A Compa ison o Machine Lea ning Techniques Applied
o Landsa -5 TM Spec al Da a o Biomass Es ima ion
Pabli o M. L´opez-Se ano1,Ca losA. L´opez-S´anchez2,JuanG.
´Al a ez-Gonz´alez3, and Jo ge Ga c´ıa-Gu i´e ez4,*
1Ciencias Ag opecua ias y Fo es ales, Uni e sidad Ju´a ez del Es ado de Du ango, Neg e e 800, Cen o, 34000 Du ango,
Dgo., Mexico
2Ins i u o de Sil icul u a e Indus ia de la Made a, Uni e sidad Ju´a ez del Es ado de Du ango, Uni e sidad Ju´a ez del
Es ado de Du ango, Neg e e 800, Cen o, 34000 Du ango, Dgo., Mexico 3Depa amen o de Ingenie ´ıa Ag o o es al,
Uni e sidad de San iago de Compos ela, A enida D . ´Angel Eche e i, s/n. Campus Vida, 15782 San iago de Compos ela, C,
Spain
4Depa amen o de Lenguajes y Sis emas In o m´a icos, Uni e sidad de Se illa, Reina Me cedes s/n., Se illa 41012, Spain
Abs ac . Machine lea ning combines induc i e and au oma ed echniques o ecognizing pa e ns. These echniques can be
used wi h emo e sensing da ase s o map abo eg ound biomass (AGB) wi h an accep able deg ee o accu acy o e alua ion and
managemen o o es ecosys ems. Un o una ely, s a is ically igo ous compa isons o machine lea ning algo i hms a e sca ce.
The aim o his s udy was o compa e he pe o mance o he 3 mos common nonpa ame ic machine lea ning echniques
epo ed in he li e a u e, is., Suppo Vec o Machine (SVM), k-nea es neighbo (kNN) and Random Fo es (RF), wi h ha o
he pa ame ic mul iple linea eg ession (MLR) o es ima ing AGB om Landsa -5 Thema ic Mappe (TM) spec al e lec ance
da a, ex u e ea u es de i ed om he No malized Di e ence Vege a ion Index (NDVI), and opog aphical ea u es de i ed om
a digi al ele a ion model (DEM). The esul s ob ained o 99 pe manen si es ( o calib a ion/ alida ion o he models) es ablished
du ing he win e o 2011 by sys ema ic sampling in he s a e o Du ango (Mexico), showed ha SVM pe o med bes once he
pa ame e iza ion had been op imized. O he wise, SVM could be ou pe o med by RF. Howe e , he kNN yielded he bes o e all
esul s in ela ion o he goodness-o - i measu es. The indings con i m ha nonpa ame ic machine lea ning algo i hms a e
powe ul ools o es ima ing AGB wi h da ase s de i ed om senso s wi h medium spa ial esolu ion.
R´
esum´
e. L’app en issage au oma ique combine des echniques induc i es e au oma is´
ees pou la econnaissance des o mes.
Ces echniques peu en ˆ
e e u ilis´
ees a ec des ensembles de donn´
ees de ´
el´
ed´
e ec ion pou ca og aphie la biomasse a´
e ienne «
abo eg ound biomass » (AGB) a ec un deg ´
edep
´
ecision accep able pou l’´
e alua ion e la ges ion des ´
ecosys `
emes o es ie s.
