emo e sensing
A icle
Da a Field-Based K-Means Clus e ing o
Spa io-Tempo al Seismici y Analysis and
Haza d Assessmen
Xueyi Shang 1, Xibing Li 1,*, An onio Mo ales-Es eban 2, Gualbe o Asencio-Co és3ID
and Zewei Wang 4
1School o Resou ces and Sa e y Enginee ing, Cen al Sou h Uni e si y, Changsha 410083, China;
[email p o ec ed]
2
Depa men o Building S uc u es and Geo echnical Enginee ing, Uni e si y o Se ille, 41004 Se illa, Spain;
[email p o ec ed]
3Depa men o Compu e Science, Pablo de Ola ide Uni e si y o Se ille, 41013 Se illa, Spain;
[email p o ec ed]
4School o Ea hquake Sciences and Enginee ing, Sysu, Sun Ya -Sen Uni e si y, Guangzhou 510275, China;
wangzw[email p o ec ed]
*Co espondence: [email p o ec ed]; Tel.: +61-041-129-4835
Recei ed: 22 Janua y 2018; Accep ed: 14 Ma ch 2018; Published: 15 Ma ch 2018
Abs ac : Mic oseismic sensing aking ad an age o senso s can emo ely moni o seismic ac i i ies
and e alua e seismic haza d. Compa ed wi h expe s’ seismic e en clus e s, clus e ing algo i hms
a e mo e objec i e, and hey can handle many seismic e en s. Many me hods ha e been p oposed
o seismic e en clus e ing and he K-means clus e ing echnique has become he mos amous one.
Howe e , K-means can be a ec ed by noise e en s (la ge loca ion e o e en s) and ini ial clus e
cen e s. In his pape , a da a ield-based K-means clus e ing me hodology is p oposed o seismici y
analysis. The applica ion o syn he ic da a and eal seismic da a ha e shown i s e ec i eness in
emo ing noise e en s as well as inding good ini ial clus e cen e s. Fu he mo e, we in oduced
he ime pa ame e in o he K-means clus e ing p ocess and applied i o seismic e en s ob ained
om he Chinese Yongshaba mine. The esul s show ha he ime-e en loca ion dis ance and da a
ield-based K-means clus e ing can di ide seismic e en s by bo h space and ime, which p o ides
a new insigh o seismici y analysis compa ed wi h e en loca ion dis ance and da a ield-based
K-means clus e ing. The K zanowski-Lai (KL) index ob ains a maximum alue when he numbe o
clus e s is i e: he ene gy index (EI) shows ha clus e s C1, C3 and C5 ha e e y c i ical pe iods.
In conclusion, he ime-e en loca ion dis ance, and he da a ield-based K-means clus e ing can
p o ide an e ec i e me hodology o seismici y analysis and haza d assessmen . In addi ion, u he
s udy can be done by conside ing ime-e en loca ion-magni ude dis ances.
Keywo ds:
seismici y analysis; haza d assessmen ; spa io- empo al analysis; da a ield; K-means
clus e ; ime-e en loca ion dis ance
1. In oduc ion
Seismic e en clus e ing p o ides an e ec i e way o unde s and he unde lying in o ma ion
(such as geological s uc u e in e p e a ion and seismic haza d assessmen ; a de ailed use o seismic
e en clus e s is shown in Sec ion 2) o mic oseismic e en s [
1
,
2
]. This ask can be conduc ed by
expe s, ollowing a wo-s ep clus e ing p ocess: selec ing he ime pe iod conce ned and di iding
seismic e en s in o clus e s isually by e en loca ions. Howe e , expe s’ clus e s a e subjec i e,
non-quan i a i e and ha e ouble handling a la ge numbe o seismic e en s [
3
]. Mo i a ed by
his, a ious clus e ing algo i hms ha e been p oposed o seismici y analysis (e.g., K-means clus e ,
Remo e Sens. 2018,10, 461; doi:10.3390/ s10030461 www.mdpi.com/jou nal/ emo esensing
Remo e Sens. 2018,10, 461 2 o 22
hie a chical clus e ing, and sel -o ganizing map (SOM)), among which K-means clus e ing echnique
is he mos well-known one. Ye , K-means canno emo e noise e en s (which ha e ela i ely la ge
e en loca ion e o s) and i uses andom ini ial clus e cen e s (which ha e a la ge in luence on clus e
esul s). In addi ion, no K-means clus e ing-based me hodologies p e iously applied o his p oblem
ha e conside ed ime pa ame e s. In ac , seismic e en s a e no only ela ed o he e en loca ion bu
also o he e en ime [1].
In his wo k, a da a ield-based K-means clus e ing me hodology has been p oposed o spa io- empo al
seismici y analysis. This me hod uses a da a ield-based h eshold alue o emo e noises and a new
dis ance-based me hod o selec good ini ial clus e cen e s o K-means. Fu he mo e, we in oduced
he ime-e en loca ion dis ance in o he K-means clus e ing p ocess, which p o ides a spa io- empo al
insigh in o he seismici y analysis. The eal seismic da a applica ion shows i s e ec i eness in
seismic haza d assessmen . In addi ion, we compa ed i s pe o mance wi h classical K-means clus e ,
hie a chical clus e ing and SOM clus e ing. The es o his pape is o ganized as ollows. In Sec ion 2,
ela ed wo ks abou seismic e en clus e ing a e in oduced. Then, in Sec ion 3, he da a ield heo y
is b ie ly illus a ed, and he da a ield-based algo i hm is p oposed o be e selec K-means ini ial
clus e cen e s. In Sec ion 4, he p oposed da a ield-based K-means clus e ing was applied o 1210
mic oseismic e en s ob ained om he Chinese Yongshaba mine and he ene gy index (EI) is selec ed
o assess seismic haza d o he clus e ing zones. The applica ion de ail e ec and compa isons wi h
classical K-means clus e , hie a chical clus e ing and SOM clus e ing a e discussed in Sec ion 5. Finally,
b ie conclusions o he wo k and u u e wo k a e shown in Sec ion 6.
2. Rela ed Wo ks
Seismic e en clus e ing using clus e ing algo i hms has been s udied since he 1990s, and he
K-means clus e ing algo i hm has become he mos amous one. K-means is a ha d-pa i ioning
algo i hm p oposed by Ha igan and Wong [
4
]. I s a s wi h K andomly selec ed ini ial clus e cen e s
and uses an i e a i e p ocess un il no da a poin changes he clus e assigna ions. Bu on e al. [
5
] and
Wea he ill and Bu on [
6
,
7
] p oposed a line-sou ce K-means clus e ing echnique o be e iden i y
ini ial clus e cen e s and hey applied i o cap u e he seismic spa ial a ia ion, in e p e he aul ype
and analyze he p obabilis ic seismic haza d in he Ja a island and he Aegean egion. Ramdani e al. [
8
]
ook ad an age o he inal K-Means clus e cen e s o ind subduc ion e idence benea h he Gib al a
A c and he Andean egions. Rehman e al. [
9
] u ilizes he K-means algo i hm o iden i y he ea hquake
spa ial di e ences and es ima e seismic haza d and isk in Pakis an. Mo ales-Es eban e al. [
10
]
p oposed an e icien adap i e Mahalanobis-based K-means algo i hm and his has been applied
o s udy he seismic ca alogues o C oa ia and he Ibe ian Peninsula. Shang e al. [
11
] p oposed a
K zanowski–Lai and Silhoue e combined index o selec he op imum numbe o clus e s o K-means
and hey in e p e ed he geological s uc u e in he Chinese Yongshaba mine. The K-means clus e is
use ul o a la ge da ase clus e , and some s udies ha e been done o educe he e ec o ini ial clus e
cen e s. Ne e heless, he abo e-men ioned me hods ha e no conside ed he ime pa ame e and he
e ec o noise e en s.
