A Comparison of Machine Learning Techniques Applied to Landsat-5 TM Spectral Data for Biomass Estimation

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. 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