Softcomputing in identification of the origin of Voynich manuscript by comparison with ancient dialects

Applied So Compu ing 138 (2023) 110217 Con en s lis s a ailable a ScienceDi ec Applied So Compu ing jou nal homepage: www.else ie .com/loca e/asoc So compu ing in iden i ica ion o he o igin o Voynich manusc ip by compa ison wi h ancien dialec s I an Zelinka a,∗, Mel in La a b, Leah C. Windso c, René Lozi d aDepa men o Compu e Science, FEI VSB Technical Uni e si y o Os a a, T . 17. Lis opadu 15, Os a a, Czechia bDepa men o Cybe ne ics and Biomedical Enginee ing, Facul y o Elec ical Enginee ing and Compu e Science, VSB–Technical Uni e si y o Os a a, 708 00, Os a a-Po uba, Czechia cDepa men o English (Applied Linguis ics), Ins i u e o In elligen Sys ems, The Uni e si y o Memphis, Memphis, TN 38152, USA dUni e si y Cô e d’Azu , Depa men o Ma hema ics, CNRS, Labo a o y J.A. Dieudonne, Pa c Val ose, 06108 Nice, F ance a icle in o A icle his o y: Recei ed 12 June 2022 Recei ed in e ised o m 7 Ma ch 2023 Accep ed 14 Ma ch 2023 A ailable online 17 Ma ch 2023 Keywo ds: Voynich Manusc ip Deep lea ning Simila i y Dialec abs ac The Voynich manusc ip is a mo e han 600-yea -old his o ical manusc ip . I is conside ed one o he mos mys e ious books in he wo ld. O e he las 100 yea s, his book has esis ed a emp s o deciphe i s con en ; hence, i is w i en in uniden i ied language. Since he disco e y o he manusc ip , many known and unknown c yp og aphe s ha e unsuccess ully ied o deciphe his book. Also, many ma hema ical me hods ha e been implemen ed o de e mine whe he i is a audulen his o ical ex o an au hen ic ex con aining aluable in o ma ion. This a icle aims o show he use o deep lea ning ne wo ks and classical me hods o measu e he simila i y be ween he indi idual cha ac e s o he alphabe and be ween o he alphabe s and Voynich. The i s pa o he a icle demons a es he e ec i eness o ou me hod in de e mining he simila i ies be ween indi idual cha ac e s o he Voynich alphabe . In he second pa , we ind he simila i y be ween he Voynich Manusc ip and o he indi idual alphabe se s (languages). In o he wo ds, his a icle shows ano he possible di ec ion in he esea ch o Voynich manusc ip o iden i y he language dialec amily om which Voynich manusc ip can heo e ically come. ©2023 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by-nc-nd/4.0/). Code me ada a Pe manen link o ep oducible capsule: h ps://doi.o g/10. 24433/CO.5645180. 2. 1. In oduc ion Voynich manusc ip is one o he mos mys e ious and one o he mos inspi ing books in he wo ld, alongside o he mys- e ious books such as (Book o Soyga, Codex Se aphinianus, Hyp- ne o omachia Poliphili, he Oe a Linda Book, he Ripley Sc olls, he Smi h ield Dec e als, he Rohonc Codex, he Red Book, P odigio um Ac Os en o um Ch onicon) among he o he s. Howe e , he Voyn- ich manusc ip ,1[1], occupies i s place in his se o mys e ious The code (and da a) in his a icle has been ce i ied as Rep oducible by Code Ocean: (h ps://codeocean.com/). Mo e in o ma ion on he Rep oducibili y Badge Ini ia i e is a ailable a h ps://www.else ie .com/physical-sciences-and- enginee ing/compu e -science/jou nals. ∗Co esponding au ho . E-mail add esses: [email p o ec ed] (I. Zelinka), [email p o ec ed] (L.C. Windso ), [email p o ec ed] (R. Lozi). URL: h ps://www.i anzelinka.eu (I. Zelinka). 