s udies [
17
]. Some examples a e as ollows: (i) Mille [
18
] es ablished 9 indica o s
o sus ainable ou ism h ough a Delphi su ey o ou ism esea che s; (ii) Liu e al. [
19
] conside ed
20 indica o s acco ding o he pa ies in e es ed: ou is s, local esiden s, go e nmen al agencies,
and business owne s; (iii) Blancas e al. [
20
] used a se o 32 indica o s o assess he sus ainabili y
o coas al ou is des ina ions based on 3 dimensions: social, economic, and en i onmen al. In a
subsequen s udy [
21
], hese au ho s conside ed a se o 89 indica o s o assess he sus ainable ou ism
based on he same dimensions (social, economic, and en i onmen al); (i ) Nes ic
ò
and Maselli [
22
]
es ablished a se o 23 indica o s o he economic e alua ion o ou ism p ojec s in he islands; and
( ) Cas ellani and Sala [
23
] used 20 indica o s conce ned wi h: ou ism cha ac e is ics o he egion
unde in es iga ion; en i onmen al ac o s; economic and social condi ions o local communi ies; and
demog aphic dynamics.
In any case, he use o a se o indica o s will allow he beha iou o di e en aspec s o ou ism o
be e alua ed in he di e en egions o each s udy. Th ough his e alua ion, he necessa y co ec i e
policies may be es ablished by he go e nmen o he egion.
1.2. Da a Analysis o Sus ainabili y Indica o s
To es ablish co ec i e measu es, an essen ial aspec is he ea men o he compiled in o ma ion
o he moni o ed indica o s [
24
]. Some o hese analyses a e based on spa ial dis ibu ion h ough
maps o he sus ainabili y o a egion. In his ega d, H
é
ly and An oni [
25
] de eloped a g id analysis
map o he Besançon egion (F ance) om which he s eng hs and weaknesses o he e i o y can
be iden i ied in e ms o sus ainabili y. In ano he simila s udy, Palmisano e al. [
26
] analysed he
spa ial dis ibu ion o a se o u al sus ainabili y indica o s o es ablish a common Ru al Sus ainable
De elopmen s a egy o alloca e he Eu opean Ag icul u al Fund o Ru al De elopmen Budge .
Th ough hese indica o analyses, decisions could be es ablished using di e en me hods, such as
decision-making ma ix [27] and uzzy logic [28].
Howe e , he analysis o sus ainabili y indica o s could be complex when a ious ypologies a e
analysed. In his sense, many s udies ha e e alua ed he possibili y o conduc ing a clus e analysis.
A clus e analysis is a mul i a ian s a is ical echnique which allows a se o objec s o be classi ied
in a way ha , on he one hand, simila objec s a e in he same conglome a ion and, on he o he
hand, di e en objec s a e in se e al g oups, esul ing in a ious homogeneous g oups among hem.
Thus, his analysis has been used in p e ious esea ch s udies o make g oups be ween indica o s: (i)
Akande e al. [
29
] classi ied 32 indica o s o he Sma le el and o sus ainabili y o Eu opean ci ies
in 5 componen s h ough hie a chical clus e ing; (ii) Yi e al. [
30
] assessed he sus ainabili y o he 17
ci ies o he a ea o Shandong (China). Fo his pu pose, hey used 21 indica o s o en i onmen al,
social, and economic dimensions and classi ied he 17 ci ies in 4 g oups h ough he a e age alues and
g ow h alues; (iii) Dang e al. [
31
] applied a classi ica ion analysis o he indica o s included in he
ce i ica ions o China’s new Assessmen S anda d o G een Eco-dis ic s (ASGE) and o Leade ship in
Ene gy and En i onmen al Design o Neighbou hood De elopmen (LEED-ND). To do his, au ho s
used
k
-means o make g oups; and (i ) Ne i e al. [
32
] conduc ed clus e analyses in an indica o
amewo k o inpu -s a e-ou pu o g oup 83 coun ies acco ding o hei sus ainabili y. A o al o
3 indica o s ( he eme gency low pe capi a, he Gini index o income dis ibu ion and he G oss
Domes ic P oduc pe Capi a (GDP)) and he k-median algo i hm we e used o he analysis. Howe e ,
Sus ainabili y 2020,12, 1536 3 o 16
mo e esea ch s udies analysing new me hodologies a e equi ed o assess he sus ainable ou ism
wi h he aim o educe cu en exis ing limi a ions [
33
]. Assessmen me hodologies o egions a e
included in such new me hodologies. P e ious esea ch s udies did no analyse he limi a ions o
g oup echniques when he a ious moni o ed indica o s a e indi idually analysed. Addi ionally,
he e a e ew esea ch wo ks analysing a b oad sample o sus ainabili y indica o s.
