Analyzing physics-inspired metaheuristic algorithms in feature selection with K-Nearest-Neighbor

Ci a ion: P iyada shini, J.; P emala ha, M.; ˇ Cep, R.; Jayasudha, M.; Kali a, K. Analyzing Physics-Inspi ed Me aheu is ic Algo i hms in Fea u e Selec ion wi h K-Nea es -Neighbo . Appl. Sci. 2023,13, 906. h ps:// doi.o g/10.3390/app13020906 Academic Edi o s: Juan A. Gómez-Pulido and Michele Gi olami Recei ed: 12 Sep embe 2022 Re ised: 30 Decembe 2022 Accep ed: 6 Janua y 2023 Published: 9 Janua y 2023 Copy igh : © 2023 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 ps:// c ea i ecommons.o g/licenses/by/ 4.0/). applied sciences A icle Analyzing Physics-Inspi ed Me aheu is ic Algo i hms in Fea u e Selec ion wi h K-Nea es -Neighbo Jaya aju P iyada shini 1, Ma iappan P emala ha 1, Robe ˇ Cep 2, Mu ugan Jayasudha 1and Kanak Kali a 3,* 1School o Compu e Science and Enginee ing, Vello e Ins i u e o Technology, Chennai 600027, India 2Depa men o Machining, Assembly and Enginee ing Me ology, Facul y o Mechanical Enginee ing, VSB-Technical Uni e si y o Os a a, 17. Lis opadu 2172/15, 708 00 Os a a, Czech Republic 3Depa men o Mechanical Enginee ing, Vel Tech Ranga ajan D . Sagun hala R&D Ins i u e o Science and Technology, A adi 600062, India *Co espondence: [email p o ec ed] Abs ac : In ecen yea s, ea u e selec ion has eme ged as a majo challenge in machine lea ning. In his pape , conside ing he p omising pe o mance o me aheu is ics on di e en ypes o applica ions, six physics-inspi ed me apho algo i hms a e employed o his p oblem. To e alua e he capabili y o dimensionali y educ ion in hese algo i hms, six di e se-na u ed da ase s a e used. The pe o mance is compa ed in e ms o he a e age numbe o ea u es selec ed (AFS), accu acy, i ness, con e gence capabili ies, and compu a ional cos . I is ound h ough expe imen s ha he accu acy and i ness o he Equilib ium Op imize (EO) a e compa a i ely be e han he o he s. Finally, he a e age ank om he pe spec i e o a e age i ness, a e age accu acy, and AFS shows ha EO ou pe o ms all o he algo i hms. Keywo ds: op imiza ion; non- adi ional algo i hms; ea u e educ ion; KNN; algo i hms 1. In oduc ion Da a mining is he p ocess o inding meaning ul in o ma ion o ex ac ing knowledge om la ge amoun s o da a. Da a mining has he challenging p oblem o dealing wi h huge da a dimensions. When wo king wi h da a ha has a la ge numbe o dimensions, e en he ad an ages o echnology can be a hassle [ 1 ]. The da a-mining p ocess may su e due o a huge numbe o dimensions. I may also equi e a lo o compu ing ime and space. T adi ional machine-lea ning (ML) me hods canno handle hese huge da ase s [ 2 ]. The da ase is made up o se e al samples ha collec i ely gi e in o ma ion abou a speci ic case o he p oblem. Each sample has a a ie y o a ibu es o ea u es. The da ase may ha e se e al supe luous o duplica e a ibu es, in addi ion o i s huge dimensionali y. The model may be complex, and he da ase may include a subs an ial amoun o noise. The bes subse o he use ul ea u es ha will con ibu e o he ou pu is chosen ia a p e-p ocessing echnique called ea u e selec ion (FS) [ 2 ]. FS can educe he aining ime as well as he huge numbe o dimensions in he da a. Mo eo e , he model’s accu acy is enhanced in addi ion o he simpli ica ion o he model and he bes u iliza ion o compu ing esou ces [3]. The wo main FS app oaches a e w appe me hods and il e me hods. The majo d awback o he il e me hods is ha hey wo k independen ly o he ML classi ie s and do no ake any inpu om hem [ 4 ]. Meanwhile, he w appe me hod uses he classi- ie di ec ly and picks he ea u es using an op imiza ion algo i hm [ 5 ]. Op imiza ion algo i hms p o ide he ad an age o choosing an op imal o nea ly op imal subse o ea u es in a easonable amoun o ime as opposed o he con en ional exhaus i e sea ch. An exhaus i e sea ch becomes imp ac ical, because i inds he solu ion by c ea ing all easible ea u e subse s (2 m di e en solu ions o m ea u es) [ 6 ]. In he li e a u e, op imiza- ion algo i hms a e ca ego ized in o se e al g oups, such as e olu ion-based algo i hms, Appl. Sci. 2023,13, 906. h ps://doi.o g/10.3390/app13020906 h ps://www.mdpi.com/jou nal/applsci Appl. Sci. 2023,13, 906 2 o 19 swa m-based algo i hms, human beha io -inspi ed algo i hms, physics-inspi ed algo- i hms, e c. [ 7 ]. Swa m-based algo i hms mimic he collec i e bu decen alized in elligence o li ing c ea u es, such as bi ds [ 8 ], wol es [ 9 ], whales [ 10 ], bac e ia [ 11 ], e c. E olu iona y algo i hms mimic he eme gence o he i es and heal hies indi iduals o e gene a ions. A ew examples a e he Gene ic Algo i hm (GA) [ 12 ], Di e en ial E olu ion (DE) [ 13 ], Biogeog aphy-Based Op imiza ion (BBO) [ 14 ], e c. Human beha io -inspi ed algo i hms mimic he collec i e in elligen beha io o human beings in di e en eal-li e si ua ions, such as poli ics [ 15 ], spo s [ 16 ], co po a ions [ 7 ], e c. Finally, physics-based algo i hms a e inspi ed by he laws o na u e, such as he g a i a ional law [ 17 ], black holes [ 18 ], galaxies [19], e c. In ecen yea s, me apho -based algo i hms ha e ex ensi ely been used o sol e FS p oblems om di e en domains. Examples include ea u e selec ion using Pa icle Swa m Op imiza ion (PSO) o documen clus e ing [ 20 ], he use o a eal- alued G asshoppe Op i- miza ion Algo i hm (GOA) o ea u e selec ion [ 21 ], hyb idiza ion o he Whale Op imiza ion Algo i hm (WOA) and Simula ed Annealing (SA) o he ea u e selec ion p oblem [ 22 ], ea u e selec ion o in usion de ec ion in wi eless mesh ne wo ks inco po a ing gene ic ope - a o s in WOA [ 23 ], he inco po a ion o le y ligh and opposi ion-based lea ning in chao ic Cuckoo Sea ch (CS) o ea u e selec ion [ 24 ], ea u e selec ion using Mo h Flame Op imiza ion (MFO) [ 25 ], ea u e selec ion using he Fi e ly Algo i hm (FA) [ 26 ], he hyb idiza ion o SA wi h Ha is Hawk Op imiza ion (HHO) o he ea u e selec ion p oblem [ 27 ] and ea u e selec ion using bina y Teaching–Lea ning-Based Op imiza ion (TLBO). Acco ding o he No-F ee-Lunch (NFL) heo em [ 28 ], no single op imiza ion algo i hm is capable o sol ing e e y op imiza ion p oblem by ou pe o ming all o he op imiza ion echniques. Because o his, one op imize can pe o m be e han he o he s on some p oblems, bu no on all o hem. Hence, i is c ucial o compa e se e al op imiza ion algo i hms on a a ie y o da ase s o ind he op imum solu ion o he ea u e selec ion p oblem. Since he e a e hund eds o op imiza ion algo i hms in he li e a u e, in his s udy, a ew well-known and highly ci ed physics-inspi ed algo i hms a e chosen o his pu pose. The a ionale is o ca y ou a compa ison o he a ious me apho s d awn om physics and e alua e hei e ec i eness. To e alua e he pe o mance o hese algo i hms, six small- o-la ge-sized classi ica ion da ase s a e used. The accu acy, con e gence, and a e age i ness o hese algo i hms a e compa ed. This pape has he ollowing con ibu ions: • The main no el y o ou pape lies in i s compa a i e analysis o six well-ci ed physics- inspi ed me apho algo i hms o he p oblem o ea u e selec ion. • To he bes o ou knowledge, his is he i s ime hese physics-inspi ed algo i hms ha e been compa ed o his speci ic p oblem, and ou indings p o ide aluable insigh s in o hei pe o mance. • Ou s udy also has b oade implica ions o he ield o machine lea ning and da a min- ing, as i helps o shed ligh on he e ec i eness o di e en op imiza ion algo i hms o ea u e selec ion. • Ou wo k con ibu es o he g owing body o esea ch on me aheu is ics and hei po en ial applica ions in machine lea ning and da a mining, and i highligh s he po en ial alue o using physics-inspi ed op imiza ion algo i hms o ea u e selec ion. • Addi ionally, ou use o a iable-sized classi ica ion da ase s allows us o assess he applicabili y o hese algo i hms on a wide ange o p oblems, making ou esul s mo e gene alizable and applicable o p ac i ione s. O e all, we belie e ha ou pape ep esen s a signi ican con ibu ion o he ield and has he po en ial o impac he way p ac i ione s app oach he p oblem o ea u e selec ion. The es o he pape is o ganized as ollows. The me hodology is discussed in Sec ion 2. Sec ion 3, namely, he Resul s and Discussion, co e s he esul s and compa a i e analysis o all six algo i hms, and he concluding ema ks a e gi en in Sec ion 4. Appl. Sci. 2023,13, 906 3 o 19 2. Me hodology 2.1. W appe Me hod o Fea u e Selec ion Fo ea u e selec ion, we employed a w appe me hod. To accomplish hei ask, w appe echniques use a lea ning algo i hm ha applies a sea ch s a egy o explo e he space o easible ea u e subse s, anking hem acco ding o he quali y o hei pe o mance in a speci ic algo i hm. In mos cases, w appe app oaches ou pe o m il e me hods, since he ea u e selec ion p ocess is ailo ed o he speci ic classi ica ion algo i hm being employed. W appe me hods, on he o he hand, a e p ohibi i ely ime- and esou ce- in ensi e o high-dimensional da a, since hey equi e e alua ing each ea u e se wi h he classi ie algo i hm. Figu e 1depic s he way in which w appe me hods unc ion. Appl. Sci. 2023, 12, x FOR PEER REVIEW 3 o 20 Sec ion 2. Sec ion 3, namely, he Resul s and Discussion, co e s he esul s and compa a- i e analysis o all six algo i hms, and he concluding ema ks a e gi en in Sec ion 4. 2. Me hodology 2.1. W appe Me hod o Fea u e Selec ion Fo ea u e selec ion, we employed a w appe me hod. To accomplish hei ask, w appe echniques use a lea ning algo i hm ha applies a sea ch s a egy o explo e he space o easible ea u e subse s, anking hem acco ding o he quali y o hei pe o - mance in a speci ic algo i hm. In mos cases, w appe app oaches ou pe o m il e me h- ods, since he ea u e selec ion p ocess is ailo ed o he speci ic classi ica ion algo i hm being employed. W appe me hods, on he o he hand, a e p ohibi i ely ime- and e- sou ce-in ensi e o high-dimensional da a, since hey equi e e alua ing each ea u e se wi h he classi ie algo i hm. Figu e 1 depic s he way in which w appe me hods unc- ion. Figu e 1. W appe ea u e selec ion amewo k. In his pape , K-Nea es Neighbo (k-NN) is used as he e alua o algo i hm. The k- NN me hod uses a se o K neighbo s o de e mine how an objec should be ca ego ized. A posi i e in ege alue o K is p e-decided be o e unning he algo i hm. To classi y a eco d, he Euclidean dis ances be ween he unclassi ied eco d and he classi ied eco ds a e de e mined and anked. 