Hie a chical clus e ing is also widely used in seismici y pa i ioning. I is based on he co e idea
ha an e en is mo e ela ed o a nea one han o a a e en , and i connec s e en s in o clus e s
based on a p ese dis ance. Hie a chical clus e ing does no need o se a clus e numbe (jus selec
a p ese dis ance) and i can clus e e en s in o di e en shapes. Wa dlaw e al. [
12
], F ohlich and
Da is [
13
], Da is and F ohlich [
14
], Hudyma and Po in [
15
], and Hashemi and Mehdizadeh [
16
]
used hie a chical clus e ing (single-link analysis) o s udy ea hquake ca alogues and seismic ac i i ies.
No wi hs anding, hie a chical clus e ing has a endency o o m seismic e en s in o linea g oups [
13
]
and he e may be many clus e s ha jus ha e ew e en s (see he discussion).
Ano he commonly used seismic e en clus e me hod is he SOM [
17
]. The SOM con e s high
dimension inpu space in o a low-dimension ( ypically wo-dimensional), which has a e y good
isualizing image. Zamani and Hashemi [
3
] compa ed hie a chical clus e ing (Wa d’s me hod) and
Remo e Sens. 2018,10, 461 3 o 22
SOM clus e ing wi h an applica ion o seismic zoning in I an. Mo eo e , Zamani e al. [
18
] applied
he SOM o clus e ing ec onic zoning in I an. The same me hod was es ed in Zamani e al. [
19
],
in which Wilk’s Lambda c i e ion was used o selec an op imum numbe o clus e s. Moja ab e al. [
20
]
discussed he e ec o SOM inpu pa ame e s and p oposed a combined model o selec a clus e
numbe o I an seismici y analysis. Besheli e al. [
21
] pe o med a K-means clus e ing along wi h a
SOM on an I anian o eshock da abase and hey ound a o eshock zone which has a e y close ela ion
wi h la ge ea hquakes. None heless, esea ch esul s [
11
,
22
] ha e shown ha he SOM clus e ing
may only be alid o high seismic ac i i y a eas, while o low seismic ac i i y zones i may ha e bad
clus e esul s. Fu he mo e, he SOM clus e ing may ha e discon inuous zones, which makes i ha d
o in e p e clus e esul s [11,22].
Some o he clus e me hods a e p oposed o seismici y analysis. Ansa i e al. [
23
], Beni ez e al. [
24
]
and Monem and Hashemy [
25
] used uzzy clus e s, including Ga h-Ge a clus e ing, p oposed
Ga h-Ge a clus e ing, uzzy c-means clus e ing and Gus a son-Kessel (GK) clus e ing, o s udy seismic
spa ial pa e n ecogni ion in I an, sou h-wes Colombia and he Ghaz in canal i iga ion ne wo k. The
uzzy clus e s can be used o a la ge da ase clus e ; howe e , i s clus e esul is sensi i e o he ini ial
clus e cen e s. Mukhopadhyay e al. [
26
] used a poin densi y clus e ing o gain insigh in o subduc ion
kinema ics and seismic po en iali y. Geo goulas e al. [
1
] modi ied a densi y-based clus e ing (DBC)
algo i hm and hen used a hie a chical agglome a i e scheme o seismic clus e ing. Nanda and
Panda [
27
] p oposed wo DBC algo i hms and compa ed hem wi h he DBSCAN (densi y-based
spa ial clus e ing o applica ions wi h noise). DBC can emo e noise e en s, ye when he densi y a ies
much, i usually ob ains bad clus e esul s. Ma ínez-Ál a ez e al. [
22
] used a T iGen-based clus e ing
algo i hm [
28
,
29
] o seismic zoning in he Ibe ian Peninsula. A compa ison o using di e en seismic
clus e s can be ound in [11,30,31].
Only a ew o he abo e in es iga ions ha e conside ed he ime ac o . Ne e heless, he ime
pa ame e can play an impo an ole in seismic e en clus e s. The commonly used clus e ing
echniques conside ing a ime pa ame e a e he ime-e en loca ion and ime-e en loca ion-magni ude
dis ance-based clus e s. F ohlich and Da is [
13
] and Da is and F ohlich [
14
] sugges ed equalizing
he ime and space in e als using a scaling cons an and in oduced he ime-e en loca ion dis ance
by
lij =qdij2+ (a ij)2
, whe e d
ij
and
ij
a e he e en loca ion dis ance and ime in e al espec i ely.
Then, hey used he hie a chical clus e o seismic e en clus e s. Baiesi and Paczuski [
32
] de ined
he ime–e en loca ion-magni ude dis ance be ween e en iand jby
nij =C ijlijd
10
−bmi
, whe e
d
is
he ac al dimension o epicen e s, bis he Gu enbe g–Rich e b- alue and
mi
is he e en magni ude.
A single link me hod was used in his wo k o he seismic e en clus e . Zaliapin e al. [
33
] and
Zaliapin and Ben-Zion [
34
–
38
] de ined he
nij
by magni ude-no malized ime componen
Tij
and space
componen
Rij
(
Tij = ij
10
−qbmi
and
Rij =lijd
10
−pbmi
, whe e q+p= 1). E en jis clus e ed o he main
e en ii i sa is ies he ollowing condi ions:
Tij <T0
,
Rij <R0
and
mj<mi
. I is clea ha no ime
pa ame e has been applied in K-means clus e ing. In his wo k, we jus in oduced he ime-e en
loca ion dis ance in o a K-means clus e ing algo i hm. Fu he s udy can be done by using a ime-e en
loca ion-magni ude dis ance.
3. P elimina y S udies and he P oposed Me hod
In i s place, o p o e he limi a ions o he K-means echnique, a b ie s udy wi h syn he ic da a
was pe o med in Sec ion 3.1. Nex , he da a ield heo y is in oduced in Sec ion 3.2. Then, he da a
ield-based K-means clus e ing p ocedu e is p oposed in Sec ion 3.3. Finally, an applica ion es o da a
ield-based K-means clus e ing is shown in Sec ion 3.4.
Remo e Sens. 2018,10, 461 4 o 22
3.1. K-Means Clus e ing P elimina y S udy
The classical K-means algo i hm is based on he ollowing s eps: ake a da ase o poin s (
x1
,
x2
,
. . .
,
xn
), andomly selec Kpoin s om he da a se as he ini ial clus e cen e s and alloca e each poin
xi
o he nea es cen e poin . Then, i calcula es he mean o each pa ame e espec i ely o each
g oup o make up a se o new upda ed clus e cen e s. This p ocedu e is epea ed un il no poin s
change hei clus e o he numbe o i e a ions eaches a p ese maximum.
The mos widely used dis ance is he Euclidean unc ion and his was chosen o his wo k.
The Euclidean dis ance be ween e en
xi
and
xj
is de ined in Equa ion (1). Then, he mean o he widely
used clus e ing c i e ion-sum o Euclidean dis ance (SED) is used o e alua e he clus e pe o mance.