1.3. Aim o This S udy
Fo his eason, his s udy makes di e en me hodologies o g oup he ci ies o a egion based on
hei sus ainabili y indica o s. In his way, he s a egical decision-making o local go e nmen s a e
con ibu ed o be in acco dance wi h he Uni ed Na ions Sus ainable De elopmen Goals [
34
]. This
s udy he e o e aims o analyse he mos app op ia e me hodology o make simila i y classi ica ions
among ci ies o a egion acco ding o sus ainabili y indica o s. Fo his pu pose, he case s udy used is
he Alga e egion due o he impo ance o ou ism in he egion [
35
]. The sus ainabili y indica o s in
he egion a e moni o ed h ough he Obse a o y o Sus ainabili y o he Alga e Region o Tou ism
(OBSERVE) pla o m [
36
]. Based on he da a compiled by OBSERVE in 105 sus ainabili y indica o s
be ween 2011 and 2015, his s udy conduc s di e en me hodological clus e analysis app oaches.
The esul s de e mined he mos app op ia e me hodological app oach o g oup he 105 indica o s
app op ia ely and gua an eed consis en classi ica ions o he ci ies o es ablish app op ia e policies in
each indica o . Thus, he esul s o his s udy also analysed he possibili ies o de e mining simila i ies
among ci ies when analysing a la ge numbe o sus ainabili y indica o s.
2. Me hodology
2.1. A ea o S udy: Alga e Region
The Alga e Region is in he sou h o Po ugal and is made up o 16 municipali ies whose names
come om he capi al ci y o each (see Figu e 1). This egion has a coas o abou 200 km long and is he
mos impo an ou is des ina ion in Po ugal [
35
] (wi h 43.8% o he o al o e nigh s ays [
37
]) and in
Eu ope [
38
]. This aspec becomes impo an as he incomes om ou ism in Po ugal co esponded o
7% o he GDP o he coun y and 6.3% o employmen in he yea 2016 [
39
]. Sus ainabili y is he e o e
one o he 10 challenges p oposed by he Po uguese ou ism policy o he nex 10 yea s [
40
]. I is
impo an o no e ha ou ism has e ol ed con inuously since he cons uc ion o he Fa o Ai po
in 1965 [
41
], hus implying a la ge numbe o isi o s in he p esen days. In his sense, he egion
ecei ed a ound 2.7 million in e na ional isi o s in 2015 [42].
Sus ainabili y 2020,12, 1536 4 o 16
Sus ainabili y 2020, 12, 1536 4 o 17
Figu e 1. The Alga e egion and municipali ies (capi al ci ies a e d awn wi h a ci cle).
The beaches o he egion a e he main ou is a ac ion [35] and adi ionally he mos alued
a ibu e by ou is s [43]. The e o e, his des ina ion a ac s bo h na ional and in e na ional ou is s
[44,45]. I is also impo an o highligh he ele ance o gol acili ies in he Alga e egion. In his
ega d, he egion has expanded i s ange o gol since 1990 [46], hus making his ype o ou ism
one o he bes coun e weigh s o he s ong seasonali y o he egion [47].
In addi ion, he e is a wide ange o exis ing accommoda ion, including luxu y ho els and hos els
[48]. Consequen ly, he Alga e is he egion o Po ugal wi h he g ea es ou is ac i i y.