2.2. Fi ness Func ion The e ec i eness o an op imize is e alua ed by i s i ness unc ion. The i ness unc- ion in ea u e selec ion is dependen on he classi ica ion e o a e and he numbe o ea u es used o classi ica ion. I is deemed o be a good solu ion i he selec ed ea u e subse educes he classi ica ion e o a e and he numbe o ea u es chosen. The ollow- ing i ness unc ion is used in his pape [29]: ↓ 𝐹𝑖𝑡𝑛𝑒𝑠𝑠 =𝜆𝛾𝑆(𝐷)+(1−𝜆)|𝑆| |𝐹| (1) whe e 𝛾𝑆(𝐷) is he classi ica ion e o compu ed by he classi ie , |𝑆| is he educed numbe o ea u es in he new subse , |𝐹| is he o al ea u es in he da ase , and 𝜆 𝜖 [0,1] Figu e 1. W appe ea u e selec ion amewo k. In his pape , K-Nea es Neighbo (k-NN) is used as he e alua o algo i hm. The k-NN me hod uses a se o K neighbo s o de e mine how an objec should be ca ego ized. A posi i e in ege alue o K is p e-decided be o e unning he algo i hm. To classi y a eco d, he Euclidean dis ances be ween he unclassi ied eco d and he classi ied eco ds a e de e mined and anked. 2.2. Fi ness Func ion The e ec i eness o an op imize is e alua ed by i s i ness unc ion. The i ness unc ion in ea u e selec ion is dependen on he classi ica ion e o a e and he numbe o ea u es used o classi ica ion. I is deemed o be a good solu ion i he selec ed ea u e subse educes he classi ica ion e o a e and he numbe o ea u es chosen. The ollowing i ness unc ion is used in his pape [29]: ↓Fi ness =λγS(D) + (1−λ)|S| |F|(1) whe e γS(D) is he classi ica ion e o compu ed by he classi ie , |S| is he educed numbe o ea u es in he new subse , |F| is he o al ea u es in he da ase , and λ e [0, 1] is a ac o co esponding o he impo ance o he classi ica ion pe o mance and leng h o he educed subse . 2.3. Physics-Inspi ed Me apho Algo i hms In his pape , six well-ci ed physics-inspi ed me apho algo i hms a e employed o sol e he p oblem o ea u e selec ion. In his sec ion, he unc ioning o hese algo i hms and hei posi ion-upda ing mechanisms a e discussed. Appl. Sci. 2023,13, 906 4 o 19 2.3.1. Simula ed Annealing Simula ed Annealing is a undamen al na u e-inspi ed algo i hm ha was p oposed in 1983 by Ki kpa ick e al. [ 30 ]. The sou ce o inspi a ion behind his algo i hm is he annealing p ocess o me als. The p ocess o annealing, which s a s a a e y high empe - a u e and p og essi ely cools down, is used o physically ha den me als. The algo i hm in ol es h ee main pa ame e s, including he cooling a e ( c ), he inal empe a u e ( T ), and he s a ing empe a u e ( T0 ). The s a ing empe a u e is kep e y high ini ially, and he cooling a e g adually educes un il i eaches he inal empe a u e. The p ocess is mimicked by andomly gene a ing a candida e solu ion. The algo i hm uns i e a i ely, and a new solu ion is gene a ed in he neighbo hood o he cu en solu ion in each i e a ion. The i ness o he cu en and neighbo solu ions is compa ed. I he i ness o he new solu ion is be e , hen he posi ion o he cu en solu ion is upda ed. Mo eo e , he bes solu ion keeps he bes posi ion ound so a . The e mina ing condi ion o he epe i i e p ocess is eaching he T . In each i e a ion, Tis upda ed as ollows: T=T∗C, 0 <c<1 (2) SA is a global op imiza ion algo i hm, because i can explo e as well as exploi he sea ch space. The explo a ion is pe o med by upda ing he cu en solu ion wi h a wo se neighbo ing solu ion in ea ly i e a ions based on he alue o T and he wo se alue o he neighbo ing solu ion. The chance o accep ing he wo se neighbo is compu ed using he ollowing equa ion: exp−δ T≤ (3) whe e exp is he exponen ial unc ion, δ is equal o he i ness di e ence o cu en and neighbo ing solu ions, and is andomly gene a ed in he ange [0, 1]. 2.3.2. G a i a ional Sea ch Algo i hm This algo i hm is inspi ed by New on’s law o g a i a ion and he second law o mo ion [ 17 ]. I ea s each candida e solu ion in he sea ch space as an objec whose mass is conside ed o be i s i ness. Hea ie objec s a e conside ed i e han ligh e objec s. The objec s a e a ached o each o he wi h some g a i a ional o ce ha causes objec s o explo e he sea ch space. The hea ies objec is conside ed he global bes solu ion. Since he hea ie objec s a ac o he objec s wi h mo e o ce, he whole popula ion ul ima ely con e ges owa d he hea ies objec , called he global bes solu ion. The algo i hm is comp ised o a ew ma hema ical equa ions ha a e exp essed below. Fo ce calcula ion: The o ce om an objec j on an objec i is calcula ed using he ollowing equa ion: Fd ij( ) = G( )Mpi( )×Maj( ) Rij( ) + e(xd j( )−xd i( )) (4) In he abo e equa ion, G is he g a i a ional cons an ha con ols he sea ch accu acy, Mpi is he passi e g a i a ional mass o solu ion i , Maj is he ac i e g a i a ional mass o solu ion j , he dis ance be ween solu ion i and solu ion j is deno ed by Rij , xd is he posi ion o a solu ion in d h dimension, and eis a small cons an . The ul ima e o ce on a solu ion (mass) is calcula ed by aking he weigh ed sum o all he o ces on ha solu ion om he kbes solu ions, which a e calcula ed as ollows: Fd i( ) = ∑ j∈kbes ,j6=i andjFd ij( )(5) Appl. Sci. 2023,13, 906 5 o 19 Accele a ion calcula ion: Once he o al o ce on a solu ion in a pa icula dimension d is calcula ed, he accele a ion o he solu ion in ha dimension can be compu ed using he ollowing equa ion: ad i( ) = Fd i( ) Mii( )(6) whe e Mii is he mass o ine ia o solu ion i. Veloci y calcula ion: Based on he accele a ion, he eloci y o a solu ion