We called his he MSED index. (The numbe o undenoised and denoised e en s is di e en , so we
used he MSED ins ead o he SED o e alua e he clus e ing pe o mance). MSED is de ined in
Equa ion (2), he smalle he MSED index o clus e s he be e he clus e ing esul s.
dij =
u
u
p
∑
l=1
(xi,l−xj,l)2(1)
MSED =1
n
K
∑
k=1
∑
xi∈Ck
u
u
p
∑
l=1
(xi,l−mk,l)2(2)
whe e
dij
is he dis ance be ween e en
xi
and
xj
,pis he dimension o he pa ame e s, C
k
is he k h
clus e , Kis he clus e numbe , mkis he clus e cen e o Ck, and nis he numbe o clus e e en s.
F om he p inciple o K-means clus e ing, we know ha he algo i hm may be a ec ed by he
ini ial clus e cen e s. To p o e his issue, a syn he ic wo-dimension da ase wi h ou well-di e enced
clus e s is used o es he e ec o K-means ini ial clus e cen e s (Figu e 1a). The algo i hm was es ed
15 imes by using andomly gene a ed ini ial clus e cen e s (using K= 4 o all he expe imen s) and
hei MSED indexes a e shown in Figu e 1b. I is clea ha he K-means clus e ing can be hea ily
a ec ed by he ini ial clus e cen e s: he MSED index a ies om 0.100 o 0.192. The K-means
clus e ing esul s o six ypical MSED alues a e shown in Figu e 1c–h. I is clea ly seen ha o
high MSED alues, qui e a lo o close e en s a e in di e en clus e s (Figu e 1c,h); o ela i ely high
MSED alues, many close e en s a e in di e en clus e s (Figu e 1d,g); while o low MSED alues,
he K-means clus e has good esul s (Figu e 1e, ). In conclusion, he lowe he MSED index, he be e
he clus e ing esul . The e o e, he e is a high need o op imize he K-means ini ial clus e cen e s.
Fu he mo e, he e a e some noise e en s placed in in e -clus e egions, which should be emo ed
be o e clus e ing.
Remo e Sens. 2018,10, 461 5 o 22
Remo e Sens. 2018, 10, x FOR PEER REVIEW 5 o 22
Figu e 1. K-means clus e ing esul s using di e en ini ial clus e cen e s o a ypical da ase . The
colo ed ci cles a e he e en s and he same colo ed e en s co espond o a same clus e . (a) Da ase ;
(b) MSED indexes o di e en andomly selec ed ini ial clus e cen e s (K = 4); (c–h) The clus e
esul s o execu ions 2nd, 3 d, 4 h, 9 h, 11 h and 12 h o he K-means clus e ing p ocess (K = 4).
Figu e 1.
K-means clus e ing esul s using di e en ini ial clus e cen e s o a ypical da ase .
The colo ed ci cles a e he e en s and he same colo ed e en s co espond o a same clus e . (
a
) Da ase ;
(
b
)MSED indexes o di e en andomly selec ed ini ial clus e cen e s (K= 4); (
c
–
h
) The clus e esul s
o execu ions 2nd, 3 d, 4 h, 9 h, 11 h and 12 h o he K-means clus e ing p ocess (K= 4).

Remo e Sens. 2018,10, 461 6 o 22
3.2. Da a Field Theo y
Mo i a ed by physical ield heo y, Wang e al. [
39
] p oposed a da a ield heo y o desc ibe he
in e ac ion among a se o e en s. The po en ial alue (scala ield s eng h) o e en
xi
in he global
da a ield is de ined as:
ϕ(xi) =
n
∑
j=1
mj×K(kxi−xjk
σ)(3)
whe e
mj
is he mass o e en
xj
,K(x) is he uni po en ial unc ion,
kxi−xjk
ep esen s he dis ance
be ween e en xiand e en xj, and σis he impac ac o .
The
mj
is se o 1, o all he j alues, and he commonly used unc ion
K(β) = e−β2
is selec ed.
Then, he po en ial alue in he global da a ield o e en
xi
can be w i en as in Equa ion (4), whe e
kxi−xjkwas de ined by he Euclidean unc ion.
ϕ(xi) =
n
∑
j=1
e−(kxi−xjk/σ)2=
n
∑
j=1
e−(
p
∑
l=1
(xi,l−xj,l)2/σ2)(4)
The impac ac o con ols he in e ac ed dis ance be ween e en s and i s alue can ha e a hea y
impac on po en ial alues. The ela ionship be ween he in e ac ed dis ance and he po en ial alue
o Equa ion (4) is shown in Figu e 2a. I is easy o see ha he longe he dis ance be ween e en s
he lowe he po en ial alue o a same impac ac o , and he highe he impac ac o he la ge he
po en ial alue o a same in e ac ed dis ance. In o he wo ds, o a low impac ac o , he e will be
many local maximum po en ial alues; while o a la ge impac ac o , he e will be ew local maximum
po en ial alues. Some esea ch [
39
,
40
] has used po en ial en opy o ob ain an op imum impac ac o ,
and he minimum po en ial en opy co esponds o he op imum impac ac o . The po en ial en opy
is de ined as in [39]:
H=−
n
∑
i=1
ϕ(xi)
Zlogϕ(xi)
Z(5)
whe e Z=n
∑
i=1
ϕ(xi), 0 ≤H≤log(n).
The po en ial en opy using di e en impac ac o s is shown in Figu e 2b. The po en ial en opy
has a minimum alue when
σ=
0.028. Then, he po en ial alue is calcula ed o each e en using
Equa ion (4). The con ou map o po en ial alue is shown in Figu e 2c. I is easy o see ha he
po en ial alue con ou has a good ag eemen wi h he da ase densi y. Po en ial alue may p o ide a
good way o clus e ing (e.g., Figu e 2c): a po en ial h eshold alue can be used o di ide he da ase
in o small da ase s. No wi hs anding, o an i egula da ase , i is di icul o p oduce adequa e
clus e s based on a po en ial h eshold alue (e.g., Figu es 5a and 6). The e o e, ins ead o using a
po en ial alue o clus e seismic e en s, we jus applied po en ial h eshold alues o emo e noise
e en s and be e selec ed K-means ini ial clus e cen e s.
Remo e Sens. 2018,10, 461 7 o 22
Remo e Sens. 2018, 10, x FOR PEER REVIEW 7 o 22
Figu e 2. Da a ield applica ion (a–c) and K-means clus e ing esul s based on he da a ield (d– ); (a)
Po en ial alues based on di e en impac ac o s; (b) Rela ionship be ween po en ial en opy and he
impac ac o ; (c) Con ou map o po en ial alues ( 0.028
σ
=); (d) The MSED indexes based on
di e en po en ial h eshold alues
p
o
ϕ
, whe e Min, O1, O2, …., O7 a e he minimum, i s , second,
…, and se en h oc iles o po en ial alues, espec i ely; (e) The da a ield-based K-means clus e ing
esul s using undenoised da a when he po en ial h eshold alue
p
o
ϕ
is equal o he second oc ile;
( ) The da a ield-based K-means clus e ing esul s wi h 7.5% da a emo ed and
p
o
ϕ
is equal o he
second oc ile.
Figu e 2.
Da a ield applica ion (
a
–
c
) and K-means clus e ing esul s based on he da a ield (
d
–
);
(
a
) Po en ial alues based on di e en impac ac o s; (
b
) Rela ionship be ween po en ial en opy and
he impac ac o ; (
c
) Con ou map o po en ial alues (
σ=
0.028); (
d
) The MSED indexes based on
di e en po en ial h eshold alues
ϕpo
, whe e Min, O
1
,O
2
,
. . .
., O
7
a e he minimum, i s , second,
. . .