Malheu eusemen , des compa aisons s a is iquemen igou euses des algo i hmes d’app en issage au oma ique son a es. Le
bu de ce e ´
e ude ´
e ai de compa e les pe o mances des 3 m´
e hodes d’app en issage au oma ique non pa am´
e iques les plus
´
equemmen appo ´
ees dans la li ´
e a u e, is., les machines `
a ec eu s de suppo « Suppo Vec o Machine » (SVM), les k
plus p oches oisins « k-nea es neighbo » (kNN) e les o ˆ
e s al´
ea oi es « Random Fo es » (RF), a ec celle de la ´
eg ession
lin´
eai e mul iple pa am´
e ique (MLR) pou l’es ima ion de l’AGB p o enan des donn´
ees de ´
e lec ance spec ale de Landsa -5
Thema ic Mappe (TM), des ca ac ´
e is iques de ex u e d´
e i ´
ees de l’indice de ´
eg´
e a ion pa di ´
e ence no malis´
ee « No malized
Di e ence Vege a ion Index » (NDVI) e des ca ac ´
e is iques opog aphiques d´
e i ´
ees d’un mod`
ele num´
e ique de e ain « digi al
ele a ion model » (DEM).Les ´
esul a s ob enus pou 99 si es pe manen s (pou la calib a ion/ alida ion des mod`
eles) ´
e ablis au
cou s de l’hi e 2011 pa l’´
echan illonnage sys ´
ema ique dans l’ ´
E a de Du ango (Mexique), on mon ´
e que les SVM mon en
leu s meilleu es pe o mances une ois que le pa am´
e age a ´
e ´
e op imis´
e. Pa ailleu s, les SVM pou aien ˆ
e e su pass´
ees pa les
RF. Cependan , les kNN on donn´
e les meilleu s ´
esul a s globaux pa appo aux mesu es d’ajus emen . Les ´
esul a s con i men
que les algo i hmes d’app en issage au oma ique non pa am´
e iques son des ou ils puissan s pou l’es ima ion de l’AGB a ec
des ensembles de donn´
ees p o enan de cap eu s a ec une ´
esolu ion spa iale moyenne.
INTRODUCTION
Fo es biomass plays an impo an ole in he global clima e
sys em because o es ecosys ems abso b app oxima ely 1/12
*Co esponding au ho e-mail: [email p o ec ed].
o Ea h’s a mosphe ic ca bon s ocks e e y yea (Malhi e al.
2002), and much o his ca bon is s o ed as abo eg ound biomass
(AGB). The impo ance o o es biomass has been unde -
lined by he Uni ed Na ions F amewo k Con en ion on Clima e
Change (UNFCCC), which has iden i ied AGB as an Essen-
ial Clima e Va iable (GCOS 2010). Mo eo e , quan i ica ion
o AGB and modeling o he associa ed dynamics a e impo an
o suppo decision-making models in di e en ields, includ-
ing ene gy and ma e ials p o ision o human use (FAO 2001,
2006), o es agmen a ion (e.g., Malhi and Phillips 2004), and
biodi e si y conse a ion (e.g., Bunke e al. 2005). Accu a e
moni o ing o o es biomass and how i changes a local o
global scales is, he e o e, o c i ical impo ance owa d a be e
unde s anding o hese p ocesses (Lu 2006; Ha ig e al. 2012;
Le Toan and Quegan 2015).
The mos accu a e me hod o es ima ing o es biomass is
based on ield measu emen s; howe e , es ima ing biomass in
la ge a eas is no an easy ask and is hinde ed by he high cos s
(bo h ime and money) associa ed wi h ieldwo k (Lu e al.
2016).
Remo e sensing has been shown o be a p ac ical op ion ha
helps o o e come hese limi a ions because i enables ob aining
o es in o ma ion in la ge a eas wi h easonable e o . This is
now he p ima y da a sou ce o la ge-scale biomass es ima ion
(e.g., Ande sen e al. 2011; Lu e al. 2016). O e he pas ew
decades, he so-called passi e senso s (i.e., senso s ha use
he sola adia ion e lec ed o emi ed by he objec s de ec ed
a Ea h’s su ace) ha e been used o es ima e AGB (e.g., Lu
e al. 2012; F azie e al. 2014). Conside ing he ad an ages and
limi a ions o di e en emo e sensing images, he medium-
esolu ion (pixel size, 30 m) Landsa -5 TM senso is one o
he mos widely used o biomass es ima ion (e.g., Aga wal
e al. 2014; P lugmache e al. 2014; Dube and Mu anga 2015;
Zhu and Liu 2015). The ad an ages o using he Landsa -5 TM
senso o e high- esolu ion senso s, pa icula ly o analysis o
la ge ´
a eas, a e ha nume ous his o ical spa io empo al a chi es
a e a ailable (images since 1972) and he Landsa da a is ee
o cos o use s. Fo a e iew o Landsa image y-based AGB
es ima ions, see Wu e al. (2016).