1h p://www. oynich.nu/ manusc ip s. The Voynich manusc ip (VM) became inc easingly well-known only in he wen ie h cen u y, and since i s dis- co e y, many scien is s, ma hema icians, c yp ologis s, and o he esea che s ha e ied o deciphe and ead i . No one has suc- ceeded ye . Wha makes his manusc ip pa icula ly unique is i s impossibili y o deciphe ing i s language and meaning. Be- sides mys e iously-looking ex w i en in he unknown alphabe sys em, i also con ains images o objec s, mainly o a biological na u e, which a e mos ly unknown o mode n biology. I is a e y p o oca i e manusc ip , which by i s e y na u e, a ac s he a en ion o mode n scien is s. I seems o be ha nowa- days, science shall able o deploy cu ing-edge ma hema ical and linguis ic me hods o help deciphe / ead i and de e mine i s o igin. Expe s in c yp ology and c yp og aphic aces ha e a emp ed o decode i , as hey could deciphe e en sec e codes du ing Wo ld Wa II wi hou any p oblems, including he Na ional Se- cu i y Agency in he Uni ed S a es. Likewise, a ious en husias s, whe he p o essionals o ama eu s, ha e no succeeded in de- mys i ying he Voynich manusc ip . This con inuous and ui less e o has gi en ise o he belie ha he manusc ip is a his o i- cal hoax and con ains no meaning ul in o ma ion. On he o he hand, i mus be said ha many di e en s ic ma hema ical h ps://doi.o g/10.1016/j.asoc.2023.110217 1568-4946/©2023 The Au ho s. Published by Else ie B.V. This is an open access a icle unde he CC BY-NC-ND license (h p://c ea i ecommons.o g/licenses/by- nc-nd/4.0/). I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 1. Ne wo k based on Voynich manusc ip as epo ed in [2]. The node size and colou ep esen an impo ance o he wo d in he selec ed ex . analyses ha e been pe o med, mainly h ough he op ics o s a is ics and compu a ional linguis ics, o example, [1,3], which sugges ha i is some o m o na u al language. Wo ks such as [4], o example, compa e he p ope ies o language se s om classic books, h ee pieces o a ious p og amming codes, monkey yping ex o e en he DNA sequences. O he wo ks ha deal wi h he manusc ip a e, o example, [5], which analyses he Voynich manusc ip om he in o ma ion- heo y poin o iew and many o he s. In addi ion o classical app oaches, me hods, such as ac al geome y, see [2], ha e been u ilized, and his is compa ed wi h he same analysis o o e 120 language mu a ions o he Hemingway’s no el [6]. Also, [7] p esen s a new app oach o he solu ion o manusc ip analysis in he o m o ex con- e sion in o ne wo ks (Fig. 1) and subsequen con e sion in o a g aphical global iew o he ex , Fig. 2. These images a e based on ou p e ious publica ions [2,7] and show ou i s expe imen s wi h Voynich manusc ip in he ol- lowing sense. To ge Fig. 2, we i s need o con e he ex in o a complex ne wo k by ea ing he wo ds o he manusc ip as hey lie consecu i ely in he ex as e ices o he ne wo k, and he o ien ed edges exp ess hei succession in he ex in he ne wo k, Fig. 1. Di e en -leng h windows ha scan ex and con e i in o ne wo ks esul in di e en -sized complex ne wo ks. The so-called cen ali y can be calcula ed o each ne wo k. When we mo e a gi en window o e he ex o gene a e changes in he ne wo k, we ge di e en cen ali y alues o di e en window posi ions in he ex . We can epea his o he whole ex wi h di e en leng hs o windows and hus ge h ee ypes o da a: he leng h o he scanning window, i s posi ion om he beginning in he ex , and he co esponding cen ali y. I we exp ess cen ali y in he o m o colou and ake he leng h o he window and i s posi ion om he beginning in he ex as he x and ycoo dina es, we ge Fig. 2, which hen gi es us a so o global iew o he complexi y o he ex . This kind o analysis is in some sense compa able o he analysis o a signal using he well-known