can be compu ed by adding he accele a ion o a ac ion o he p e ious eloci y o ha solu ion. The equa ion o compu e eloci y is gi en below: d i= andi× d i( ) + ad i( )(7) Posi ion upda ing: To upda e he posi ion o a solu ion, he upda ed eloci y is simply added o he old posi ion o he solu ion, as o mula ed below: xd i( +1)=xd i( ) + d i( +1)(8) G a i a ional cons an upda ing: To upda e G, he ollowing ela ion is used: G( ) = G0exp−α max (9) whe e G0 is he ini ial g a i a ional cons an , and α is a cons an . and max ep esen he cu en and inal i e a ion numbe s. 2.3.3. Sine Cosine Algo i hm The Sine Cosine Algo i hm (SCA) [ 31 ] has a e y unique sou ce o inspi a ion. I u ilizes wo sine and cosine unc ions o upda e he posi ion o solu ions when sea ching he space o ind he global op imum. The posi ion-upda ing model o his algo i hm is e y simple and is o mula ed below: X +1 i=(X i+ 1×sin( 2)× 3P i−X i, 4<0.5 X i+ 1×cos( 2)× 3P i−X i, 4≥0.5 (10) In he abo e equa ion, Xi deno es a solu ion in he i h dimension, and Pi deno es he global bes solu ion, namely, he des ina ion solu ion in he pape . The abo e equa ion in ol es a ew o he a iables ha a e de ined below. 1 is an adap i e pa ame e ha is linea ly educed wi h he cou se o i e a ions. I s a s om a p e ixed alue and linea ly dec eases in each i e a ion. I is compu ed as ollows: 1=α− α T(11) whe e αis cons an . • 2is andomly gene a ed in he ange o 0 o 2π. • 3is also a andom numbe ha is gene a ed in he ange o 0 o 2. • 4 is also a andom numbe ha is gene a ed in he ange o 0 o 1, and based on i s alue, i is decided whe he o use he sine unc ion o he cosine unc ion in upda ing he posi ion o he cu en solu ion. When mul iplied by 1 , he ange o alues p o ided by sin( 2 ) and cos( 2 ) shi s om [ − 1, 1] o [ − 2, 2]. Due o a linea dec ease in he alues o he pa ame e 1 , he ange begins a [ − 2, 2] and linea ly declines o [0, 0] du ing i e a ions. The posi ion- upda ing equa ion o SCA c ea es wo egions a ound he des ina ion P: an inne egion ha p omo es exploi a ion and an ou e egion o p omo e explo a ion. The p econdi ion o sea ch he inne egion is {−1<= 1Xcos( 2)<=1} o {−1<= 1Xsin( 2)<=1} , Appl. Sci. 2023,13, 906 6 o 19 and he p econdi ion o sea ch he ou e egion is { 1Xcos( 2)} , o { 1Xsin( 2)} gi es a alue g ea e han 1 o lesse han −1. 2.3.4. A om Sea ch Op imiza ion A om Sea ch Op imiza ion (ASO) [ 32 ], which is inspi ed by molecula dynamics, has shown a emendous pe o mance on a a ie y o applica ions in he li e a u e. Each a om is conside ed a candida e solu ion, and he mass is mapped wi h he i ness in he op imiza ion algo i hm, whe e he highe he mass, he i e he solu ion. E e y a om in he popula ion pulls o epels o he a oms in he sea ch space. The hea ie a oms gene a e mo e o ce and pull ligh e objec s apidly, and he hea ie objec s a e pulled slowly owa ds he o he s due o hei mass. The slowly mo ing a oms c ea e exploi a ion in he algo i hm, because hey can sea ch mo e locally, whe eas he apidly mo ing a oms allow he algo i hm o explo e he sea ch space because o longe and quicke jumps. The algo i hm s a s wi h andom ini ializa ions. In e e y i e a ion, he a oms mo e and accele a e, and he loca ion o he a om ha has pe o med he bes up o ha poin is also likewise adjus ed. A omic accele a ion is also caused by wo o he ac o s: L-J po en ial and cons ain o ces. The accele a ion helps o upda e he eloci y o he solu ions (a oms). Finally, he eloci y is added o he p e ious posi ion o upda e he cu en posi ion o he solu ion. The posi ion-upda ing mechanism o he algo i hm is discussed below. The popula ion is gene a ed by andomly gene a ing posi ion and eloci y ec o s o each a om in he popula ion. Xi=hX1 i,X2 i, . . . , XD ii(12) Vi=hV1 i,V2 i, . . . , VD ii(13) The i ness o each solu ion in he popula ion is compu ed, and he global bes Xbes is de e mined. The mass o each a om is compu ed using he ollowing equa ion: mi=Mi ∑N j=1Mj (14) whe e M is compu ed om he i ness o he cu en solu ion, he bes solu ion, and he wo s solu ion. The alue o Kis compu ed, whe e Kdeno es he size o he subse o a oms: K=N−(N−2) T(15) whe e Nis he size o he popula ion. The in e ac ion o ce on an a om is calcula ed, which is accomplished using he ollowing equa ion: Fid=∑ j∈K andjFijd(16) whe e andjis a andom numbe in he ange o [0, 1]. The cons ain o ce is compu ed using he ollowing equa ion: Gd i=λXd bes −Xd i(17) whe e λis he Lang angian mul iplie ha is compu ed as ollows: λ=βe−20 T(18) whe e βis he mul iplie weigh . Appl. Sci. 2023,13, 906 7 o 19 Once he mass, cons ain o ces, and in e ac ion o ces a e compu ed, he accele a ion is compu ed as ollows: ad i=Fd i md i +Gd i md i (19) Once he accele a ion is compu ed, he eloci y o an a om can be compu ed as ollows: Vd i( +1)= 1Vd i( ) + ad i( )(20) Using he upda ed eloci y, he posi ion o a solu ion is upda ed as ollows: Xd i( +1)=Xd i( ) + Vd i( +1)(21) 2.3.5. Hen y Gas Solubili y Op imiza ion Hen y Gas Solubili y Op imiza ion (HGSO) is inspi ed by Hen y’s gas law [ 33 ], which is s a ed below: “A a cons an empe a u e, he amoun o a gi en gas ha dissol es in a gi en ype and olume o liquid is di ec ly p opo ional o he pa ial p essu e o ha gas in equilib ium wi h ha liquid”. This law can be in e p e ed as he