Rega dless o hep ype o senso used, model accu acy and
e o es ima ion a y in ela ion o a se ies o ac o s such as
he s uc u e o he ield da a and he s a is ical echniques used
(Ghosh e al. 2014). The mos common model used in es ima ing
o es biomass om emo e sensing da a is he eg ession-based
model (e.g., Tian e al. 2012; Lu e al. 2012; Næsse e al. 2013);
howe e , he accu acy o es ima es ob ained wi h small num-
be s o sample plo s o when he e is a weak linea ela ionship
be ween a iables and biomass is a he low (Lu e al. 2016).
Nonpa ame ic modeling app oaches, which make no assump-
ions abou he s a is ical dis ibu ions o he o iginal da a and
ela ionships be ween p edic o and esponse a iables, ha e
also been used o ela e AGB and emo ely sensed ea u es.
Va ious ecen s udies ha e explo ed he use o nonpa ame ic
app oaches o es ima ing AGB wi h emo e sensing da a (e.g.,
B eidenbach e al. 2012; Mu anga e al. 2012; Jung e al. 2013;
Fassnach e al. 2014).
Machine lea ning in ol es di e en echniques (mainly non-
pa ame ic) ha ocus on au oma ed and induc i e lea ning o
ecognize pa e ns (C acknell and Reading 2014) in da a (e.g.,
pa e ns in emo e sensing da a ela ed o AGB in a se o loca ed
plo s); once he pa e n is lea ned, i can be applied o yield a
p edic ion o classi ica ion in a eas whe e i is no possible o
ca y ou ieldwo k o quan i y an objec i e a iable (e.g., AGB).
In he las decade, a ious machine lea ning echniques such as
Suppo Vec o Machine (SVM), k-nea es neighbo (kNN) and
Random Fo es (RF) ha e been used o de elop p edic i e mod-
els o AGB in la ge a eas. Thus, Sha aee (2013) showed ha
kNN pe o med be e han SVMs, RF, and A i icial Neu al
Ne wo ks (ANN) o es ima ing biophysical a iables such as
basal a ea. Mo e ecen ly, Ga cia-Gu ie ez e al. (2015) showed
ha SVM models pe o med bes o es ima ing o es a iables
om Ligh De ec ion and Ranging (LIDAR), while Wang e al.
(2016) showed ha RF ou pe o med SVM and ANN o es-
ima ing whea biomass om emo e sensing da a. Fo a mo e
comple e e iew o esea ch being ca ied ou o e ie e ege a-
ion biomass om emo e sensing da a, using machine lea ning
me hods, see Ali e al. (2016).
The goodness-o - i p o models de i ed om spec al da a
a e usually e alua ed by he coe icien o de e mina ion (R2)
and he oo mean squa e e o (RMSE). These measu es epo
he pe o mance o he model in p edic ing he da a used o i
he model; howe e , because he quali y o he i does no nec-
essa ily e lec he quali y o he p edic ion, assessmen o hei
alidi y is o en needed o ensu e ha he p edic ions ep esen
he mos likely ou come in he eal wo ld (Yang e al. 2004). The
only me hod ha can be ega ded as “ ue” alida ion in ol es
he use o a new independen da ase (P e zsch e al. 2002; Yang
e al. 2004); howe e , he sca ci y o such da a o ces he use
o al e na i e app oaches, such as C oss Valida ion (CV), o en-
able e alua ion o he quali y o a pa icula i ing echnique
and minimize he isk o o e i ing (Molina o e al. 2005). Un-
o una ely, mos s udies in ol ing es ima ion o AGB do no
use CV as pa o he model de elopmen .