heo y o wa ele s: he leng h o he scanning window is compa able o he suppo o he wa ele , i s posi ion om he beginning in he ex is compa able o he posi ion o he cen e o he wa ele . I we compa e his isualiza ion wi h exis ing known ex s, we can see ha he Voynich manusc ip esembles, o example, he Bible [2], in i s isualized s uc u e. In ou wo ks [2,7] we also applied his o andomly gene a ed ex s, and he isual images we e signi ican ly di e en . Fo mo e de ails on hese expe imen s, we ecommend eading publica ions [2,7]. These no el app oaches gi e a global pseudo- ac al iew o he manusc ip ex . In [7], i can be seen ha he alphabe is compa ed wi h andomly gene a ed ex s, and he esul s indi- ca e ha Voynich manusc ip is p obably an exp essi e language con aining speci ic in o ma ion. Many di e en p ojec s and web- si es ha e also been c ea ed on Voynich’s manusc ip , which con ains a comple e desc ip ion and analysis o his mys e ious manusc ip . Resea che s a e democ a izing he analysis o he Voynich Manusc ip , such as he p ojec con aining in e ac i e on -end2. Ano he simila nascen p ojec 3uses c owd-sou cing o analysis and objec iden i ica ion in he manusc ip . 2h p://www. oynichese.com/ 3h p:// oynich-c owdsou ced.cz/ 2 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 2. Global iew on Voynich manusc ip based on ne wo k analysis in [2]. Fig. 3. Selec ed examples o he simila le e s be ween Khojki dialec (le , ed) and Voynich ( igh , black) based on image co esponding poin s, [2]. One possible heo y ha could lead us owa d he eading o VM is ha he manusc ip is w i en in a language ha is no a i icially de eloped bu comes om an old dialec ha has i s his o ical de elopmen in he sense o a g aphic change o w i ing. I is based on ou p e ious esea ch [2], which discussed alphabe s simila i y based on classical me hods. Figs. 3 and 4 show ha g aphical simila i y measu emen amongs alphabe s is possible and useable. Fig. 3 demons a es he simila i y o Voynich manusc ip le - e s o each o he , whe e indi idual le e s a e g ouped acco ding o hei simila i y, and Fig. 4, whe e we ha e e i ied ha he simila i y measu e also wo ks be ween he Voynich manusc ip alphabe and a andomly selec ed old Indian dialec . These de- ails we e measu ed using he ImageCo espondingPoin ,4 unc- ion, which was used o c ea e ec o s o numbe s whose simila - i y was hen measu ed, [2]. Howe e , since in his pape we need o measu e he simila i y no only be ween le e s o one alphabe o wo alphabe s bu be ween many alphabe s, we decided o use deep lea ning o measu e he simila i y as desc ibed below. In his pape , we aim o show how speci ic me hods and deep lea ning [8–10] can be used o compa e he simila i y be ween in- di idual cha ac e s o he Voynich alphabe o a eason explained in Sec ion 2. We also use he same app oach o compa e he simi- la i y be ween he Voynich alphabe and o he selec ed alphabe s om a ew selec ed old Indian dialec s based on isual simila i y 4Ma hema ica®. Fig. 4. Simila i y o alphabe s wi hin Voynich manusc ip . Alphabe s a e g ouped in o clus e s acco ding i s simila i y, [2]. amongs he alphabe s. Ou analysis aims o es he me hod based on deep lea ning, o comp ehensi e o e iew see [8–10], in o de o de e mine in u u e a leas app oxima ely o which amily o languages he Voynich manusc ip could belong. Thus, his pape is a p oo o concep - a mo e ex ensi e se o alphabe s is needed o gain a ‘‘ inal’’ decision. This is an open esea ch chance o anyone. Simila esea ch in he applica ion o ne wo ks on dialec iden- i ica ion has