2.2. OBSERVE Pla o m
Con olling he sus ainabili y le el o a egion h ough obse a o ies is essen ial o gua an ee
he co ec de elopmen o u ban en i onmen s [49]. Fo his eason, he sus ainabili y o he Alga e
egion can be measu ed by he OBSERVE pla o m [36], whose objec i e is o moni o a ious
sus ainabili y indica o s classi ied in 4 dimensions (also known as pilla s) (see Figu e 2):
en i onmen al, ins i u ional, economic, and sociocul u al. The indica o s o each o hese pilla s
we e chosen based on he consensus o a ious public bodies and ins i u ions, such as he Alga e
Ho els Associa ion (in Po uguese, Associação dos Ho éis e Emp eendimen os Tu ís icos do Alga e)
and he Alga e Regional Coo dina ion and De elopmen Commission (in Po uguese, Comissão de
Coo denação e Desen ol imen o Regional do Alga e) [36]. Thanks o mee ings and su eys, he
indica o s o be moni o ed by OBSERVE we e de e mined [36]. Table 1 summa ises he OBSERVE
pla o m's sus ainabili y indica o s [36].
Figu e 1. The Alga e egion and municipali ies (capi al ci ies a e d awn wi h a ci cle).
The beaches o he egion a e he main ou is a ac ion [
35
] and adi ionally he mos
alued a ibu e by ou is s [
43
]. The e o e, his des ina ion a ac s bo h na ional and in e na ional
ou is s
[44,45]
. I is also impo an o highligh he ele ance o gol acili ies in he Alga e egion. In
his ega d, he egion has expanded i s ange o gol since 1990 [
46
], hus making his ype o ou ism
one o he bes coun e weigh s o he s ong seasonali y o he egion [47].
In addi ion, he e is a wide ange o exis ing accommoda ion, including luxu y ho els and
hos els [48]. Consequen ly, he Alga e is he egion o Po ugal wi h he g ea es ou is ac i i y.
2.2. OBSERVE Pla o m
Con olling he sus ainabili y le el o a egion h ough obse a o ies is essen ial o gua an ee he
co ec de elopmen o u ban en i onmen s [
49
]. Fo his eason, he sus ainabili y o he Alga e
egion can be measu ed by he OBSERVE pla o m [
36
], whose objec i e is o moni o a ious
sus ainabili y indica o s classi ied in 4 dimensions (also known as pilla s) (see Figu e 2): en i onmen al,
ins i u ional, economic, and sociocul u al. The indica o s o each o hese pilla s we e chosen based
on he consensus o a ious public bodies and ins i u ions, such as he Alga e Ho els Associa ion
(in Po uguese, Associaç
ã
o dos Ho
é
is e Emp eendimen os Tu
í
s icos do Alga e) and he Alga e
Regional Coo dina ion and De elopmen Commission (in Po uguese, Comiss
ã
o de Coo denaç
ã
o
e Desen ol imen o Regional do Alga e) [
36
]. Thanks o mee ings and su eys, he indica o s o
be moni o ed by OBSERVE we e de e mined [
36
]. Table 1summa ises he OBSERVE pla o m’s
sus ainabili y indica o s [36].
Sus ainabili y 2020,12, 1536 5 o 16
Sus ainabili y 2020, 12, 1536 5 o 17
Figu e 2. The 4 dimensions o he OBSERVE pla o m’s sus ainabili y indica o s.
Table 1. The OBSERVE pla o m's sus ainabili y indica o s [36].
Pilla
Subjec A ea Indica o
En i onmen al
Ai quali y index Ai quali y index
Ene gy managemen
Consump ion o elec ic ene gy by inhabi an
Consump ion o mo o uel by inhabi an
P oduc ion o elec ic ene gy using enewable sou ces
En i onmen al
managemen
En i onmen al expendi u e o municipali ies by 1000 inhabi an s
Numbe o blue lags, beaches and ma inas
Numbe o ba hing wa e s and quali y classes
Ma e ials and
was e managemen
Pe cen age o municipal was e p epa ed o euse and ecycling
U ban was e selec i ely collec ed pe inhabi an
U ban was e collec ed pe capi a
Mobili y
Numbe o emba ked and disemba ked passenge s in Fa o
Ai po
Numbe o passenge s pe kilome e ca ied by en e p ises
explo ing inland anspo a ion
Mo emen o passenge s in inland wa e ways
Numbe o emba ked and disemba ked passenge s o c uise ships
in Po imão Po
Cha ging s a ions o elec ic ehicles
A e age daily a ic on main oads and seconda y oads
Walking and cycling ou es
Na u al capi al
managemen
Bu n a ea
In es men s on p o ec ion o biodi e si y and landscapes o
municipali ies
Wa e cycle
managemen
Pe cen age o sa e wa e
F esh wa e supplied pe inhabi an
Was ewa e sewe age pe capi a
Ins i u ional Go e nance and
ci izenship
Abs en ion a e
Pe cen age o capi al expendi u e
B oadband in e ne access pe 100 inhabi an s
Figu e 2. The 4 dimensions o he OBSERVE pla o m’s sus ainabili y indica o s.