pa ial p essu e o a gas and he solubili y o ha gas being di ec ly p opo ional. I one inc eases, hen he o he inc eases, oo. This ela ion is exp essed h ough he ollowing equa ion: Sg=H×Pg(22) whe e he gas solubili y is deno ed by Sg , Hen y’s cons an is deno ed by H , and he pa ial p essu e o he gas is ep esen ed by Pg . The p opo ionali y cons an H is highly dependen on he empe a u e, as i a ies wi h he change in he empe a u e. In HGSO, each gas pa icle is conside ed a candida e solu ion, whe eas all pa icles collec i ely make up he popula ion. Ini ially, gas pa icles (popula ion) a e andomly gene a ed, and hen gas pa icles upda e hei posi ions in he cou se o i e a ions by explo ing and exploi ing he sea ch space. HGSO in ol es he ollowing s eps. Popula ion ini ializa ion: A popula ion o N gas pa icles is andomly gene a ed using he ollowing equa ion: Xi( +1)=X{min}+ ×X{max}−X{min}(23) whe e Xi deno es he ini ial posi ion o he i h solu ion, X{min} and X{max} a e he lowe and uppe bounds o he p oblem unc ion unde conside a ion, is a andomly gene a ed eal numbe be ween 0 and 1, and is he i e a ion numbe . The p ope ies o each sea ch agen in HGSO can be ini ia ed using he ollowing equa ion: Hj( )=l1× and(0, 1),P{i,j}=l2× and(0, 1),Cj=l3× and(0, 1)(24) whe e Hj( ) ep esen s Hen y’s cons an o he j h clus e , P{i,j} deno es he pa ial p essu e o he i h pa icle in he j h clus e , and Cj indica es he ini ial cons an alue o he j h clus e . Clus e ing: This s ep di ides he sea ch agen s in o K clus e s o map di e en ypes o gases, whe e he same ypes o gases a e g ouped in o a clus e . The e o e, each clus e has he same alue o Hen y’s cons an Hj. Fi ness E alua ion: In his s ep, each sea ch agen in he j h clus e is e alua ed h ough he objec i e unc ion o ind he bes solu ion Xj,bes in he j h clus e . Once all he clus e s a e e alua ed, hen he gases a e anked o ind he global bes pa icle Xbes . Appl. Sci. 2023,13, 906 8 o 19 Upda e Hen y’s coe icien : The pa ial p essu e o each gas pa icle changes in each i e a ion. The e o e, he alue o Hen y’s coe icien Hj is upda ed using he ollowing equa ion: H( +1)=exp−Cj×1 T−1 T0×Hj( ), ; T( ) = exp( − {max}!) (25) whe e Hj ep esen s he alue o Hen y’s cons an o he j h clus e , T indica es he empe - a u e, T0 deno es a e e ence empe a u e equi alen o 298.15 K, and {max} ep esen s he maximum i e a ions. Upda e solubili y: In his s ep, he solubili y S{i,j} o he i h pa icle in he j h clus e is upda ed using he ollowing equa ion: S{i,j}( )=K×Hj( +1)×P{i,j}( )(26) whe e Kis a cons an , and P{i,j}is he pa ial p essu e o gas iin clus e j. Upda e posi ion: The p ope ies o pa icles compu ed in he p e ious s eps a e u ilized o upda e he posi ion o he i h gas pa icle in he j h clus e acco ding o he ollowing equa ion: X{i,j}( +1)=X{i,j}( )+F× 1×γ×X{j,bes }( )−X{i,j}( ) +F× 2×a×S{i,j}( )×X{bes }( )−X{i,j}( )(27) γ=β× expn acnF{bes }( )+eonF{i,j}( )+eoo, ; e=0.05 (28) whe e he posi ion o he i h sea ch agen in he j h clus e is ep esen ed by Xij , he bes agen in he j h clus e is deno ed by Xj,bes , and he global bes pa icle in he en i e popula ion is ep esen ed by Xbes . Mo eo e , 1 and 2 a e wo andom alues in he ange [0, 1], is he cu en i e a ion, F is a lag used o di e si ica ion pu poses and changes he di ec ion o he solu ion, γ indica es he abili y o he i h pa icle in he j h clus e o in e ac wi h o he agen s in i s clus e , a ep esen s he impac o o he gases on he i h pa icle, β is ixed as β = 1, F i,j is he i ness o he i h pa icle in he j h clus e , and F{bes } is he i ness o he bes pa icle. Escape om local op imum: To a oid s agna ion in local op ima, all he pa icles a e e alua ed, and he wo s N w agen s a e selec ed and eini ialized using he ollowing equa ion: Nw=N×( and(c2−c1)+c1), ; c1=0.1 ; and ;c2=0.2 (29) whe e N is he popula ion size. Mo eo e , c1 and c2 a e cons an s ha de ine he pe cen age o wo s pa icles. 2.3.6. Equilib ium Op imize (EO) Con ol olume mass balance models, which a e used o es ima e bo h dynamic and equilib ium s a es, se e as an inspi a ion o he Equilib ium Op imize (EO), a ecen ly p oposed physics-inspi ed algo i hm [ 34 ]. The pa icles a e conside ed o be he solu ions, and hei posi ions map he concen a ion o he pa icles. This algo i hm cons uc s an equilib ium pool o i e e e ence solu ions ( ou bes so- a pa icles and one a i hme ic mean o hem) called equilib ium candida es. Each pa icle upda es i s posi ion wi h e e ence o a andomly selec ed candida e om he pool. The algo i hm is aided by wo ca e ully designed pa ame e s called he exponen ial e m ( F ) and he gene a ion a e ( G ). Mo eo e , a concep o memo y sa ing is used, which allows a solu ion o upda e i s concen a ion only i i imp o es as compa ed o i s p e ious concen a ion. The explo a ion, exploi a ion, and he balance be ween hem a e con olled h ough hese pa ame e s: he equilib ium pool and he gene a ion p obabili y. Appl. Sci. 2023,13, 906 9 o 19 EO uses a mass-balance equa ion o desc ibe he conse a ion o mass wi hin a sys em. The gene ic mass-balance equa ion is gi en as: VdC d =QC{eq}−QC +G(30) whe e VdC d ep esen s he a e o change o mass in a con ol olume, Q is he low a e, he concen a ion a an equilib ium s a e is deno ed by QC{eq} , and G