, and se en h oc iles o po en ial alues, espec i ely; (
e
) The da a ield-based K-means clus e ing
esul s using undenoised da a when he po en ial h eshold alue
ϕpo
is equal o he second oc ile;
(
) The da a ield-based K-means clus e ing esul s wi h 7.5% da a emo ed and
ϕpo
is equal o he
second oc ile.
Remo e Sens. 2018,10, 461 8 o 22
3.3. Da a Field-Based K-Means Clus e ing P ocedu e
The da a ield-based K-means clus e ing akes ad an age o he e en wi h high po en ial alue
being mo e likely o be an ini ial clus e cen e and ha he dis ance be ween ini ial clus e cen e s
should ha e a la ge dis ance. The e is a low e en densi y a ound he noise e en s and hey ha e
la ge dis ances o mos e en s, which usually implies small po en ial alues. Then, a h eshold alue
ϕ h
can be se o emo e noise e en s. The low diag am o he da a ield-based K-means clus e ing
p ocess is shown in Figu e 3con aining he ollowing s eps:
S ep 1: Inpu da ase Uda ase (xi∈Uda ase ,i= 1, 2, . . . , nda ase ,nda ase =n).
S ep 2: Selec he impac ac o o he da a ield by he impac ac o -po en ial en opy cu e
calcula ed by Equa ion (5) and calcula e he po en ial alue
ϕ
(x
i
) o each e en in
Uda ase
using
Equa ion (4).
S ep 3: Remo e noise e en s and ob ain a new da ase
Uda ase -noise
(
xj∈Uda ase -noise
,j= 1, 2,
. . .
,n
da ase -noise
,n
da ase -noise ≤
n): I a po en ial alue is smalle han a p ede ined h eshold alue
ϕ h
, hen i s co esponding e en is ma ked as a noise e en and i is o be emo ed om he da ase
Uda ase
. I he e a e no noise e en s, hen he e is no need o do S ep 3 o a
ϕ h
ha is smalle han he
minimum po en ial alue can be se o do S ep 3.
ϕ h
= Min-0.1 is used in his pape o no denoising,
whe e Min-0.1 means he minimum po en ial alue minus 0.1.
S ep 4: Selec K-means ini ial clus e cen e s based on he po en ial alue and a maximum
dis ance-based algo i hm.
(4-1) Selec possible ini ial clus e cen e s
Upo
(
xk∈Upo
,k= 1, 2,
. . .
,n
po
,n
po ≤
n) by choosing
e en s which ha e po en ial alues la ge han a p ede ined h eshold alue ϕpo;
(4-2) Selec K-means ini ial clus e cen e s based on a maximum dis ance-based algo i hm.
The maximum dis ance-based algo i hm con ains he ollowing s eps:
(4-2-1) The e en which has a maximum po en ial alue in
Upo
is se o he i s ini ial clus e
cen e m1;
(4-2-2) Calcula e he dis ances be ween
m1
and each poin in
Upo
-
m1
, and he la ges dis ance
co esponding e en is se o he second ini ial clus e cen e m2;
(4-2-3) Calcula e he dis ances be ween
m1
,
m2
and each poin in
Upo
-
m1
-
m2
, hen selec he
smalles dis ance o ob ain he dis ance se
Vsd
. Fo example, o e en
xi
(
xi∈Upo
-
m1
-
m2
), he e a e
wo dis ances (
m1
,
xi
) and (
m2
,
xi
), and he Min((
m1
,
xi
), (
m2
,
xi
)) is se o
Vi
sd
. Calcula e he smalle
dis ance o each e en in
Upo
-
m1
-
m2
, hen he smalles dis ances make up he dis ance se
Vsd
.
The poin wi h he la ges alue in Vsd co esponds o he hi d ini ial clus e cen e m3;
(4-2-4) Repea S ep (4-2-3) o ob ain m4,m5, . . . , mK.
S ep 5: Pe o m he K-means clus e ing o da ase
Uda ase -noise
using he
m1
,
m2
,
. . .
,
mK
as he
ini ial clus e cen e s.
S ep 6: Selec he op imum numbe o clus e s using he K zanowski-Lai (KL) index
(see Sec ion 4.3.2) and in e p e he clus e ing esul s.
Remo e Sens. 2018,10, 461 9 o 22
Remo e Sens. 2018, 10, x FOR PEER REVIEW 9 o 22
Figu e 3. The low diag am o he da a ield-based K-means clus e ing.
3.4. Applica ion Tes
The ela ionship be ween he MSED index and he h eshold alue
p
o
ϕ
o da a ield-based K-
means clus e ing using undenoised da a is shown in Figu e 2d, whe e O1, O2, …., O7 a e he i s ,
second, …, and se en h oc iles o po en ial alues, espec i ely. I is clea ha he da a ield-based K-
means clus e ing usually ob ains a smalle MSED index han he classical K-means algo i hm. This
indica es ha he da a ield-based K-means clus e ing ob ains be e clus e s han hose p oduced by
Figu e 3. The low diag am o he da a ield-based K-means clus e ing.
3.4. Applica ion Tes
The ela ionship be ween he MSED index and he h eshold alue
ϕpo
o da a ield-based
K-means clus e ing using undenoised da a is shown in Figu e 2d, whe e O
1
,O
2
,
. . .
., O
7
a e he i s ,
second,
. . .
, and se en h oc iles o po en ial alues, espec i ely. I is clea ha he da a ield-based
Remo e Sens. 2018,10, 461 16 o 22
Remo e Sens. 2018, 10, x FOR PEER REVIEW 16 o 22
Figu e 9. LogEI o he i e clus e s in Figu e 8a.
4.3.3. Seismici y Analysis
(1) Ene gy index
The commonly used s a is ical pa ame e -ene gy index (EI) is selec ed o e alua e mic oseismic
ac i i y. EI is a pa ame e ela ed o he concen a ion and accumula ion o s ess in a ock mass [45],
and i is de ined as he a io be ween he adia ed ene gy and he a e age ene gy (expec ed ene gy)
o a gi en seismic momen M. An EI > 1 signi ies ha mo e ene gy has been eleased han expec ed,
while an EI < 1 signi ies ha less ene gy has been eleased han expec ed. Resea ch has shown ha
when an EI > 1 he ock mass is accumula ing s ess, and when he ock mass s a s o ail, he EI
d ops below one [46]. The EI is de ined as in [47]:
log
()10
cd M
EE
EI EM
+
==
(8)
whe e
2
2
4c
c
J
E R
F
πρ
=
is he seismic adia ion ene gy,
ρ
is he ock densi y, is he wa e
p opaga ion speed, c
J
is he in eg al o he squa ed g ound speed, Fc is he adia ion pa e n
Figu e 9. LogEI o he i e clus e s in Figu e 8a.
4.3.3. Seismici y Analysis
(1) Ene gy index
The commonly used s a is ical pa ame e -ene gy index (EI) is selec ed o e alua e mic oseismic
ac i i y. EI is a pa ame e ela ed o he concen a ion and accumula ion o s ess in a ock mass [
45
],
and i is de ined as he a io be ween he adia ed ene gy and he a e age ene gy (expec ed ene gy)
o a gi en seismic momen M. An EI > 1 signi ies ha mo e ene gy has been eleased han expec ed,
while an EI < 1 signi ies ha less ene gy has been eleased han expec ed. Resea ch has shown ha
when an EI > 1 he ock mass is accumula ing s ess, and when he ock mass s a s o ail, he EI d ops
below one [46]. The EI is de ined as in [47]:
EI =E
E(M)=E
10c+dlog M(8)
whe e E=4πρ R2Jc
Fc2is he seismic adia ion ene gy, ρis he ock densi y, is he wa e p opaga ion
speed,
Jc
is he in eg al o he squa ed g ound speed, F
c
is he adia ion pa e n pa ame e : o a P

Remo e Sens. 2018,10, 461 17 o 22
wa e F
c
is 0.52, while o an S wa e F
c
is 0.63.