Table 1. The OBSERVE pla o m’s sus ainabili y indica o s [36].
Pilla Subjec A ea Indica o
En i onmen al
Ai quali y index Ai quali y index
Ene gy managemen
Consump ion o elec ic ene gy by inhabi an
Consump ion o mo o uel by inhabi an
P oduc ion o elec ic ene gy using enewable sou ces
En i onmen al
managemen
En i onmen al expendi u e o municipali ies by 1000 inhabi an s
Numbe o blue lags, beaches and ma inas
Numbe o ba hing wa e s and quali y classes
Ma e ials and was e
managemen
Pe cen age o municipal was e p epa ed o euse and ecycling
U ban was e selec i ely collec ed pe inhabi an
U ban was e collec ed pe capi a
Mobili y
Numbe o emba ked and disemba ked passenge s in Fa o Ai po
Numbe o passenge s pe kilome e ca ied by en e p ises explo ing
inland anspo a ion
Mo emen o passenge s in inland wa e ways
Numbe o emba ked and disemba ked passenge s o c uise ships in
Po imão Po
Cha ging s a ions o elec ic ehicles
A e age daily a ic on main oads and seconda y oads
Walking and cycling ou es
Na u al capi al
managemen
Bu n a ea
In es men s on p o ec ion o biodi e si y and landscapes o
municipali ies
Wa e cycle managemen
Pe cen age o sa e wa e
F esh wa e supplied pe inhabi an
Was ewa e sewe age pe capi a
Ins i u ional
Go e nance and
ci izenship
Abs en ion a e
Pe cen age o capi al expendi u e
B oadband in e ne access pe 100 inhabi an s
Inno a ion and
knowledge
G oss expendi u e on esea ch and de elopmen o ins i u ions and
en e p ises
G oss expendi u e on esea ch and de elopmen as pe cen age o g oss
domes ic p oduc

Sus ainabili y 2020,12, 1536 6 o 16
Table 1. Con .
Pilla Subjec A ea Indica o
Economic
Economic impac
G oss alue added o en e p ises
Appa en labou p oduc i i y in es ablishmen s, ood and be e age
se ice ac i i ies
In la ion
Pe capi a pu chasing powe
Numbe o es ablishmen s and economic ac i i y
Pe sons employed o es ablishmen s and economic ac i i y
Tu no e o es ablishmen s and economic ac i i y
Rela i e con ibu ion o es ablishmen s, ood and be e age se ice
ac i i ies o he Alga e Economy (GVA o En e p ises)
Job Employmen by gende and economic sec o
Seasonali y Seasonal employees
Es ablishmen s open all yea
Tou is occupa ion
Lodging capaci y in ho el es ablishmen s
Nigh s in ho el es ablishmen s
Re enue pe a ailable oom (Re Pa ) o ho el es ablishmen s
A e age s ay in ho el es ablishmen s
Accessibili y Numbe o accessible beaches
Cul u e Numbe o cul u al p ope ies
Municipali ies’ expendi u es on cul u al he i age
Sociocul u al
Demog aphy
Annual popula ion balances: na u al and mig a o y
Residen popula ion
Fo eign popula ion wi h s a us o esiden
Educa ion Popula ion educa ion le el wi h 15 and mo e yea s
Heal h ca e Heal h Ca e
P essu e
Lodging capaci y in ho el es ablishmen s by 1000 inhabi an s
Tou is in ensi y
Regional ou is densi y
Municipal ou is densi y
Sa e y C ime a e
Numbe o egis e ed c imes
Social cohesion
Regional de elopmen composi e index (cohesion)
Bene icia ies o social in eg a ion income, o social secu i y pe 1000
inhabi an s in ac i e age
Numbe o seconda y houses pe 100 houses
2.3. G oup App oaches
The e is much in o ma ion compiled by he OBSERVE pla o m. Howe e , i is necessa y o
es ablish app op ia e p ocedu es o analyse indica o s and, in his way, o es ablish he mos app op ia e
pe o mance pa e ns o mi iga e possible unsus ainable alues in some zones o he Alga e. One o
he i s s eps should be he classi ica ion o he ci ies o he egion acco ding o he alues eco ded in
each sus ainabili y indica o .