al eady been done also in [11] (on dis inguishing simila oday exis ing languages and dialec s), [12] (Con olu ional neu al ne wo ks and language embeddings o dialec ecogni ion — acous ic and linguis ic ea u es o he dialec iden i ica ion ask on he A abic dialec al speech da ase ), [13] (Ge man dialec iden i ica ion sha ed ask including ou Ge man dialec s: Basel, Be n, Luce ne and Zu ich) o [14] (discuss mul ilingual encod- ing me hod o dialec iden i ica ion using con olu ional neu al ne wo k da ase o A abic and English language) amongs he o he s. All hese esea ch pape s ha e one hing in common. They wo k and discuss he iden i ica ion and di e en ia ion o languages and dialec s only om he p esen ime — ha is, languages and dialec s known. In hese pape s, isual simila i y is no examined, bu ex o phone ic ea u es a e used. In ou ap- p oach, we wo k wi h languages o unknown o igin and ancien dialec s. The s uc u e o he a icle is as ollows. We begin wi h a sho sec ion on Mo i a ion, explaining in mo e de ail how so - compu ing me hods can be applied o old ex analysis, ollowed by a sec ion desc ibing he Expe imen s Design. In his sec ion, a eade can ind wha echnologies, algo i hms, so wa e, and ha dwa e has been used. We hen desc ibe he cou se o expe - imen s and he esul s ob ained. Finally, we p esen a summa y o all he indings in he Conclusion sec ion. The opic we p esen he e is, in i s comple e o m, complex and ce ainly exceeds he con en o one a icle. The e o e, we limi ou sel es o demons a ing he p oposed me hods and hei applica ion o a small selec ed subse o a ious ancien Indian dialec s. The aim o his a icle is o in o m no only he so com- pu ing communi y abou he Voynich manusc ip bu also o poin ou some in e es ing issues and unsol ed p oblems o his manusc ip , whe e so compu ing can be applied o a ascina ing opic. Thus, he mos essen ial ideas and con ibu ions o his pape a e in hose highligh s: 3 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 5. The wo k low o epo ed esea ch on VM. •In oduce Voynich manusc ip o he compu e science com- muni y and he possibili y o applying a ious algo i hms o i s analysis •In oduce selec ed me hods and algo i hms om AI in o de o help iden i y he amily o he language o igin o Voynich manusc ip •Apply selec ed algo i hms o measu e he simila i y be- ween old dialec s and Voynich manusc ip o es he p o- posed app oach •Discuss possible u u e esea ch on Voynich manusc ip and open esea ch ques ions To gi e a mo e clea idea, a he end o his sec ion, we p esen Fig. 5, which cap u es he main poin s o he esea ch p ocedu e desc ibed in his pape and hus summa izes he s uc u e o his pape . 2. Mo i a ion The mo i a ion o ou esea ch does no s em om he in- en ion o deciphe he Voynich manusc ip , which has p o ed almos impossible so a , bu a he o y known me hods in he ield o so -compu ing/a i icial in elligence o de e mine a pos- sible o igin o co ela ion wi h o he ancien language amilies. Such co ela ion/simila i y can be likely, o cou se, app oxima ely done by some s a is ical ex analysis. Howe e , in his case, he iden i ica ion o he language amily is no based on such analyses o ex s uc u e analyses bu on isual simila i ies. The main idea behind ou expe imen s and he mo i a ion o his a icle is ha he le e s o di e en languages and dialec s g adually e ol ed as he language’s cul u e e ol ed.5,6Thus, i can be said ha each language has i s g aphic e olu ion, and new compu a ional echniques o e he oppo uni y o ace he o i- gin o he selec ed language less o mo e (wi h he p esump ion ha we ha e enough da a). This a icle ocuses on using selec ed algo i hms om he so -compu ing a ea o iden i y he isual simila i y o le e s a he han on he linguis ic analysis o a single language ‘‘g aphical e olu ion’’. 