E(M)
is he a e age ene gy de i ed om he logE s.
logM ela ion o a gi en momen M, and cand da e he eg ession cons an s.
(2) Seismici y analysis o clus e s
The leas squa es linea eg essions be ween log(ene gy) and log(momen ) o he i e clus e s o
Figu e 8a a e shown in Figu e S2. Then, we calcula ed he EI h ough Equa ion (8) and he logEI o he
i e clus e s a e shown in Figu e 9. Some esea ch [
48
,
49
] de ined he p edic i e pe iod and c i ical
pe iod om he EI ime se ies: when he EI dec eases, his indica es ha pa s o he ock mass a e
beginning o ha e an uns able s a us. This pe iod could be seen as a s ain-so ening s age. I is he
beginning o po en ial damage and ega ded as a wa ning indica o . This pe iod is called a p edic i e
pe iod. An inc easing EI means ha he ock mass is en e ing an uns able s a e, and his pe iod is
called a c i ical pe iod. The quicke he EI dec eases, he la ge he isk o a big mic oseismic e en
happening. So, when he EI dec eases sha ply, we can sugges he mine s o be ca e ul in he p edic i e
pe iod and no wo k in he upcoming c i ical pe iod in he co esponding clus e a ea.
Fo C1, he logEI has a sha p dec ease om 5 Ap il o 6 Ap il (a p edic i e pe iod)– he mine s
should be ca e ul when mining in his a ea–and he logEI inc eases om 7 Ap il o 13 Ap il (a c i ical
pe iod)– he mine s should no wo k in his a ea on hese days. Then, he e is a ela i ely small
p edic i e pe iod ( om 13 Ap il o 14 Ap il) and a c i ical pe iod (15 Ap il). Fo C2, he logEI slowly
dec eases om 23 Ap il o 27 Ap il (p edic i e pe iod), and he mine s should be ca e ul on 28 Ap il
when mining. Fo C3, he logEI quickly dec eases on 10 Ap il (a p edic i e pe iod and special a en ion
should be paid) and hen he logEI inc eases om 13 Ap il o 16 Ap il (a c i ical pe iod and he mine s
should no wo k in his a ea). Fo C4, he logEI inc eases and dec eases al e na ely, which means
he ock sys em eleases and abso bs ene gy s eadily and he e a e no p edic i e pe iods and c i ical
pe iods. Fo C5, he e a e high logEI om 16 Ap il o 19 Ap il and he e is a sha p logEI dec easing
om 25 Ap il o 28 Ap il (a p edic i e pe iod and he mine s should be e y ca e ul when mining),
hen he logEI inc eases om 22 Ap il o 24 Ap il (a c i ical pe iod and he mine s should no wo k in
his a ea). Though Figu e 8a shows ha C4 and C5 ha e a simila loca ion a ea, C5 has c i ical pe iods
while C4 has no c i ical pe iods, which p o es ha he ime pa ame e can p o ide a new insigh o
seismic clus e ing analysis. In conclusion, he e a e e y c i ical pe iods o C1, C3 and C5 when he
mine s should no wo k.
5. Discussion
This pape p oposed a da a ield-based K-means clus e ing me hodology o denoise noise e en s
and selec ini ial clus e cen e s. Howe e , his can be a ec ed by he h eshold alue
ϕpo
, and i s
pe o mance wi h espec o classical K-means clus e ing using denoised and undenoised e en s
should be discussed. In addi ion, we also chose he commonly used hie a chical clus e ing and SOM
clus e ing as compa isons. The MSED indexes o ime-e en loca ion dis ance and da a ield-based
K-means clus e ing (
ϕpo
= Min-0.1, Q1, Median and Q3, whe e Min, Q1, Median and Q3 co espond
o he minimum, he i s qua ile, he second qua ile and he hi d qua ile o he po en ial alues,
espec i ely), classical K-means clus e ing using denoised and undenoised e en s ( andomly selec ed
ini ial clus e cen e s) and SOM clus e ing a e d awn in Figu e 10. Fo denoised e en clus e ing, his
shows ha he MSED index o he da a ield-based K-means clus e ing is usually smalle han ha
o he classical K-means clus e s. Fo a small clus e numbe (K= 2 and K= 3), he da a ield-based
K-means (
ϕpo
= Min-0.1, Q1 and Median) has a simila MSED index o he classical K-means. This is
because he classical K-means clus e ing has a ela i ely good global sea ch o a small numbe o
clus e s. The da a ield-based K-means clus e ing (
ϕpo
=Q3) p oduces be e clus e esul s han
he classical K-means algo i hm (K= 3 and K= 4). This is due o he highe po en ial alue e en
being mo e likely o be a inal clus e cen e . Fo a ela i ely la ge clus e numbe (K= 5~7), he da a
ield-based K-means clus e ing usually imp o es he classical K-means clus e ing, which p o es he
e ec i eness o he da a ield-based algo i hm in selec ing ini ial clus e cen e s. Fo a la ge clus e
Remo e Sens. 2018,10, 461 18 o 22
numbe (K= 8~10), he da a ield-based K-means clus e ing (
ϕpo
=Q3) has a esul ha is nea ly as
equal/bad as he classical K-means clus e ing. This is caused by he da a ield densi y-based algo i hm
using a h eshold alue
ϕpo
o selec high po en ial alue e en s. Ye , he low po en ial alue e en s
may ha e use ul ini ial clus e cen e s o a la ge clus e numbe , which esul s in he andomly
selec ed ini ial clus e cen e s a imes ha ing a be e clus e esul . The da a ield-based K-means
clus e (
ϕpo
=Q1 and
ϕpo
= Median) has a good clus e esul in gene al and a h eshold alue
ϕpo
be ween Q1 and he Median, and a clus e numbe smalle han 9 is sugges ed in he da a ield-based
K-means clus e ing algo i hm.
Remo e Sens. 2018, 10, x FOR PEER REVIEW 18 o 22
numbe (K = 8~10), he da a ield-based K-means clus e ing (
p
o
ϕ
= Q3) has a esul ha is nea ly as
equal/bad as he classical K-means clus e ing. This is caused by he da a ield densi y-based algo i hm
using a h eshold alue
p
o
ϕ
o selec high po en ial alue e en s. Ye , he low po en ial alue e en s
may ha e use ul ini ial clus e cen e s o a la ge clus e numbe , which esul s in he andomly
selec ed ini ial clus e cen e s a imes ha ing a be e clus e esul . The da a ield-based K-means
clus e (
p
o
ϕ
= Q1 and
p
o
ϕ
= Median) has a good clus e esul in gene al and a h eshold alue
p
o
ϕ
be ween Q1 and he Median, and a clus e numbe smalle han 9 is sugges ed in he da a ield-based
K-means clus e ing algo i hm.
The classical K-means clus e ing using denoised e en s usually has a smalle MSED index han
ha o classical K-means clus e ing using undenoised e en s. This is caused by he noise e en s being
ela i ely a away om mos e en s (Figu e 11a). The SOM clus e ing has a e y la ge MSED index
compa ed wi h K-means-based clus e s (Figu e 10). This is due o he SOM clus e s some imes mixing
oge he (Figu e 11b). Fu he mo e, he mixed clus e s make i ha d o in e p e he clus e esul s.