Fo his eason, his s udy assessed he possibili ies o g oup he 16 ci ies o he Alga e (see
Figu e 1). A o al o 105 indica o s om he OBSERVE pla o m ela ed o he sus ainabili y o he
egion we e selec ed. Some o he indica o s co espond o de elopmen s o a pa icula indica o . Fo
example, he c ime a e indica o was di ided in o di e en subca ego ies, such as c imes agains people
and c imes agains he i age. Likewise, some subjec a eas included in Table 1we e no conside ed
as da a o each ci y we e no a ailable (e.g., he subjec a ea o mobili y). Addi ionally, indica o s
we e in ended o be analysed in a long empo a y pe iod. Fo his s udy, he pe iod 2011–2015 was
conside ed as a wide sample o indica o s wi h da a o whe e he esea ch is a ailable.
A o al o 4 a ious app oaches we e used o clus e analyses. Such app oaches we e based on he
s uc u e used by he OBSERVE pla o m o classi y indica o s: To al app oach (TA), Pilla app oach
(PA), Subjec a ea app oach (SAA), and Indica o app oach (IA). These app oaches suppose ha he
da ase used in he clus e analysis has a lowe numbe o a iables om le o igh , so ha he TA
g oups all indica o s (i.e., i co esponds o a mul idimensional g oup), whe eas he IA co esponds o
indi idual analysis o each indica o (i.e., i co esponds o a 1D clus e ).
Sus ainabili y 2020,12, 1536 7 o 16
The analysis was ca ied ou o he pe iod 2011–2015, and he app oaches we e independen ly
analysed in each yea . Table 2includes he clus e analysis pe app oach and yea . The esul s o his
esea ch a e based on a o al o 620 clus e s.
Table 2. Clus e analyses ca ied ou in he esea ch.
Yea
App oach
TA PA SAA IA
2011 1 4 14 105
2012 1 4 14 105
2013 1 4 14 105
2014 1 4 14 105
2015 1 4 14 105
2.4. k-Means
The algo i hm
k
-means was used o clus e analyses.
k
-means is an i e a i e clus e ing
algo i hm based on he cen oid concep o a g oup o indi iduals [
50
]. The me hod is based
on an
X
sample o
n
indi iduals classi ied in
k
g oups, o which a
W
pa i ion o such sample wi h
W=(w1,. . . ,wa,. . . ,wb,. . . ,wk)
is conside ed, hus achie ing ha he o al sum o he sums o squa es
o he Euclidean dis ances wi hin each g oup is minimum:
a gmin
W
k
X
a=1
X
xi∈wa
p
X
=1
(xi −µa )2(1)
A he pe o mance le el, he k-means algo i hm’s s eps a e as ollows:
•S ep 1: he numbe o kg oups is iden i ied o ca y ou he analysis.
•S ep 2: kindi iduals om he da ase a e andomly selec ed, cons i u ing he ini ial cen oids.
•
S ep 3: by using he associa ion measu emen chosen, he dis ance o each indi idual o each
k
cen oid is calcula ed.
•S ep 4: kg oups a e c ea ed by alloca ing each indi idual o he closes cen oid.
•S ep 5: he new cen oids o each kg oup a e iden i ied.
•
S ep 6: s eps 3 and 4 a e epea ed. This s ep could lead o wo si ua ions: (i) going o s ep 5 i
in s ep 4 some o he indi iduals change he g oup, hus epea ing he cycle; and (ii) he clus e
analysis p ocess is inished when no indi idual changes he g oup in s ep 4.