5h ps://use ulcha s.com/blogs/cha s/e olu ion-o - he-english-alphabe 6h p://webspace.ship.edu/cgboe /e olalpha.h ml Fig. 6. An example o co esponding poin s in an image. Calcula ed by he unc ion ImageCo espondingPoin s in Ma hema ica®. To compa e Voynich’s w i ing wi h o he languages and di- alec s, we use a supe compu e 7which can handle he compu- a ionally in ensi e p ocessing equi ed o such kind o analysis. The eason o using a supe compu e in ou pape was a he p epa a o y han necessa y. The expe imen desc ibed in his pape can, o cou se, also be un on a desk op compu e ; howe e , since we a e p epa ing a much la ge and mo e massi e simu- la ion whe e he numbe o possible dialec s will undoub edly go in o he hund eds, and maybe e en mo e, we decided o use he possibili y o easy access o he supe compu e which is pa o ou uni e si y, which we do no mean ha a supe - compu e is necessa y o sol e such a p oblem, bu i will un- doub edly speed up he simula ions. We aim o de ine he land- scape/ oadmap o possible di ec ions o esea ch in analysing he Voynich manusc ip and demons a e he applicabili y o machine lea ning o sol ing he mys e y o his codex. 7h ps://www.i 4i.cz/en 4 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 7. Au o-Encode . Fig. 8. Voynich Le e s - da a-Se . 3. Design o expe imen Ou expe imen s a e based on he idea ha a language ex- p essed in he o m o le e s is he esul o he e olu ion o w i ing s yle om he olde o ms o dialec languages owa d he mode n e sions. They a e essen ially based on a g aphical compa ison o he cu en unknown alphabe sys em and he sea ch o alphabe s close o i in i s g aphic o m. Fo his need, a speci ic algo i hm mus be selec ed and used o compa e he simila i y o indi idual le e s and whole alphabe s. We use neu al ne wo ks o compa e he alphabe o Voynich’s manusc ip and some selec ed ancien Indian dialec s wi h e e ence o ou p e ious expe imen s, whe e he isual simila i y measu e was based only on he g aphical a ibu es o le e s. Bo h me hods a e compa able. Howe e , deep lea ning ANNs can also handle isual simila i y no only be ween le e s bu also amongs he alphabe sys ems. To demons a e p oo -o -concep , he Indian sc ip s and dialec s as he Assamese (Fig. 19), Guja a i (Fig. 20), Hindi (Fig. 21), Khojki Ji a (Fig. 22), Konkani (Fig. 23), Panjabi (Fig. 24) and U du (Fig. 25) has been chosen. The eason is ha ancien India is he home o he wo ld’s oldes w i en language sys ems. India and he Sansk i -based sc ip s we e selec ed as ou s a ing poin s. Why India? The isual inspec ion o he Voynich Manusc ip shows naked-eyes simila i ies be ween he alphabe o Voynich’s manusc ip and some o he ancien Indian dialec s. The eason o choosing hese dialec s was hus ela i ely p osaic. Table 1 Table - Ha dwa e speci ica ions. I ems Speci ica ion P ocesso In el(R) Co e(TM) i7-10750H CPU @ 2.60 GHz, 2592 Mhz, 6 Co e(s), 12 Logical P ocesso (s) RAM Memo y 16 GBs OS Edi ion: Windows 11 Home Ve sion: 21H2 OS build: 22000.1219 Expe ience: Windows Fea u e Expe ience Pack 1000.22000.1219.0 Sys em Model, Sys em Type Ni o AN517-52; x64-based PC GPU NVIDIA GeFo ce RTX 2060 OS Name Mic oso Windows 11 Home The code is accessible a Gi Hub8 o eade s o use and expand ou expe imen s. 3.1. Ha dwa e and so wa e The speci ica ions o he ha dwa e whe e he expe imen was conduc ed is as ollow, see Table 1. As he p og amming equip- men was used Py hon Ve sion 3.9.12 and lib a ies (only he main ones): Tenso low(Ke as), Sklea n, Openc , Ma plo lib amongs he o he s. Bo h expe imen s we e designed, conduc ed, and e alua ed using he shown ha dwa e; howe e , i ano he ha dwa e is used, he in e ence and aining ime migh change. 