Fo igo ous compa ison o he pe o mance o di e en ma-
chine lea ning echniques, he s udy should also be accompa-
nied by s a is ical alida ion o he esul s wi hin a s a is ical
amewo k (i.e., no me ely calcula ing s a is ics such as R2o
RMSE). Al hough his is well known in he ield o machine
lea ning (Ga c´
ıa e al. 2010), his ype o alida ion is no com-
mon in emo e sensing, e en hough machine lea ning plays an
impo an ole in many biomass es ima ion s udies. This ac
migh ha e led o some deg ee o disco dance in he scien i ic
li e a u e, in which we can ind examples o kNN, SVM, and
RF ou pe o ming each o he (Sha aee 2013; Ga cia-Gu ie ez
e al. 2015; Wang e al. 2016).
The objec i e o his s udy was o analyze and s a is ically
compa e he pe o mance o 3 nonpa ame ic echniques (SVM,
kNN, and RF) and he pa ame ic Mul iple Linea Reg ession
(MLR) echnique o es ima ing AGB. The echniques we e
es ed wi h Landsa -5 TM su ace spec al e lec ance da a, ex-
u e ea u es de i ed om he No malized Di e ence Vege a-
ion Index (NDVI), and opog aphical ea u es de i ed om
a digi al ele a ion model (DEM) in he Sie a Mad e Occi-
FIG. 1. Geog aphical loca ion o he s udy si e and sample plo s used in he s udy.
den al (s a e o Du ango, Mexico). The esul s ob ained wi h
each echnique we e compa ed a e applica ion o CV and pos-
e io s a is ical alida ion o he mean ankings ob ained o
each.
MATERIAL AND METHODS
S udy A ea
The s udy si e is loca ed in he Sie a Mad e Occiden al, in
he no h o he s a e o Du ango (Mexico), and co e s an a ea
o 1,142,916 ha (Figu e 1). The clima e is humid empe a e,
wi h ain all in summe ( ela i e humidi y, 50.1%). The a e age
empe a u e anges om 8 ◦C o20◦C, and he annual p ecipi-
a ion is om 400 mm o 1200 mm. The a e age al i ude abo e
sea le el in his a ea is 1,900 m. The ege a ion comp ises pine,
oak, Douglas i , pine-oak, and oak-pine o es , acco ding o he
desc ip ion in he Land Use and Vege a ion Co e Cha , scale
1:250,000, Se ies V (INEGI 2012). The o es s a e basically
mixed and une en-aged pine-oak s ands, wi h a canopy co e
anging om 32% o 100%. These o es s ha e been subjec o
selec i e ha es ing o almos a cen u y o p o ide a mix u e o
se ices o local communi ies. This s uc u e is he esul o he
managemen his o y, which has depended on land owne ship
and he economic and social changes ha ha e aken place in
he s a e, as well as na u al condi ions (Wehenkel e al. 2011).
Da ase
Field Da a
A ne wo k o 99 pe manen sampling plo s was es ablished
du ing he win e o 2011, ollowing he me hod desc ibed by
Co al-Ri as e al. (2009). The plo s we e loca ed by sys ema ic
sampling (wi h some excep ions o a oid non o es ed a eas) o a
g id o equidis an poin s sepa a ed by 3 km o 5 km, depending
on he accessibili y, which is limi ed by he ugged e ain o
he s udy a ea. In each plo (squa es o side 50 m), all species
o ees we e eco ded and he diame e s a b eas heigh (cm)
and o al heigh (m) o all s anding ees we e measu ed.
Species-speci ic indi idual ee models de eloped by Va gas-
La e a (2013) we e used o es ima e he o al AGB o ield plo s
by ee alue agg ega ion. The R2and he RMSE o he mod-
els used anged om 0.87 kg–0.99 kg and 22.8 kg–95.2 kg,
espec i ely. The mean, minimum, maximum and s anda d de-
ia ion o he AGB alues pe hec a e o he sample plo s a e
summa ized in Table 1.
Spec al Da a
The spec al da a we e de i ed om a sa elli e image
Landsa -5 TM ob ained in Ap il 2011 (pa h 32, ow 42) and
co e ing he en i e s udy ´
a ea.1Landsa -5 TM da a ha e a
1A ailable om he US Geological Se ice webpage, a
h p://glo is.usgs.go /
TABLE 1
To al biomass s a is ics exp essed in Mg ha−1
No. o
Obse a ions Mean
S anda d
De ia ion
Minimum
Value
Maximum
Value
99 89.03 43.45 2.70 234.03
spa ial esolu ion o 30 m wi h a e isi pe iod o 16 days.