mimics he mass gene a ion a e. He e, dC d can also be sol ed in e ms o Q V and Q V deno ed by λ o he u no e a e (i.e., λ=Q V). The e o e, he abo e equa ion can be econs uc ed as: dC λC{eq}−λC+G V =d (31) By aking he in eg a ion o he abo e equa ion, we ob ain: C=C{eq}+C0−C{eq}F+G λV(1−F)(32) which is used as an upda ing ule o each pa icle, whe e Fis calcula ed as ollows: F=exp[−λ( − 0)] (33) whe e 0 and C0 ep esen he ini ial s a ime and concen a ion. In his algo i hm, each pa icle is a solu ion, and i s posi ion ep esen s i s concen a ion. The ma hema ical o mula ion o EO is discussed in he ollowing s eps. Ini ializa ion and unc ion e alua ion: The i s s ep is o ini ialize he pa icles’ con- cen a ion acco ding o he ollowing equa ion: X{ini } {m}=X{min}+ andm(X{max}−X{min})(34) whe e X{ini } {m} ep esen s he ini ial concen a ion o he m h pa icle, X{max} shows he maximum, and X{min}shows he minimum alues. Equilib ium pool and candida es X e : In his algo i hm, ou equilib ium candida es (good solu ions) a e de e mined o guide o he pa icles and p omo e explo a ion. Mo e- o e , a pa icle cons uc ed by aking he a i hme ic mean o all hese candida es is also used, which p omo es exploi a ion. These candida es a e hen assembled o o m an equilib- ium pool. Each pa icle upda es i s posi ion wi h espec o a andomly selec ed candida e om he pool. Exponen ial e m (E): This e m is used in posi ion upda ing o balance explo a ion and exploi a ion. The exponen ial e m is compu ed as ollows: E=e{−{λ}( − 0)}(35) whe e and 0a e compu ed by ollowing equa ions, espec i ely: =1−I e Max _i e {(a2I e Max _i e )} (36) 0=1 λln−a1sign({ }−0.5)h1−e{−{λ} }i+ (37) In he abo e equa ion, a la ge alue o a1 p omo es explo a ion, and a la ge alue o a2 p omo es exploi a ion. The sign({ }−0.5) con ols he di ec ion o explo a ion and exploi a ion. Using he abo e equa ions, Eis compu ed as ollows: E=−a1sign({ }−0.5)[e{−{λ} }−1]) (38) Appl. Sci. 2023,13, 906 16 o 19 Table 6. A e age ank o all a e ages (Fi ness, accu acy, and AFS). Da ase S a s SA GSA SCA ASO HGSO EO DS1 A g. i ness ank A g. accu acy ank AFS ank 5 5 6 3 3 1 6 6 4 1 1 3 4 4 2 2 2 4 DS2 A g. i ness ank A g. accu acy ank AFS ank 6 6 4 5 5 5 3 3 1 2 2 6 4 4 3 1 1 2 DS3 A g. i ness ank A g. accu acy ank AFS ank 6 6 4 1 1 4 5 5 2 3 3 6 4 4 1 2 2 3 DS4 A g. i ness ank A g. accu acy ank AFS ank 6 5 6 4 4 4 3 3 1 5 5 5 2 2 2 1 1 3 DS5 A g. i ness ank A g. accu acy ank AFS ank 6 6 6 5 5 5 1 1 2 4 4 4 3 3 3 1 1 1 DS6 A g. i ness ank A g. accu acy ank AFS ank 6 6 6 3 3 5 4 4 2 1 1 4 5 5 1 2 2 3 A g. Rank 5.61 3.66 3.11 3.33 3.11 1.88 3.4. Compa ison wi h O he Me hods om he Li e a u e In his sec ion, he op h ee physics-inspi ed me aheu is ic algo i hms a e compa ed wi h he s a e o he a . Fo his compa ison, esul s om o he KNN-me aheu is ic commina ions epo ed by Elminaam e al. [ 37 ] we e chosen. The me aheu is ics chosen o compa ison d aw hei me apho inspi a ion om a ious sou ces. Fo example, he G ey Wol Op imize (GWO) and Whale Op imiza ion Algo i hm (WOA) may be classi ied as mammal inspi ed, whe eas mo h Flame Op imiza ion (MFO) and he Bu e ly Op imiza ion Algo i hm (BFO) a e insec inspi ed. Simila ly, Ha is Hawk Op imiza ion (HHO) and he Ma ine P eda o Algo i hm (MPA) a e inspi ed by p eying beha io seen in na u e. Addi ionally, esul s based on popula ML algo i hms such as Nai e Bayes, Logis ic Reg ession, Random Fo es , Suppo Vec o Machine (SVM), K-NN, Decision T ee, and S ochas ic G adien Descen (SGD) a e also compa ed, along wi h hei p incipal componen analysis (PCA)-enhanced e sions. In e ms o classi ica ion accu acy (Table 7), in wo ou o he h ee da ase s compa ed, EO ou pe o med all he o he me hods. In ac , o he b eas cance da ase and ionosphe e da ase , EO was on a e age 12.75% and 7.12% be e , espec i ely, han he me aheu is ics p esen ed in [ 37 ]. In he sona da ase , oo, EO and SCA we e wi hin 2.5% o he bes solu ion epo ed in [ 37 ]. Addi ionally, when compa ed wi h he ML algo i hms, he EO solu ion o he b eas cance da ase was on a e age 17.89% be e . An a e age supe io i y o 5.68% was seen o EO when compa ed wi h he PCA-ML me hods epo ed in [38]. The a e age ea u es selec ed o he b eas cance , ionosphe e, and sona da ase s by he a ious me aheu is ics a e epo ed in Table 8. I can be obse ed ha he ea u e educ ions by he cu en physics-inspi ed me aheu is ics a e much highe . Fo he b eas cance , ionosphe e, and sona da ase s, he a e age pe cen ea u e educ ion achie ed by he h ee physics- inspi ed algo i hms was 85.11%, 88.24%, and 84.89%, espec i ely, and o he me aheu is ic algo i hms om [37], i was only 67.62%, 64.71%, and 67.14%, espec i ely. Thus, om he comp ehensi e compa isons shown so a , i is clea ha he cu - en KNN hyb idized physics-inspi ed me aheu is ic algo i hms (especially EO, SCA, and HGSO) a e supe io o hose epo ed in he li e a u e. Mo eo e , i is seen ha e en solu- ions by hyb idized ML algo i hms ( o example, by dimensionali y educ ion echniques such as PCA) we e in e io o cu en solu ions. This is wo h highligh ing, since he cu en w appe me hods a e much simple in e ms o compu a ional complexi y as compa ed o he PCA-hyb idized ML me hods. Appl. Sci. 2023,13, 906 17 o 19 Table 7. Compa ison o classi ica