3.2. Alphabe s as g aphical objec s The expe imen s in his a icle a e based on a simple idea o he simila i y o le e s as g aphic objec s. As has al eady been said, in e e y cul u e, he sc ip u es change mo e o less g adually. These changes can be conside ed as a g aphic mu a ion, which can be used o iden i y he oo o a gi en language, p o ided we ha e enough samples o cap u e hese mu a ions. Bu on he o he hand, he e is a chance o iden i y he o iginal 8h ps://gi hub.com/Vinmel24/On-Compa ing-o -Voynich-Manusc ip s- wi h-Alphabe s-o -o he -Languages-a Xi -bio-a Xi -.gi 5 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 9. Au o Encode A chi ec u e. Table 2 Neu al ne wo k a chi ec u e — De ails. Laye Ac i a ion Func ion Laye Type Ou pu Shape Inpu Laye 28 ×28 ×1 RELU COV2D 28 ×28 ×32 Ma ×pooling2D(2 ×2) 14 ×14 ×32 RELU COV2D 14 ×14 ×16 Ma ×pooling2D(2 ×2) 7 ×7×16 RELU COV2D 7 ×7×8 Fla en (Reshape) 392 Hidden Laye s SIGMOID Dense Connec ed Laye 3 RELU Dense Connec ed Laye 392 Reshape 7 ×7×8 RELU COV2D 7 ×7×16 Upsampling 14 ×14 ×16 RELU COV2D 14 ×14 ×32 UpSampling 28 ×28 ×32 Ou pu Laye SIGMOID COV2D 28 ×28 ×1 language e en wi hou hese mu a ions, p o ided ha he sc ip has no changed adically. The e o e, he le e s and alphabe simila i y was e alua ed a he le el o simila i y o g aphic objec s. Image simila i y [15,16] consis s o inding ea u es o ade- qua ely desc ibing he image con en and inding a sui able me - ic o assessing he simila i y based on ea u e space. The ea u e se can be compu ed globally o he en i e image (e.g. co e- sponding poin s, see Fig. 6, [7]) o locally o a small g oup o pixels such as egions o objec s. We ha e used a unc ion in Ma hema ica®, named ImageCo espondingPoin s,9which inds a se o ma ching in e es poin s (including i s nea es su ound- ings) in image 1 and 2 and e u ns no only pixel coo dina es, bu also in o ma ion calcula ed on i s su oundings. Such poin s can hen be p ojec ed in o one o he used images, as demons a ed in Fig. 6. The localiza ion o such co esponding poin s is no i ial. Nowadays, he e a e me hods like scale-in a ian ea u e ans o m (SIFT) [17,18] o O ien ed FAST and Ro a ed BRIEF (ORB) algo i hm in [19] amongs he o he s. Ex ac ing co esponding poin s in wo images, and educing he image in o ma ion o a se o pai s o poin s, can be com- plica ed. Since he e iciency o egis a ion depends hea ily on how accu a ely he poin s a e iden i ied, he poin s can usually be in e ac i ely selec ed by he use . The poin s can ep esen some hing o he han salien and p ecisely loca able poin s o he mo phology o he isible objec s uc u e. Any ma ching poin s ha he use can con iden ly and unambiguously iden i y in bo h images will se e his pu pose. One o he disad an ages 9h ps:// e e ence.wol am.com/language/ e /ImageCo espondingPoin s.h ml Fig. 10. Loss Values pe Epoch. o manual me hods is ha hey equi e a ime-consuming and edious ask o be pe o med by a use who is knowledgeable in he ield. This disad an age, along wi h he a guably mo e signi ican disad an ages o epea abili y and a iabili y, jus i ies using exis ing algo i hms o his pu pose. Fo hese easons, we used he unc ion ImageCo espondingPoin s o he so wa e Ma hema ica®, which can