Fo he hie a chical clus e ing, we ied di e en clus e numbe s: o a small clus e numbe , 99% o
seismic e en s a e in one clus e ; o 100 clus e s, 36% and 50% o e en s a e in wo clus e s; o 200
clus e s, 42% and 28% o e en s a e in wo clus e s; and o 400 clus e s, 25% and 12%, 5%, 7% o
e en s a e in ou clus e s. Fo hese numbe s o clus e s, e e y o he clus e makes up less han 1%.
This is b ough abou by he hie a chical clus e ing connec ing close e en s oge he . Al hough he e
a e some a away e en s in he seismic da a, e e y e en will usually be di ided in o one clus e o
se e al close e en s connec ed in o one clus e . The e o e, i is ha d o ob ain a ce ain numbe o
clus e s which con ain a ela i ely la ge numbe o e en s, and he e a e many e en s ha will be
ea ed as noises ( he clus e s wi h ew e en s). In conclusion, he da a ield-based K-means clus e ing
can ha e a good clus e esul as well as a good in e p e a ion compa ed wi h he abo e discussed
clus e s.
Figu e 10. The MSED indexes o ime-e en loca ion dis ance and da a ield-based K-means
clus e ing, classical K-means clus e ing using denoised and undenoised e en s and SOM
clus e ing using denoised e en s. The Min, Q1, Median and Q3 co espond o he
minimum, i s qua ile, second qua ile and hi d qua ile o po en ial alues, espec i ely.
Figu e 10.
The MSED indexes o ime-e en loca ion dis ance and da a ield-based K-means clus e ing,
classical K-means clus e ing using denoised and undenoised e en s and SOM clus e ing using denoised
e en s. The Min, Q1, Median and Q3 co espond o he minimum, i s qua ile, second qua ile and
hi d qua ile o po en ial alues, espec i ely.
The classical K-means clus e ing using denoised e en s usually has a smalle MSED index han
ha o classical K-means clus e ing using undenoised e en s. This is caused by he noise e en s being
ela i ely a away om mos e en s (Figu e 11a). The SOM clus e ing has a e y la ge MSED index
compa ed wi h K-means-based clus e s (Figu e 10). This is due o he SOM clus e s some imes mixing
oge he (Figu e 11b). Fu he mo e, he mixed clus e s make i ha d o in e p e he clus e esul s.
Fo he hie a chical clus e ing, we ied di e en clus e numbe s: o a small clus e numbe , 99%
o seismic e en s a e in one clus e ; o 100 clus e s, 36% and 50% o e en s a e in wo clus e s; o
200 clus e s, 42% and 28% o e en s a e in wo clus e s; and o 400 clus e s, 25% and 12%, 5%, 7%
o e en s a e in ou clus e s. Fo hese numbe s o clus e s, e e y o he clus e makes up less han
1%. This is b ough abou by he hie a chical clus e ing connec ing close e en s oge he . Al hough
he e a e some a away e en s in he seismic da a, e e y e en will usually be di ided in o one
clus e o se e al close e en s connec ed in o one clus e . The e o e, i is ha d o ob ain a ce ain
numbe o clus e s which con ain a ela i ely la ge numbe o e en s, and he e a e many e en s ha
will be ea ed as noises ( he clus e s wi h ew e en s). In conclusion, he da a ield-based K-means
clus e ing can ha e a good clus e esul as well as a good in e p e a ion compa ed wi h he abo e
discussed clus e s.
Remo e Sens. 2018,10, 461 19 o 22
Remo e Sens. 2018, 10, x FOR PEER REVIEW 19 o 22
Figu e 11. The ime-e en loca ion dis ance based clus e esul s (K = 5) o classical K-means using
undenoised e en s and SOM clus e ing using denoised e en s. (a) Classical K-means using
undenoised e en s; (b) SOM clus e ing using denoised e en s.
6. Conclusions
In his pape , a da a ield-based K-means clus e ing me hod has been p oposed o spa io-
empo al seismici y analysis. This me hod akes ad an age o a da a ield-based h eshold alue o
emo e noises as well as a new dis ance-based algo i hm o ob ain good ini ial clus e cen e s o K-
means. The me hod has been es ed by i s applica ion o mic oseismic e en s ob ained om he
Chinese Yongshaba mine, which conside s bo h a ime pa ame e and loca ion pa ame e s. The KL
index shows ha he me hod has he bes clus e ing esul when K = 5 and he EI shows ha C1, C3
and C5 ha e e y c i ical pe iods. C4 and C5 ha e simila clus e zones. Ne e heless, C4 has no
c i ical pe iods, which p o es ha he ime-e en loca ion dis ance-based K-means clus e ing can
p o ide a new way o seismici y analysis compa ed wi h e en loca ion dis ance-based K-means
clus e ing. The da a ield-based K-means clus e ing usually achie es be e clus e esul s compa ed
wi h classical K-means clus e ing when he h eshold alue
po
ϕ
is be ween Q1 and he Median o
he po en ial alues and he clus e numbe is smalle han 9. Compa isons wi h he classical K-means
clus e ing, hie a chical clus e ing and SOM clus e ing show he e ec i eness o he p oposed
clus e ing me hod. The po en ial alue-based denoising is e y applicable o o he da ase s, whe e
e en s need o be di ided in o clus e ed and non-clus e ed e en s. Also, he po en ial alue can be
used o show e en densi y. The p oposed maximum dis ance-based algo i hm can also p o ide good
ini ial clus e cen e s o some o he clus e s, such as he FCM clus e . The e ec i eness o
in oducing spa io- empo al dis ance in o K-means shows ha i may also be use ul in o he clus e
algo i hms. Mo eo e , u he s udy can be done by in oducing ime-e en loca ion-magni ude
dis ance in o he da a ield-based K-means clus e ing o seismici y analysis.
Supplemen a y Ma e ials: The ollowing a e a ailable online a www.mdpi.com/link. Figu e S1: Seismic e en
loca ions wi h 5%, 7.5%, 12.5% and 15% o da a emo ed. (a) Seismic e en loca ions wi h 5% o da a emo ed;
Figu e 11.
The ime-e en loca ion dis ance based clus e esul s (K= 5) o classical K-means using
undenoised e en s and SOM clus e ing using denoised e en s. (
a
) Classical K-means using undenoised
e en s; (b) SOM clus e ing using denoised e en s.
6. Conclusions
In his pape , a da a ield-based K-means clus e ing me hod has been p oposed o spa io- empo al
seismici y analysis. This me hod akes ad an age o a da a ield-based h eshold alue o emo e
noises as well as a new dis ance-based algo i hm o ob ain good ini ial clus e cen e s o K-means.
The me hod has been es ed by i s applica ion o mic oseismic e en s ob ained om he Chinese
Yongshaba mine, which conside s bo h a ime pa ame e and loca ion pa ame e s. The KL index
shows ha he me hod has he bes clus e ing esul when K= 5 and he EI shows ha C1, C3 and
C5 ha e e y c i ical pe iods. C4 and C5 ha e simila clus e zones. Ne e heless, C4 has no c i ical
pe iods, which p o es ha he ime-e en loca ion dis ance-based K-means clus e ing can p o ide
a new way o seismici y analysis compa ed wi h e en loca ion dis ance-based K-means clus e ing.
The da a ield-based K-means clus e ing usually achie es be e clus e esul s compa ed wi h classical
K-means clus e ing when he h eshold alue
ϕpo
is be ween Q1 and he Median o he po en ial
alues and he clus e numbe is smalle han 9. Compa isons wi h he classical K-means clus e ing,
hie a chical clus e ing and SOM clus e ing show he e ec i eness o he p oposed clus e ing me hod.