ion accu acy wi h li e a u e esul s. Me hod B eas Cance % Imp o emen &Ionosphe e % Imp o emen Sona % Imp o emen EO 0.995 Bes Solu ion 0.986 Bes Solu ion 0.976 2.46% SCA 0.986 0.91% 0.971 1.54% 0.976 2.46% HGSO 0.986 0.91% 0.986 Bes Solu ion 0.951 5.15% GWO [37] 0.970 2.58% 0.951 3.68% 0.970 3.09% MFO [37] 0.605 64.46% 0.774 27.39% 0.547 82.82% WOA [37] 0.973 2.26% 0.957 3.03% 0.976 2.46% SSA [37] 0.982 1.32% 0.985 0.10% 1.000 Bes Solu ion BOA [37] 0.903 10.19% 0.901 9.43% 0.881 13.51% HHO [37] 0.929 7.10% 0.929 6.14% 0.833 20.05% MPA [37] 0.982 1.32% 0.985 0.10% 0.976 2.46% Nai e Bayes [38] 0.845 17.75% -- - - Logis ic Reg ession [38] 0.879 13.20% -- - - Random Fo es [38] 0.995 Bes Solu ion -- - - SVM [38] 0.620 60.48% -- - - K-NN [38] 0.900 10.56% -- - - Decision T ee [38] 0.880 13.07% -- - - SGD [38] 0.903 10.19% -- - - PCA-Nai e Bayes [38] 0.975 2.05% -- - - PCA-Logis ic Reg ession [38] 0.975 2.05% -- - - PCA-Random Fo es [38] 0.962 3.43% -- - - PCA-SVM [38] 0.942 5.63% -- - - PCA-K-NN [38] 0.921 8.03% -- - - PCA-Decision T ee [38] 0.905 9.94% -- - - PCA-SGD [38] 0.916 8.62% -- - - &% imp o emen achie ed by he bes solu ion wi h espec o he compa ed algo i hms. Table 8. Compa ison o AFS wi h li e a u e esul s. Me hod B eas Cance % Fea u e Reduc ion &Ionosphe e % Fea u e Reduc ion Sona % Fea u e Reduc ion EO 4.8 84% 5 85% 11.4 81% SCA 4.8 84% 3.4 90% 8 87% HGSO 3.8 87% 3.6 89% 7.8 87% GWO [37] 7 77% 4 88% 11 82% MFO [37] 6 80% 23 32% 31 48% WOA [37] 8 73% 7 79% 26 57% SSA [37] 11 63% 14 59% 16 73% BOA [37] 12 60% 20 41% 26 57% HHO [37] 12 60% 10 71% 20 67% MPA [37] 12 60% 6 82% 8 87% & % Fea u e educ ion is calcula ed as 100% minus he a io o AFS by each algo i hm and maximum ea u es in he co esponding da ase . A highe alue o % ea u e educ ion is desi ed. 4. Conclusions In his pape , six well-ci ed physics-inspi ed me apho algo i hms we e employed o ea u e selec ion. Fea u e selec ion is one o he majo challenges being aced in he ield o da a mining and machine lea ning. The objec i e o his esea ch was o iden i y he mos p omising physics-inspi ed algo i hms o he p oblem o ea u e selec ion. To accomplish his, six small- o la ge-sized da ase s we e used. The pe o mance o EO was ound o be supe io on mos o he da ase s, and he me ics ha we e used o he compa a i e analysis we e aken om he li e a u e and included accu acy, i ness, he a e age numbe o ea u es selec ed, and con e gence analysis. The cu en physics-inspi ed me apho algo i hms, especially EO, SCA, and HGSO comp ehensi ely ou pe o med o he me aheu is ics, as well as he ML-based solu ions seen in ecen li e a u e. Based on ou indings, we highly ecommend using EO o he ea u e selec ion p oblem. Au ho Con ibu ions: Concep ualiza ion, R. ˇ C. and K.K.; Da a cu a ion, J.P., M.P. and M.J.; Fo mal analysis, J.P., M.P. and M.J.; In es iga ion, J.P., M.P. and M.J.; Me hodology, R. ˇ C. and K.K.; So wa e, R. ˇ C. and K.K.; Valida ion, J.P., M.P. and M.J.; Visualiza ion, J.P., M.P. and M.J.; W i ing—o iginal d a , J.P., M.P. and M.J.; W i ing— e iew and edi ing, R. ˇ C. and K.K. All au ho s ha e ead and ag eed o he published e sion o he manusc ip . Appl. Sci. 2023,13, 906 18 o 19 Funding: This esea ch ecei ed no ex e nal unding. Ins i u ional Re iew Boa d S a emen : No applicable. In o med Consen S a emen : No applicable. Da a A ailabili y S a emen : The da a p esen ed in his s udy a e a ailable h ough email upon eques o he co esponding au ho . Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. Köppen, M. The cu se o dimensionali y. In P oceedings o he 5 h Online Wo ld Con e ence on So Compu ing in Indus ial Applica ions (WSC5), Online, 4–18 Sep embe 2000; Volume 1, pp. 4–8. 2. Iko un, A.M.; Almu a i, M.S.; Ezugwu, A.E. K-Means-Based Na u e-Inspi ed Me aheu is ic Algo i hms o Au oma ic Da a Clus e ing P oblems: Recen Ad ances and Fu u e Di ec ions. Appl. Sci. 2021,11, 11246. [C ossRe ] 3. Khalid, S.; Khalil, T.; Nas een, S. A su ey o ea u e selec ion and ea u e ex ac ion echniques in machine lea ning. In P oceedings o he Science and In o ma ion Con e ence (SAI), London, UK, 27–29 Augus 2014; pp. 372–378. 4. Po kodi, R. Compa ison o il e based ea u e selec ion algo i hms: An o e iew. In . J. Inno . Res. Technol. Sci. 2014 ,2, 108–113. 5. Jo i´c, A.; B ki´c, K.; Boguno i´c, N. A e iew o ea u e selec ion me hods wi h applica ions. In P oceedings o he 2015 38 h In e na ional Con en ion on In o ma ion and Communica ion Technology, Elec onics and Mic oelec onics (MIPRO), Opa ija, C oa ia, 25–29 May 2015; pp. 1200–1205. 6. B ezoˇcnik, L.; Fis e , I.; Podgo elec, V. Swa m In elligence Algo i hms o Fea u e Selec ion: A Re iew. Appl. Sci. 2018 ,8, 1521. [C ossRe ] 7. Aska i, Q.; Saeed, M.; Younas, I. Heap-based op imize inspi ed by co po a e ank hie a chy o global op imiza ion. Expe Sys . Appl. 2020,161, 113702. [C ossRe ] 8. Rahman, A.; Sokkalingam, R.; O hman, M.; Biswas, K.; Abdullah, L.; Kadi , E.A. Na u e-Inspi ed Me aheu is ic Techniques o Combina o ial Op imiza ion P oblems: O e iew and Recen Ad ances. Ma hema ics 2021,9, 2633. [C ossRe ] 9. Mi jalili, S.; Mi jalili, S.M.; Lewis, A. G ey wol op imize . Ad . Eng. So w. 2014,69, 46–61. [C ossRe ] 10. Mi jalili, S.; Lewis, A. The whale op imiza ion algo i hm. Ad . Eng. So w. 2016,95, 51–67. [C ossRe ] 11. Passino, K.M. Bac e ial o aging op imiza ion. In . J. Swa m In ell. Res. (IJSIR) 2010,1, 1–16. [C ossRe ] 12. Whi ley, D. A gene ic algo i hm u o ial. S a . Compu . 