The me hod is sensi i e o ini ial cen oids, so di e en esul s could be gi en by a ying he
ini ial alues o
k
. In his sense, he g ea e he
k
used in he algo i hm, he lowe he a ia ion wi hin
g oups (i.e., mo e indi idual g oups a e usually c ea ed, hus losing he main po en ial o he analysis:
o de ec simila i y pa e ns among indi iduals). I he a iables ha e a ious uni s (as in his esea ch),
a p e-p ocessing o no malise da a should be conduc ed be o e he clus e analysis (i.e., he a iables
a e escaled be ween 0–1 by using a min-max no malisa ion).
To op imally selec he numbe o clus e s, a o al o 3 di e en analyses we e used in his esea ch.
Such analyses we e based on he Elbow me hod, he silhoue e index (
s(i)
), and he a io be ween he
sum o squa es and he o al sum o squa es (BSS/TSS).
The Elbow me hod consis s in selec ing he op imal numbe o
k
by minimising he o al
wi hin-clus e sum o squa es (WSS) [51]. The Elbow me hod is made up o 4 phases:
1. k-means is applied o di e en alues o k.
Sus ainabili y 2020,12, 1536 8 o 16
2. Fo each k, WSS is calcula ed:
WSS =
K
X
k=1
X
i∈Sk
p
X
j=1
xij −xkj2(2)
whe e
Sk
is he se o ins ances g ouped in he
k
- h clus e , and
xkj
is he j- h a iable o he clus e
cen e o he k- h clus e .
3. The WSS cu e is plo wi h espec o he numbe o kg oups.
4.
The loca ion o he elbow in he g aphic is gene ally conside ed as an indica o o he op imal
numbe o g oups (see Figu e 3).
Sus ainabili y 2020, 12, 1536 8 o 17
The Elbow me hod consis s in selec ing he op imal numbe o k by minimising he o al wi hin-
clus e sum o squa es (WSS) [51]. The Elbow me hod is made up o 4 phases:
1. 𝑘-means is applied o di e en alues o 𝑘.
2. Fo each 𝑘, WSS is calcula ed:
𝑊𝑆𝑆 =  𝑥 −𝑥



∈


(2)
whe e 𝑆 is he se o ins ances g ouped in he k- h clus e , and 𝑥 is he j- h a iable o he clus e
cen e o he 𝑘- h clus e .
3. The WSS cu e is plo wi h espec o he numbe o 𝑘 g oups.
4. The loca ion o he elbow in he g aphic is gene ally conside ed as an indica o o he op imal
numbe o g oups (see Figu e 3).
Figu e 3. Example o he o al wi hin-clus e sum o squa es o each clus e conduc ed in he s udy.
The elbow o he g aphic can be clea ly seen [51]. This cha ac e is ic especially akes place in
cases in which he e is a g adual and con inuous da a ansi ion. Fo hese cases, he me hod does no
p o ide a unique possible solu ion, bu se e al possible solu ions which should be inspec ed o
de e mine he bes . Fo his eason, his s udy combines he Elbow me hod wi h wo indica o s: 𝑠(𝑖)
and BSS/TSS.
The BSS/TSS a io is a ela ion o he clus e compac ness. I is a pe cen age ela ion, wi h alues
be ween 0 and 100%. The g ea e he a io alue, he g ea e he compac ness o indi iduals wi hin a
g oup. Likewise, gi en ha TSS=BSS+WSS, by ha ing a g ea e BSS, WSS will be lowe . The a io
o mula ion is as ollows:
𝐵𝑆𝑆
𝑇𝑆𝑆 =∑∑𝑥

 −𝑥






∑∑𝑥

 −𝑥





 +∑∑∑𝑥 −𝑥




∈


(3)
whe e 𝑥 is he g and mean o he means o each g oup.
Finally, 𝑠(𝑖) is among he mos used indexes in he clus e analysis [52]. The index shows he
simila i y o an indi idual wi h he es o he indi iduals o a same g oup. So, i measu es he quali y
o a g oup. Fo his pu pose, he ollowing equa ion is used:
𝑠(𝑖)=𝑏(𝑖)−𝑎(𝑖)
𝑚𝑎𝑥󰇝𝑎(𝑖),𝑏(𝑖)󰇞 (4)
whe e 𝑎(𝑖) is he a e age dis ance be ween he indi idual (i) and he es o poin s o he same
g oup; and 𝑏(𝑖) is he minimum dis ance be ween he indi idual and he es o g oups. The
Figu e 3. Example o he o al wi hin-clus e sum o squa es o each clus e conduc ed in he s udy.