Bands 1, 2, 3, 4, 5, and 7 (le el L1T) o Landsa -5 TM we e
used in he p esen s udy; band 6 was no used because o i s
he mal cha ac e is ics, i s coa se spa ial esolu ion (120 m), and
he low con as in he o es a ea (NASA 2011). The sa elli e
images we e adiome ically, a mosphe ically, and opog aphi-
cally co ec ed by using he ATCOR3 Rmodule (Geosys ems
2013), ega ded as pa icula ly sui able o moun ainous zones.
The ATCOR3 Rmodule i s calcula es he adiance a senso
le el (W s −1m−2) om he image pixel. Se e al inpu pa-
ame e s we e equi ed o his calcula ion and we e e ie ed
om he image me ada a (heade ile): da e o acquisi ion, scale
ac o s, geome y (sola zeni h angle and sola azimu h), and
o he in o ma ion abou he senso calib a ion ile (“gain and
bias”). O he pa ame e s we e adjus ed by aking in o accoun
he cha ac e is ics o he inpu da ase s and he condi ions o he
image y da es, e.g., isibili y (35 km), pixel size o he DEM
(15 m), ae osol ype ( u al), among o he s. Because he image
was cloudless and no sui able wa e apo bands we e a ailable,
dehazing/cloud emo al and a mosphe ic wa e e ie al se ings
we e kep as “de aul ,” which, in his case, is ecommended by
he ATCOR3 RUse Manual (Geosys ems 2013). The co ec-
ions we e implemen ed wi h he ERDAS RIMAGINE R2013
so wa e. (ERDAS Inc. 2014). A numbe o ege a ion indices
we e compu ed om he a mosphe ically and opog aphically
co ec ed image bands and included in he biomass es ima ion
models o e alua ion as possible eg esso ea u es (Table 2).
Tex u e Fea u es
The ex u e ea u es homogenei y, con as , dissimila i y,
mean, s anda d de ia ion, en opy, second-o de angula mo-
men , and co ela ion (Ha alick e al. 1973) we e calcula ed
om he NDVI image based on g ey le el cooccu ence ma-
ices, wi h he aim o including in o ma ion combining he
spa ial and spec al domain o he emo ely sensed image y in
he biomass es ima ion models. We used NDVI ex u e ea u es
a he han each spec al band o Landsa -5 TM o a oid sa -
u a ing high biomass alues (Mu anga and Skidmo e 2004).
Because i also becomes mo e di icul o ob ain an op imal sub-
se as he numbe o a ibu es inc eases, we he e o e aimed
o a comp omise be ween quan i y and quali y. The ea u es
we e calcula ed using PCI Geoma ica2013 Rso wa e,2and 3
2PCI Geoma ics Inc. 2013
TABLE 2
Fea u es (independen a iables) o biomass es ima ion in
compa ison o machine lea ning echniques
Abb e ia ion Va iable Re e ence
Vege a ion Index
NDVI No malized Di e ence
Vege a ion Index
Rouse e al.
(1974)
MSAVI2 Modi ied Soil-Adjus ed
Vege a ion Index
Qi e al. (1994)
SAVI Adjus ed Soil Vege a ion
Index
Hue e (1988)
IAF Lea A ea Index Ba e and Guyo
(1991)
ALB Albedo As a (1989)
Fpa F ac ion o
Pho osyn he ically
Ac i e Radia ion
As a e al.
(1984)
FSR Flow Sola Radia ion B u sae s (1975)
Tex u e (NDVI)
HOL Homogenei y Ha alick e al.