The po en ial alue-based denoising is e y applicable o o he da ase s, whe e e en s need o be
di ided in o clus e ed and non-clus e ed e en s. Also, he po en ial alue can be used o show e en
densi y. The p oposed maximum dis ance-based algo i hm can also p o ide good ini ial clus e cen e s
o some o he clus e s, such as he FCM clus e . The e ec i eness o in oducing spa io- empo al
dis ance in o K-means shows ha i may also be use ul in o he clus e algo i hms. Mo eo e , u he
s udy can be done by in oducing ime-e en loca ion-magni ude dis ance in o he da a ield-based
K-means clus e ing o seismici y analysis.
Remo e Sens. 2018,10, 461 20 o 22
Supplemen a y Ma e ials:
The ollowing a e a ailable online a www.mdpi.com/2072-4292/10/3/461/s1. Figu e
S1: Seismic e en loca ions wi h 5%, 7.5%, 12.5% and 15% o da a emo ed. (a) Seismic e en loca ions wi h 5% o
da a emo ed; (b) Seismic e en loca ions wi h 7.5% o da a emo ed; (c) Seismic e en loca ions wi h 12.5% o
da a emo ed; (d) Seismic e en loca ions wi h 15% o da a emo ed. Figu e S2: Leas squa es linea eg ession
be ween log(ene gy) and log(momen ) o he i e clus e s shown in Figu e 8a.
Acknowledgmen s:
The au ho s g a e ully acknowledge he inancial suppo o he Na ional Key Resea ch
and De elopmen P og am o China (2016YFC0600706). The au ho s would also like o hank Dong Liu,
Yongyong Zhou and Jing Yang o hei help.
Au ho Con ibu ions:
Xueyi Shang w o e he pape ; Xibing Li p o ided he o iginal idea and seismic da a;
A. Mo ales-Es eban and Gualbe o Asencio-Co és modi ied he pape and ga e some use ul sugges ions;
Zewei Wang w o e pa o he p og am code.
Con lic s o In e es : The au ho s decla e no con lic o in e es .
Re e ences
1.
Geo goulas, G.; Kons an a as, A.; Ka si a akis, E.; S ylios, C.D.; Ma a elakis, E.; Vach se anos, G.J.
“Seismic-mass” densi y-based algo i hm o spa io- empo al clus e ing. Expe Sys . Appl.
2013
,40, 4183–4189.
[C ossRe ]
2.
Fidani, C.; Ba is on, R.; Bu ge , W.J. A s udy o he co ela ion be ween ea hquakes and NOAA sa elli e
ene ge ic pa icle bu s s. Remo e Sens. 2010,2, 2170–2184. [C ossRe ]
3.
Zamani, A.; Hashemi, N. Compu e -based sel -o ganized ec onic zoning: A en a i e pa e n ecogni ion
o I an. Compu . Geosci. 2004,30, 705–718. [C ossRe ]
4.
Ha igan, J.A.; Wong, M.A. Algo i hm AS 136: A K-Means clus e ing algo i hm. J. R. S a . Soc. C-Appl.
1979
,
28, 100–108. [C ossRe ]
5.
Bu on, P.W.; Wea he ill, G.; Ka nawa i, D.; P amumijoyo, S. Seismic Haza d Assessmen and Zoning in Ja a:
New and Al e na i e P obabilis ic Assessmen Models. In P oceedings o he In e na ional Con e ence on
Ea hquake Enginee ing and Disas e Mi iga ion, Jaka a, Indonesia, 14–15 Ap il 2008.
6.
Wea he ill, G.; Bu on, P.W. Delinea ion o shallow seismic sou ce zones using K-means clus e analysis,
wi h applica ion o he Aegean egion. Geophys. J. In . 2009,176, 565–588. [C ossRe ]
7.
Wea he ill, G.; Bu on, P.W. An al e na i e app oach o p obabilis ic seismic haza d analysis in he Aegean
egion using Mon e Ca lo simula ion. Tec onophysics 2010,492, 253–278. [C ossRe ]
8.
Ramdani, F.; Ke ani, O.; Tadili, B. E idence o subduc ion benea h Gib al a A c and Andean egions om
k-means ea hquake cen oids. J. Seismol. 2015,19, 41–53. [C ossRe ]
9.
Rehman, K.; Bu on, P.W.; Wea he ill, G.A. K-means clus e analysis and seismici y pa i ioning o Pakis an.
J. Seismol. 2014,18, 401–419. [C ossRe ]
10.
Mo ales-Es eban, A.; Ma inez-Al a ez, F.; Sci o ski, S.; Sci o ski, R. A as pa i ioning algo i hm using
adap i e Mahalanobis clus e ing wi h applica ion o seismic zoning. Compu . Geosci.
2014
,73, 132–141.
[C ossRe ]
11.
Shang, X.Y.; Li, X.B.; Mo ales-Es eban, A.; Dong, L.J.; Peng, K. K-Means clus e o seismici y pa i ioning
and geological s uc u e in e p e a ion, wi h applica ion o he Yongshaba mine (China). Shock Vib.
2017
,
1–11. [C ossRe ]
12.
Wa dlaw, R.L.; F ohlich, C.; Da is, S.D. E alua ion o p ecu so y seismic quiescence in six een subduc ion
zones using single-link clus e analysis. Pu e Appl. Geophys. 1990,134, 57–78. [C ossRe ]
13.
F ohlich, C.; Da is, S.D. Single-Link clus e analysis as a me hod o e alua e spa ial and empo al p ope ies
o ea hquake ca alogues. Geophys. J. In . 1990,100, 19–32. [C ossRe ]
14.
Da is, S.D.; F ohlich, C. Single-Link clus e analysis, syn he ic ea hquake ca alogues, and a e shock
iden i ica ion. Geophys. J. In . 1991,104, 289–306. [C ossRe ]
15.
Hudyma, M.; Po in, Y.H. An Enginee ing App oach o Seismic Risk Managemen in Ha d ock Mines. Rock
Mech. Rock Eng. 2010,43, 891–906. [C ossRe ]
16.
Hashemi, S.N.; Mehdizadeh, R. Applica ion o hie a chical clus e ing echnique o nume ical ec onic
egionaliza ion o he Zag os egion (I an). Ea h Sci. In o m. 2015,8, 367–380. [C ossRe ]
17.
Kohonen, T. Sel -o ganized o ma ion o opologically co ec ea u e maps. Biol. Cybe n.
1982
,43, 59–69.
[C ossRe ]
Remo e Sens. 2018,10, 461 21 o 22
18.
Zamani, A.; Nedaei, M.; Boos ani, R. Tec onic zoning o I an based on sel -o ganizing map. J. Appl. Sci.
2009
,
9, 4099–4114. [C ossRe ]
19.
Zamani, A.; Khalili, M.; Ge ami, A. Compu e -based sel -o ganized ec onic zoning e isi ed: Scien i ic
c i e ion o de e mining he op imum numbe o zones. Tec onophysics 2011,510, 207–216. [C ossRe ]
20.
Moja ab, M.; Mema ian, H.; Za e, M.; Mo shedy, A.H.; Pishahang, M.H. Modeling o he seismo ec onic
p o inces o I an using he sel -o ganizing map algo i hm. Compu . Geosci. 2014,67, 150–162. [C ossRe ]
21.