The elbow o he g aphic can be clea ly seen [
51
]. This cha ac e is ic especially akes place in
cases in which he e is a g adual and con inuous da a ansi ion. Fo hese cases, he me hod does
no p o ide a unique possible solu ion, bu se e al possible solu ions which should be inspec ed o
de e mine he bes . Fo his eason, his s udy combines he Elbow me hod wi h wo indica o s:
s(i)
and BSS/TSS.
The BSS/TSS a io is a ela ion o he clus e compac ness. I is a pe cen age ela ion, wi h alues
be ween 0 and 100%. The g ea e he a io alue, he g ea e he compac ness o indi iduals wi hin a
g oup. Likewise, gi en ha TSS=BSS+WSS, by ha ing a g ea e BSS, WSS will be lowe . The a io
o mula ion is as ollows:
BSS
TSS =PK
k=1Pp
j=1xkj −xG2
PK
k=1Pp
j=1xkj −xG2+PK
k=1Pi∈SkPp
j=1xij −xkj2(3)
whe e xGis he g and mean o he means o each g oup.
Finally,
s(i)
is among he mos used indexes in he clus e analysis [
52
]. The index shows he
simila i y o an indi idual wi h he es o he indi iduals o a same g oup. So, i measu es he quali y
o a g oup. Fo his pu pose, he ollowing equa ion is used:
s(i)=b(i)−a(i)
maxa(i),b(i)(4)
whe e
a(i)
is he a e age dis ance be ween he indi idual (i) and he es o poin s o he same g oup;
and
b(i)
is he minimum dis ance be ween he indi idual and he es o g oups. The silhoue e index
could ob ain alues be ween -1 and 1. The meaning o such alues de e mines he sui abili y o he
Sus ainabili y 2020,12, 1536 9 o 16
clus e analysis: (i) i he alue is be ween 0 and 1, he obse a ion is co ec ly g ouped, ob aining
op imal alues hose g oups close o 1; (ii) i he alue is 0, he indi idual is be ween wo g oups, hus
meaning ha ei he he indi idual has e y di e en cha ac e is ics om he es which could no be
g ouped wi h he o he s o ha he clus e analysis has excessi ely classi ied he indi idual g oups;
and (iii) i he alue is be ween -1 and 0, he indi idual is placed in he inco ec g oup. Figu e 4shows
an example o one analysis o he silhoue e index ollowed in he esea ch.
Sus ainabili y 2020, 12, 1536 9 o 17
silhoue e index could ob ain alues be ween -1 and 1. The meaning o such alues de e mines he
sui abili y o he clus e analysis: (i) i he alue is be ween 0 and 1, he obse a ion is co ec ly
g ouped, ob aining op imal alues hose g oups close o 1; (ii) i he alue is 0, he indi idual is
be ween wo g oups, hus meaning ha ei he he indi idual has e y di e en cha ac e is ics om
he es which could no be g ouped wi h he o he s o ha he clus e analysis has excessi ely
classi ied he indi idual g oups; and (iii) i he alue is be ween -1 and 0, he indi idual is placed in
he inco ec g oup. Figu e 4 shows an example o one analysis o he silhoue e index ollowed in
he esea ch.
Figu e 4. Example o he silhoue e index o each clus e conduc ed in he s udy: (a) e olu ion o he
a e age silhoue e wi h a ia ions o he numbe o g oups; and (b) dis ibu ion o he silhoue e in
each own.
Thus, he con ol o his alue leads us o know whe he indi iduals a e co ec ly g ouped. I is
impo an o s ess ha , in a mul idimensional clus e analysis, he silhoue e index ob ained is an
a e age o he a ious dimensions. Al hough he a e age silhoue e alue is high, he e a e e oneous
simila i y pa e ns among he di e en a iables.
3. Resul s and Discussion
Fi s ly, he op imal numbe o k o each app oach was de e mined in he clus e analysis. Fo
his pu pose, he elbow me hod and he analysis o 𝑠(𝑖) and o BSS/TSS we e used. Th ough his
assessmen , he op imal numbe o k was de e mined in he 620 clus e s conduc ed in he esea ch.