(1973)
CO Con as
DI Dissimila i y
ME Mean
STD S anda d De ia ion
EN En opy
ASM Angula Second Momen
CR Co ela ion
Te ain (DEM)
Al i ude Al i ude
B Slope
TRASP T ans o med Aspec Robe s and
Coope (1989)
TSI Te ain Shape Index McNab (1989)
WI We ness Index Moo e and
Niebe (1989)
PC P o ile Cu a u e Wilson and
Gallan (2000)
PLC Plan Cu a u e
CCu a u e
di e en scales o ope a ion we e conside ed by using mo ing
window sizes o 3 ×3pixels,5×5 pixels, and 7 ×7pixels
(Table 2).
Te ain Fea u es
Te ain ea u es a e di ec ly ela ed o o es species compo-
si ion, ee heigh g ow h, and o he o es s and a iables, en-
abling hese o be modeled (McNab 1989; Robe s and Coope
1989). Fi s - and second-o de e ain ea u es we e, he e o e,
de i ed om he 5 ×5-pixel low pass il e ed DEM o he s udy
a ea wi h a spa ial esolu ion o 15 m. The DEM was de i ed
om LIDAR da a and co esponds o an a ay o ele a ion da a
in e pola ed o 15 m esolu ion om he coo dina es o he las
e u n o he pulses emi ed (INEGI 2014). The inal se o ea-
u es de i ed om Landsa -5 TM senso and om he DEM,
which we e used as possible p edic o s (independen a iables)
o es ima ing AGB (which played he ole o dependen a i-
able), a e shown in Table 2.
Finally, he sample plo s we e geoposi ioned wi h he aim o
ex ac ing he pixel alue a e age wi h an associa ed bu e o
25 m o each desc ibed ea u e, o ob ain a da abase wi h he
mean biomass alues and he associa ed ea u es o each plo .
The ex ac ion was ca ied ou using R s a is ical so wa e (R
Co e Team 2014) and he “ as e ” package.
Compa ison F amewo k
Machine Lea ning Techniques
Th ee nonpa ame ic machine lea ning echniques and one
pa ame ic echnique we e applied o da a om he s udy a ea
in o de o compa e hei pe o mance: (i) k-Nea es Neigh-
bou (kNN), (ii) Suppo Vec o Machine (SVM), (iii) Random
Fo es (RF), and (i ) Mul iple Linea Reg ession (MLR). All
hese echniques we e used o es ima e AGB, using as possible
p edic o s he a iables included in Table 2.
The pa ame ic MLR echnique is he mos commonly used
in his kind o s udy (Fassnach e al. 2014). Mo eo e , his
ype o model is easy o unde s and and is widely used in mos
scien i ic disciplines. Howe e , unlike he nonpa ame ic ap-
p oaches, MLR elies on ce ain assump ions, such as he un-
damen al leas squa es assump ion o independence and equal
dis ibu ion o e o s wi h ze o mean and cons an a iance,
which can be iola ed by ac o s such as nonno mali y o a i-
ables, mul icollinea i y o a iables, and he e oscedas ici y o
e o a iance.
Nea es neighbo (NN), a well-known machine lea ning ech-
nique used in emo e sensing (Sha aee 2013), makes a p edic ion
by using he in o ma ion abou he neighbo s o he ins ance o
be eg essed (Co e and Ha 1967). The NN depends on a
pa ame e , usually called k, which de e mines he numbe o
neighbo s used by he algo i hm. The echnique is he e o e
usually called kNN when mo e han one neighbo is used. Al-
hough he idea behind his ype o echnique is qui e in ui i e,
he esul ing model is no easy o in e p e because all esul s
depend on a aining se .
SVMs ha e been de eloped om a i icial neu al ne wo ks
(Co es and Vapnik 1995) and ha e been used in many scien i ic
ields (e.g., Abedi e al. 2012; Bayoudh e al. 2015; Ga cia-
Gu ie ez e al. 2015). SVM models a e de eloped by a se
o ec o s (o hype planes i g ea e dimension is eques ed)
ha sepa a e ins ances o di e en labels (classi ica ion) o
minimize he mean e o ( eg ession). Ke nel unc ions a e used
o o e come he limi a ions associa ed wi h linea sepa abili y
in SVM models. App op ia e selec ion o he ke nel unc ion
and he ke nel egula iza ion pa ame e s is impo an in ela ion
o he SVM model beha io , which can make his ype o ech-
nique mo e di icul o implemen o use s. As wi h kNN, he
models p oduced using SVM a e mo e di icul o in e p e han
hose o MLR.