ind hese poin s, o a leas ind hese poin s in he same way in di e en images. Thus, we ha e au o- ma ically con e ed complex on shapes in o a ec o o numbe s o co esponding poin s. The expe imen epo ed in his pape was di ided in o wo pa s. The i s pa compa es Voynich le e s among hemsel es o e i y ha his app oach is alid. To accomplish such a ask, 6 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 11. In e ence Time/pe sample — Expe imen 1. we used a speci ic a chi ec u e o a neu al ne wo k called au o- encode [20–23], Fig. 7. The au o-encode educes he dimension o he Voynich da a se o ec o s o h ee dimensions (hidden laye wi h h ee neu ons). By his educ ion, he da a can be plo ed in a 3D coo dina e sys em wi h all he poin s linked o hei co esponding images; he e o e, isually, we can iden i y how close he images a e o each o he . In his scena io, he close he poin , he mo e simila he images a e. The second me hod we used is a dimensional educ ion by au o-encode s [24–26]. Howe e , due o he numbe o images o compa e, we could no ge accu a e esul s wi h h ee dimensions o a La en Space (bo leneck) [27]. So i used a bo leneck o 4 ×4 pixels ( ec o o 16 dimensions) ins ead. A e he educ ion, he new da a se was all he le e s in hei co esponding educed ep esen a ion. The Co ela ion Ma ix was hen used o ind he simila i ies by calcula ing he Pea son co ela ion [28] among he le e s. 3.3. Au o-encode — he wo king p inciple Acco ding o [20]: Au o-encode has supe ised lea ning. The ne wo k akes he inpu ma ix and is o ced o p oduce an ou pu equal o i s co esponding inpu . The back-p opaga ion unc ion uses he inpu s as he da a o mimic. Since he ne wo k is ained o ou - pu he same inpu , he Bo leneck ep esen s a educed dimensional ep esen a ion o he knowledge o he inpu o single da a poin s. The comp essed inpu is again uncomp essed in he ou pu o m. An au o-encode , Fig. 7, consis s o 3 componen s: Encode , La en Space (o bo leneck) and Decode . The encode com- p esses he inpu and p oduces he La en Space. The decode hen econs uc s he inpu only using he alues ob ained du ing he aining p ocess in he La en Space. y(x)=a l(Wl(. . . a 1(W1∗a 0(W0X+b0)+b1)) . . . +bl) (1) whe e, 1. l, is he numbe o Laye s wi hin he ne wo k. 2. Wl, is he ma ix o weigh s in i s co esponding laye 3. X, is he ma ix o Inpu s 4. B, The ma ix o Biases in each laye 5. a l, is he ac i a ion unc ion pe laye ... The Eq. (1) shows he pass o wa d mul iplica ion compu ed du ing he aining p ocess. The ou L=L (y(x),x) (2) whe e, 1. L , is he co esponding Loss/Cos Func ion The Eq. (2) calcula es he loss o he ne wo k a e e e y Epoch; he loss is calcula ed by compu ing how di e en he ou pu and he inpu o he ne wo k a e. The used model uses Mean Squa ed E o he calcula e he loss alue. Du ing he aining p ocess, all he ainable pa ame e s will be adjus ed, so he model ou pu s he inpu alues. A e he aining p ocess, once an inpu alue is ed o he model, he bo leNeck (Wbn) p oduces a educed dimensional ep esen a ion o he inpu da a. The numbe o nodes pe laye dec eases wi h each subse- quen encode laye and inc eases back o he decode . Also, he decode is symme ic o he encode in e ms o he laye s uc u e. The au o-encode can be as deep as needed. Fig. 7 is de- pic ed au o-encode wi h i e laye s. The weigh s o La en Space a e he alues we will use and ex ac a e he aining p o- cess, which will subsequen ly se e as he educed dimensional ep esen a ion o he le e s used in expe imen s. Fig. 12. Resul o he p edic ion — Voynich-1. Fig. 13. Resul o he p edic ion — Voynich-2. 