Ramezani Besheli, P.; Za e, M.; Ramezani Umali, R.; Nakhaeezadeh, G. Zoning I an based on ea hquake
p ecu so impo ance and in oducing a main zone using a da a-mining p ocess. Na . Haza ds
2015
,78,
821–835. [C ossRe ]
22.
Ma ínez-Ál a ez, F.; Gu ié ez-A ilés, D.; Mo ales-Es eban, A.; Reyes, J.; Ama o-Mellado, J.;
Rubio-Escude o, C. A no el me hod o seismogenic zoning based on iclus e ing: Applica ion o he
Ibe ian Peninsula. En opy 2015,17, 5000–5021. [C ossRe ]
23.
Ansa i, A.; Noo zad, A.; Za a ani, H. Clus e ing analysis o he seismic ca alog o I an. Compu . Geosci.
2009
,
35, 475–486. [C ossRe ]
24.
Beni ez, H.D.; Flo ez, J.F.; Duque, D.P.; Bena ides, A.; Baque o, O.L.; Quin e o, J. Spa ial pa e n ecogni ion
o seismic e en s in Sou h Wes Colombia. Compu . Geosci. 2013,59, 60–77. [C ossRe ]
25.
Monem, M.J.; Hashemy, S.M. Ex ac ing physical homogeneous egions ou o i iga ion ne wo ks using
uzzy clus e ing me hod: A case s udy o he Ghaz in canal i iga ion ne wo k. J. Hyd oin o m.
2011
,13,
652–660. [C ossRe ]
26.
Mukhopadhyay, B.; Fnais, M.; Mukhopadhyay, M.; Dasgup a, S. Seismic clus e analysis o he
Bu mese-Andaman and Wes Sunda A c: Insigh in o subduc ion kinema ics and seismic po en iali y.
Geoma . Na . Haza ds Risk 2010,1, 283–314. [C ossRe ]
27.
Nanda, S.J.; Panda, G. Design o compu a ionally e icien densi y-based clus e ing algo i hms.
Da a Knowl. Eng. 2015,95, 23–38. [C ossRe ]
28.
Gu ié ez-A ilés, D.; Rubio-Escude o, C. Mining 3D pa e ns om gene exp ession empo al da a: A new
iclus e e alua ion measu e. Sci. Wo ld J. 2014, 624371. [C ossRe ] [PubMed]
29.
Gu ié ez-A ilés, D.; Rubio-Escude o, C.; Ma ínez-Ál a ez, F.; Riquelme, J.C. T iGen: A gene ic algo i hm
o mine iclus e s in empo al gene exp ession da a. Neu ocompu ing 2014,132, 42–53. [C ossRe ]
30.
Lesniak, A.; Isakow, Z. Space- ime clus e ing o seismic e en s and haza d assessmen in he
Zab ze-Bielszowice coal mine, Poland. In . J. Rock Mech. Min. 2009,46, 918–928. [C ossRe ]
31.
Kons an a as, A.J.; Ka si a akis, E.; Ma a elakis, E.; Skounakis, E.; Kokkinos, E.; Ka apidakis, E. In elligen
spa ial-clus e ing o seismici y in he icini y o he Hellenic Seismic A c. Ea h Sci. Res.
2012
,1, 1–10.
[C ossRe ]
32.
Baiesi, M.; Paczuski, M. Scale- ee ne wo ks o ea hquakes and a e shocks. Phys. Re . E
2004
,69, 066106.
[C ossRe ] [PubMed]
33.
Zaliapin, I.; Gab ielo , A.; Keilis-Bo ok, V.; Wong, H. Clus e ing analysis o seismici y and a e shock
iden i ica ion. Phys. Re . Le . 2008,101, 018501. [C ossRe ] [PubMed]
34.
Zaliapin, I.; Ben-Zion, Y. Asymme ic dis ibu ion o a e shocks on la ge aul s in Cali o nia. Geophys. J. In .
2011,185, 1288–1304. [C ossRe ]
35.
Zaliapin, I.; Ben-Zion, Y. Ea hquake clus e s in sou he n Cali o nia II: Classi ica ion and ela ion o physical
p ope ies o he c us . J. Geophys. Res.-Sol. EA 2013,118, 2865–2877. [C ossRe ]
36.
Zaliapin, I.; Ben-Zion, Y. Ea hquake clus e s in Sou he n Cali o nia I: Iden i ica ion and s abili y. J. Geophys.
Res.-Sol. EA 2013,118, 2847–2864. [C ossRe ]
37.
Zaliapin, I.; Ben-Zion, Y. A global classi ica ion and cha ac e iza ion o ea hquake clus e s. Geophys. J. In .
2016,207, 608–634. [C ossRe ]
38.
Zaliapin, I.; Ben-Zion, Y. Disc imina ing cha ac e is ics o ec onic and human-induced seismici y.
Bull. Seismol. Soc. Am. 2016,106, 846–859. [C ossRe ]
39.
Wang, S.; Gan, W.; Li, D.; Li, D. Da a ield o hie a chical clus e ing. In . J. Da a Wa ehous.
2011
,7, 43–63.
[C ossRe ]
40.
Wu, T. Image da a ield-based amewo k o image h esholding. Op . Lase Technol.
2014
,62, 1–11.
[C ossRe ]
41.
Li, X.B.; Wang, Z.W.; Dong, L.J. Loca ing single-poin sou ces om a i al imes con aining la ge picking
e o s (LPEs): The i ual ield op imiza ion me hod (VFOM). Sci. Rep. 2016,6, 1–12. [C ossRe ] [PubMed]

Remo e Sens. 2018,10, 461 22 o 22
42.
Shang, X.Y.; Li, X.B.; Mo ales-Es eban, A.; Dong, L.J. Enhancing mic o-seismic P-phase a i al picking:
EMD-cosine unc ion-based denoising wi h an applica ion o he AIC picke . J. Appl. Geophys
2018
,150,
325–337. [C ossRe ]
43.
Rousseeuw, P.J. Silhoue es: A g aphical aid o he in e p e a ion and alida ion o clus e analysis. J. Compu .
Appl. Ma h. 1987,20, 53–65. [C ossRe ]
44.
K zanowski, W.J.; Lai, Y.T. A c i e ion o de e mining he numbe o g oups in a da a se using
sum-o -squa es clus e ing. Biome ics 1988,44, 23–34. [C ossRe ]
45.
Hudyma, M. Analysis and In e p e a ion o Clus e s o Seismic E en s in Mines. Ph.D. Thesis, Uni e si y o
Wes e n Aus alia, C awley, Aus alia, 2008.
46.
Aswegen, G.; Bu le , A.G. Applica ions o quan i a i e seismology in Sou h A ican gold mines. In P oceedings
o he In e na ional Symposium on Rockbu s s and Seismici y in Mines, Kings on, ON, Canada,
16–18 Augus 1993.
47. Mendecki, D.A.J. Seismic Moni o ing in Mines; Chapman & Hall: London, UK, 1997; ISBN 0412753006.
48.
Liu, J.P.; Feng, X.T.; Li, Y.H.; Xu, S.D.; Sheng, Y. S udies on empo al and spa ial a ia ion o mic oseismic
ac i i ies in a deep me al mine. In . J. Rock Mech. Min. 2013,60, 171–179. [C ossRe ]
49.
Li, Y.; Yang, T.H.; Liu, H.L.; Wang, H.; Hou, X.G.; Zhang, P.H.; Wang, P.T. Real- ime mic oseismic moni o ing
and i s cha ac e is ic analysis in wo king ace wi h high-in ensi y mining. J. Appl. Geophys.
2016
,132, 152–163.
[C ossRe ]
©
2018 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access
a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion
(CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).