RF is no exac ly a classi ica ion o eg ession echnique, bu
a combina ion o o he echniques, mainly eg ession o clas-
si ica ion ees (B eiman 2001). The success o his echnique
is based on he use o nume ous ees, de eloped wi h di e -
en independen a iables ha a e andomly selec ed om he
comple e o iginal se o ea u es (e.g., Deschamps e al. 2012;
Wang e al. 2016). The numbe o p edic o s used by ees and
he numbe o ees a e es ablished by he use s.
WEKA open sou ce so wa e (Hall e al. 2009) was used o
implemen all o he echniques compa ed. Thus, linea eg es-
sion was used o MLR, IBk o kNN, SMO eg wi h polynomial
and Gaussian ke nels o SVM, and an adap a ion o he RF im-
plemen a ion o WEKA o eg ession (using M5P as he basic
eg ession echnique o he de elopmen o his ensemble).
Fea u e Selec ion, Pa ame e iza ion and Valida ion
In machine lea ning, spu ious da a ea u es mus be emo ed
be o e a model is gene a ed (Hall 1999). Thus, he a iables
ha a e po en ially mos impo an a e selec ed. Some ech-
niques (e.g., SVM and RF) ca y ou his selec ion, bu o he s
migh be se iously a ec ed by excessi ely la ge combina ions
o a iables (e.g., he Hughes e ec [Hughes 1968] in kNN and
mul icollinea i y in MLR). This is a common si ua ion in his
ype o analysis because o he la ge se o p edic o a iables
ha can be calcula ed om emo e sensing da a (Packal´
en e al.
2012). Mo eo e , co ec unc ioning o di e en machine lea n-
ing echniques depends on a p ope pa ame e iza ion (se -up o
hei pa ame e s, i.e., a iables ha modi y he beha io o he
machine lea ning echniques). In his s udy, bo h o hese s eps
( ea u e selec ion and pa ame e iza ion) we e ca ied ou ia
a me aheu is ic sea ch (Samadzadegan e al. 2012). F om he
possible me aheu is ic echniques (i.e., a me hod o op imiza-
ion ha p o ides a nea -op imal solu ion in compu a ionally
a o dable ime), we selec ed an e olu iona y algo i hm, which
is illus a ed in Figu e 2. The algo i hm s a s wi h a popula ion
o andom solu ions (Ini ial Popula ion in Figu e 2) called in-
di iduals and anks hem acco ding o i ness o he indi iduals
(Fi ness So ing in Figu e 2). In he p esen s udy, he i ness
was e alua ed by he RMSE ob ained wi h a aining se . A new
popula ion o indi iduals is hen c ea ed by ma ing pa en s ( an-
dom selec ion o coe icien s shown in Figu e 2), selec ed wi h
a p obabili y p opo ional o hei i ness, and la e mu a ing he
new indi iduals wi h a gi en p obabili y (in his case, a alue
will be andomly selec ed and changed o a new andom alue,
as can be seen in Figu e 2).

FIG. 2. Desc ip ion o he e olu iona y p ocedu e used o de e mine he bes me hods o pa ame e iza ion and ea u e selec ion.
TABLE 3
In e als used by he e olu iona y algo i hm o sea ch o he
di e en op imal pa ame e s∗
Technique Name Minimum Maximum
kNN k 1 20
SVM GAMMA (Gaussian-
ke nel-only)
0.01 2.0
EXP (Polynomial-
ke nel-only)
15
C 1 100
EPSILON 0.0 0.2
RF NT 1 100
NF 1 5
∗No e: k =numbe o neighbo s; EPSILON =de e mines he isk o
o e i ing; GAMMA =con ols he ans o ma ion p oduced by he
ke nel; EXP =ke nel’s exponen ; C =penal y ac o pe ins ance o
misclassi ica ion in aining; NT =numbe o ees ha o m each
ensemble; NF =numbe o a ibu es selec ed o cons uc ing each
ee
The gene al scheme desc ibed in Figu e 2 was modi ied
sligh ly acco ding o he speci ic eg ession echnique. Thus,
we used a speci ic design o MLR (see Ga c´
ıa-Gu i´
e ez e al.