7 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 14. Resul o he p edic ion — Voynich-3. Fig. 15. Resul o he p edic ion — Voynich4. Fig. 16. 3D Coo dina e Sys em — Voynich Le e s, di e en angle iew. 8 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 17. 3D Coo dina e Sys em — Voynich Le e s, di e en angle iew. 3.4. Pea son co ela ion coe icien In he second expe imen , as e e ed u he , he Pea son coe icien has been used o calcula e how s ong he co ela ion be ween each Voynich Le e is in i s 1D ep esen a ion o he le e s o he es o he alphabe s in hei 1D ep esen a ion. Acco ding o [29]The Pea son co ela ion coe icien is a measu e o linea associa ion be ween wo in e al- o a io-le el a iables. Al hough he e a e o he ypes o co ela ion, he Pea son co ela ion coe icien is he mos common. Co ela ions a e o en compu ed du ing a esea ch p ojec ’s explo a o y s age o see he ela ionships he di e en con inuous a iables ha e wi h each o he . The equa ion o calcula e Pea son’s co ela ion coe icien is desc ibed as ollows, PC =∑(xi−¯ x) (yi−¯ y) √∑(xi−¯ x)2∑(yi−¯ y)2 (3) whe e, xi= alues o he x- a iable in a sample ¯ x=mean o he alues o he x- a iable yi= alues o he y- a iable in a sample ¯ y=mean o he alues o he y- a iable The equa ion e u ns a alue be ween −1 and 1, whe e: •1: indica es a s ong posi i e ela ionship. • −1: indica es a s ong nega i e ela ionship. •0: indica es no ela ionship a all. A co ela ion coe icien o 1 means ha o e e y posi i e inc ease in one a iable, he e is a posi i e inc ease o a ixed p opo ion in he o he . A co ela ion coe icien o −1 means ha o e e y posi i e inc ease in one a iable, he e is a nega i e dec ease o a ixed p opo ion in he o he . The alue 0 means ha he e a e no posi i e o nega i e changes o e e y inc ease. The e o e, hey bo h a e no ela ed. 3.5. The da a se s Two basic da a se s we e selec ed o ou expe imen . The i s con ains only he Voynich alphabe i sel . On his da a se , we wan ed o es how ou me hods could compa e he le e ’s simila i y o he same alphabe and how accu a ely i compa es g aphic objec s. The second da a se ( o he 2nd expe imen ) consis s o selec ed old dialec s compa ed mu ually o each o he . As al eady men ioned, se e al ancien Indian dialec s we e chosen, namely Assamese (Fig. 19), Guja a i (Fig. 20), Hindi (Fig. 21), Khojki Ji a (Fig. 22), Konkani (Fig. 23), Panjabi (Fig. 24) and U du (Fig. 25). The i s goal is o iden i y any simila i ies among he Voynich le e s hemsel es. Fig. 8 shows he alphabe , which is composed o 25 le e s and special cha ac e s. Fo isualiza ion pu poses, 9 I. Zelinka, M. La a, L.C. Windso e al. Applied So Compu ing 138 (2023) 110217 Fig. 39. G aphical simila i y — he esul s. Fig. 40. G aphical Rep esen a ion — Final Resul o Expe imen 2. Decla a ion o compe ing in e es The au ho s decla e ha hey ha e no known compe ing inan- cial in e es s o pe sonal ela ionships ha could ha e appea ed o in luence he wo k epo ed in his pape . Da a a ailabili y Da a will be made a ailable on eques . Acknowledgemen s The ollowing g an s a e acknowledged o he inancial sup- po p o ided o his esea ch: g an o SGS No. SP2023/050, VSB-Technical Uni e si y o Os a a, Czech Republic. This wo k was suppo ed by he Eu opean Regional De el- opmen Fund in he ‘‘A Resea ch Pla o m ocused on Indus y 4.0 and Robo ics in Os a a Agglome a ion’’ p ojec , eg. No. CZ.02.1.01/0.0/0.0/17-049/0008425 wi hin he Ope a ional P o- g amme Resea ch, De elopmen and Educa ion. 16 I. Zelinka, M. La a, L.C. Windso e al. 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