1994,4, 65–85. [C ossRe ] 13. S o n, R. On he usage o di e en ial e olu ion o unc ion op imiza ion. In P oceedings o he No h Ame ican Fuzzy In o ma ion P ocessing, Be keley, CA, USA, 19–22 June 1996; pp. 519–523. 14. Simon, D. Biogeog aphy-based op imiza ion. IEEE T ans. E ol. Compu . 2008,12, 702–713. [C ossRe ] 15. Aska i, Q.; Younas, I.; Saeed, M. Poli ical Op imize : A no el socio-inspi ed me a-heu is ic o global op imiza ion. Knowl.-Based Sys . 2020,195, 105709. [C ossRe ] 16. Fadaka , E.; Eb ahimi, M. A new me aheu is ic oo ball game inspi ed algo i hm. In P oceedings o he 2016 1s Con e ence on Swa m In elligence and E olu iona y Compu a ion (CSIEC), Bam, I an, 9–11 Ma ch 2016; pp. 6–11. 17. Rashedi, E.; Nezamabadi-Pou , H.; Sa yazdi, S. GSA: A G a i a ional Sea ch Algo i hm. In . Sci. 2009 ,179, 2232–2248. [C ossRe ] 18. Ha amlou, A. Black hole: A new heu is ic op imiza ion app oach o da a clus e ing. In . Sci. 2013,222, 175–184. [C ossRe ] 19. Ze iga , D.H.; Benasla, L.; Belmadani, A.; Rahli, M. Galaxy-based sea ch algo i hm o sol e combined economic and emission dispa ch. UPB Sci. Bull. Se . C Elec . Eng. 2014,76, 209–220. 20. Abualigah, L.M.; Khade , A.T.; Hanandeh, E.S. A new ea u e selec ion me hod o imp o e he documen clus e ing using pa icle swa m op imiza ion algo i hm. J. Compu . Sci. 2018,25, 456–466. [C ossRe ] 21. Zake i, A.; Hokmabadi, A. E icien ea u e selec ion me hod using eal- alued g asshoppe op imiza ion algo i hm. Expe Sys . Appl. 2019,119, 61–72. [C ossRe ] 22. Ma a ja, M.M.; Mi jalili, S. Hyb id Whale Op imiza ion Algo i hm wi h simula ed annealing o ea u e selec ion. Neu ocompu ing 2017,260, 302–312. [C ossRe ] 23. Vijayanand, R.; De a aj, D. A No el Fea u e Selec ion Me hod Using Whale Op imiza ion Algo i hm and Gene ic Ope a o s o In usion De ec ion Sys em in Wi eless Mesh Ne wo k. IEEE Access 2020,8, 56847–56854. [C ossRe ] 24. Kelida i, M.; Hamidzadeh, J. Fea u e selec ion by using chao ic cuckoo op imiza ion algo i hm wi h le y ligh , opposi ion-based lea ning and dis up ion ope a o . So Compu . 2021,25, 2911–2933. [C ossRe ] 25. Zawbaa, H.M.; Ema y, E.; Pa , B.; Sha awi, M. Fea u e selec ion app oach based on mo h- lame op imiza ion algo i hm. In P oceedings o he 2016 IEEE Cong ess on E olu iona y Compu a ion (CEC), Vancou e , BC, Canada, 24–29 July 2016; pp. 4612–4617. 26. Sel akuma , B.; Muneeswa an, K. Fi e ly algo i hm based ea u e selec ion o ne wo k in usion de ec ion. Compu . Secu . 2019 , 81, 148–155. 27. Abdel-Basse , M.; Ding, W.; El-Shaha , D. A hyb id Ha is Hawks op imiza ion algo i hm wi h simula ed annealing o ea u e selec ion. A i . In ell. Re . 2021,54, 593–637. [C ossRe ] 28. Wolpe , D.H.; Mac eady, W.G. No ee lunch heo ems o op imiza ion. IEEE T ans. E ol. Compu . 1997,1, 67–82. [C ossRe ] Appl. Sci. 2023,13, 906 19 o 19 29. Too, J.; Liang, G.; Chen, H. Memo y-based Ha is hawk op imiza ion wi h lea ning agen s: A ea u e selec ion app oach. Eng. Compu . 2021,38, 4457–4478. [C ossRe ] 30. Be simas, D.; Tsi siklis, J. Simula ed annealing. S a . Sci. 1993,8, 10–15. [C ossRe ] 31. Mi jalili, S. SCA: A Sine Cosine Algo i hm o sol ing op imiza ion p oblems. Knowl.-Based Sys . 2016,96, 120–133. [C ossRe ] 32. Zhao, W.; Wang, L.; Zhang, Z. A om sea ch op imiza ion and i s applica ion o sol e a hyd ogeologic pa ame e es ima ion p oblem. Knowl.-Based Sys . 2019,163, 283–304. [C ossRe ] 33. Hashim, F.A.; Houssein, E.H.; Mab ouk, M.S.; Al-A abany, W.; Mi jalili, S. Hen y gas solubili y op imiza ion: A no el physics- based algo i hm. Fu u e Gene . Compu . Sys . 2019,101, 646–667. [C ossRe ] 34. Fa ama zi, A.; Heida inejad, M.; S ephens, B.; Mi jalili, S. Equilib ium op imize : A no el op imiza ion algo i hm. Knowl.-Based Sys . 2020,191, 105190. [C ossRe ] 35. Con ads, T.P.; Fusa o, V.A.; Ross, S.; Johann, D.; Rajapakse, V.; Hi , B.A.; S einbe g, S.M.; Kohn, E.C.; Fishman, D.A.; Whi ely, G.; e al. High- esolu ion se um p o eomic ea u es o o a ian cance de ec ion. Endoc .-Rela . Cance 2004 ,11, 163–178. [C ossRe ] [PubMed] 36. S ee , W.N.; Wolbe g, W.H.; Mangasa ian, O.L. Nuclea ea u e ex ac ion o b eas umo diagnosis. In P oceedings o he IS&T/SPIE 1993 In e na ional Symposium on Elec onic Imaging: Science and Technology, San Jose, CA, USA, 31 Janua y–5 Feb ua y 1993; Volume 1905, pp. 861–870. 37. Elminaam, D.S.A.; Nabil, A.; Ib aheem, S.A.; Houssein, E.H. An E icien Ma ine P eda o s Algo i hm o Fea u e Selec ion. IEEE Access 2021,9, 60136–60153. [C ossRe ] 38. Ib ahim, S.; Nazi , S.; Velas in, S.A. Fea u e Selec ion Using Co ela ion Analysis and P incipal Componen Analysis o Accu a e B eas Cance Diagnosis. J. Imaging 2021,7, 225. [C ossRe ] [PubMed] Disclaime /Publishe ’s No e: The s a emen s, opinions and da a con ained in all publica ions a e solely hose o he indi idual au ho (s) and con ibu o (s) and no o MDPI and/o he edi o (s). MDPI and/o he edi o (s) disclaim esponsibili y o any inju y o people o p ope y esul ing om any ideas, me hods, ins uc ions o p oduc s e e ed o in he con en .