2014) and an adap a ion o he gene ic algo i hm o Huang and
Wang (2006) o he nonpa ame ic echniques (kNN, SVM, and
RF). In he kNN me hod, pu e selec ion (coe icien s associa ed
wi h each ea u e as 1 o 0 depending on whe he he p edic o
is selec ed o no ) was subs i u ed by weigh ing each a ibu e
( eal alue be ween 0.0 and 1.0), which enables be e adap a-
ion o he algo i hm o he cha ac e is ics o kNN (see Ma eos
e al. 2012). In SVMs, he ype o ke nel is ano he pa ame e
o be op imized and had 2 possible alues ( adial basis unc ion
and polynomial). The pa ame e s op imized o each machine
lea ning echnique a e included in Table 3.
Fo compa ison o he di e en echniques, alida ion was
based on he lea e-one-ou CV echnique. This is a special case
o k- old CV in which kis equal o he numbe o obse a ions
and a p edic ion is ob ained as many imes as he e a e obse -
a ions in he da ase (Packal´
en e al. 2012). In o he wo ds, an
obse a ion is excluded ( a ge obse a ion), and a p edic ion is
compu ed wi h he o he obse a ions ( e e ence obse a ions).
The p edic ion can be e alua ed by he a ge obse a ion. This
p ocedu e is epea ed o e e y single obse a ion. The inal
quali y o a echnique e alua ed wi h CV is based on he a e -
aged e o ob ained. A gene al desc ip ion o he p ocedu e is
p o ided in Figu e 3.
Pa ame e iza ion o each submodel a he di e en s ages
o he CV was epea ed 5 imes o each echnique o p e-
en skew (due o he andom na u e o he e olu iona y
algo i hms applied o p edic o selec ion and pa ame e iza-
ion). The bes submodel and he a e age submodel o he 5
FIG. 3. Desc ip ion o he lea e-one-ou CV e alua ion o he echniques compa ed in he ex .
FIG. 4. Rela i e equency o ocu ence (impo ance) o each a ibu e in he bes models ob ained by each echnique (in e ms o
he sum o esiduals).
execu ions, anked in e ms o he RMSE eached in he e o-
lu iona y p ocedu e, we e used o calcula e he goodness-o - i
s a is ics.
S a is ical Analysis
The e o o he p edic ions in he CV was compa ed o each
echnique in e ms o R2and RMSE. In addi ion, o s a is ical
analysis o di e ences be ween he me hods, he absolu e e o s
o he p edic ions made by each echnique h oughou he 99
i e a ions in he CV we e compa ed ( he numbe o i e a ions is
equal o he numbe o ins ances in he da abase, which, in his
case, e e s o he 99 plo s a ailable). In heo y, his should be
ca ied ou by Analysis o Va iance (ANOVA), i he da a com-
ply wi h he unde lying assump ions o independence, no mal-
i y, and homoscedas ici y equi ed o pa ame ic es s. These
condi ions can be es ed by, espec i ely, he Shapi o-Wilk es ,
Lillie o ’s es , and Le enes’ es . I he da a do no comply wi h
hese condi ions, a nonpa ame ic es such as he F iedman’s
(aligned) es (desc ibed by Ga c´
ıa e al. 2010) should be used.
F iedman’s (aligned) es i s ob ains he mean anking o
each echnique by aking in o accoun he posi ion ob ained o
FIG. 5. Rela i e equency o ocu ence (impo ance) in he a e aged models ob ained by each echnique (in e ms o he sum o
esiduals).
FIG. 6. Absolu e equency o ela i e posi ion achie ed by each echnique ( anking) wi h he bes pa ame e iza ion o 5 execu ions.
FIG. 7. Absolu e equency o he ela i e posi ion achie ed ( anking) by each echnique wi h a e age pa ame e iza ion.
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