A e de e mining he op imal numbe o k o each app oach, he s a is ical pa ame e s
ob ained om 𝑠(𝑖) and BSS/TSS we e analysed o assess he mos app op ia e app oach o he
clus e analysis o he Alga e egion’s sus ainabili y indica o s. Figu e 5 includes he dis ibu ions
o BSS/TSS ob ained among he di e en app oaches in he 5 yea s analysed wi h iolin-plo s. Violin-
plo s a e an e olu ion o box-plo s by including in o ma ion o he ke nel densi y and o a ing hem
o bo h sides o he box [53]. As can be seen, he alues o BSS/TSS ob ained we e high as all g oups
ob ained a ions g ea e han 70% due o he p ocess o op imal selec ion o k ollowed in he
esea ch. Howe e , he use o app oaches wi h a lowe numbe o dimensions in he clus e analysis
inc eases he BSS/TSS a io. In his ega d, he use o he 1D app oach o indica o s allowed a e age
alues o BSS/TSS g ea e han 94% o be ob ained, wi h an inc ease wi h espec o he TA be ween
3.75 and 12.84% in all he yea s analysed (see Table 3). This app oach o educe he dimensions o he
clus e analysis was he only app oach ob aining be e esul s in all yea s, as in he PA and SAA, he
beha iou was di e en depending on he yea : (i) in he PA, be e esul s we e ob ained in 2013 and
2014, whe eas in he o he yea s, he BSS/TSS a io was lowe han ha o he TA; and (ii) in he SAA,
Figu e 4.
Example o he silhoue e index o each clus e conduc ed in he s udy: (
a
) e olu ion o he
a e age silhoue e wi h a ia ions o he numbe o g oups; and (
b
) dis ibu ion o he silhoue e in
each own.
Thus, he con ol o his alue leads us o know whe he indi iduals a e co ec ly g ouped. I is
impo an o s ess ha , in a mul idimensional clus e analysis, he silhoue e index ob ained is an
a e age o he a ious dimensions. Al hough he a e age silhoue e alue is high, he e a e e oneous
simila i y pa e ns among he di e en a iables.
3. Resul s and Discussion
Fi s ly, he op imal numbe o
k
o each app oach was de e mined in he clus e analysis. Fo
his pu pose, he elbow me hod and he analysis o
s(i)
and o BSS/TSS we e used. Th ough his
assessmen , he op imal numbe o k was de e mined in he 620 clus e s conduc ed in he esea ch.
A e de e mining he op imal numbe o
k
o each app oach, he s a is ical pa ame e s ob ained
om
s(i)
and BSS/TSS we e analysed o assess he mos app op ia e app oach o he clus e analysis o
he Alga e egion’s sus ainabili y indica o s. Figu e 5includes he dis ibu ions o BSS/TSS ob ained
among he di e en app oaches in he 5 yea s analysed wi h iolin-plo s. Violin-plo s a e an e olu ion
o box-plo s by including in o ma ion o he ke nel densi y and o a ing hem o bo h sides o he
box [
53
]. As can be seen, he alues o BSS/TSS ob ained we e high as all g oups ob ained a ions
g ea e han 70% due o he p ocess o op imal selec ion o
k
ollowed in he esea ch. Howe e , he
use o app oaches wi h a lowe numbe o dimensions in he clus e analysis inc eases he BSS/TSS
a io. In his ega d, he use o he 1D app oach o indica o s allowed a e age alues o BSS/TSS g ea e
han 94% o be ob ained, wi h an inc ease wi h espec o he TA be ween 3.75 and 12.84% in all he
yea s analysed (see Table 3). This app oach o educe he dimensions o he clus e analysis was he
only app oach ob aining be e esul s in all yea s, as in he PA and SAA, he beha iou was di e en
depending on he yea : (i) in he PA, be e esul s we e ob ained in 2013 and 2014, whe eas in he
o he yea s, he BSS/TSS a io was lowe han ha o he TA; and (ii) in he SAA, be e esul s we e
Sus ainabili y 2020,12, 1536 16 o 16
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