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. Applied So Compu ing 138 (2023) 110217
This wo k was suppo ed by he Eu opean Regional De elop-
men Fund in he Resea ch Cen e o Ad anced Mecha onic Sys-
ems p ojec , p ojec numbe CZ.02.1.01/0.0/0.0/16-019/0000867
wi hin he Ope a ional P og amme Resea ch, De elopmen and
Educa ion.
Re e ences
[1] D.R. Amancio, E.G. Al mann, D. Rybski, O.N. Oli ei a J ., L.d.F. Cos a, P obing
he s a is ical p ope ies o unknown ex s: applica ion o he Voynich
manusc ip , PLoS One 8 (7) (2013) e67310.
[2] I. Zelinka, O. Zmeskal, L. Windso , Z. Cai, Uncon en ional me hods in
oynich manusc ip analysis, in: Mendel, Vol. 25, 2019, pp. 1–14.
[3] C.L. Bowe n, L. Lindemann, The linguis ics o he Voynich manusc ip ,
Annu. Re . Linguis . 7 (2021) 285–308.
[4] V. Ma lach, D.G. K i ochen, J. Milička, A me hod o compa ison o gene al
sequences ia ype- oken a io, in: P oceedings o QUALICO, 2018.
[5] M.A. Mon emu o, D.H. Zane e, Keywo ds and co-occu ence pa e ns in
he Voynich manusc ip : An in o ma ion- heo e ic analysis, PLoS One 8 (6)
(2013) e66344.
[6] E. Hemingway, The Old Man and he Sea, Wo ld He i age Publishe s L d,
2015.
[7] I. Zelinka, T.T. Dao, On Voynich alphabe analysis wi h ela ion o he old
Indian dialec s, in: MENDEL, Vol. 26, 2020, pp. 15–22.
[8] Y. Guo, Y. Liu, A. Oe lemans, S. Lao, S. Wu, M.S. Lew, Deep lea ning o
isual unde s anding: A e iew, Neu ocompu ing 187 (2016) 27–48.
[9] A. Voulodimos, N. Doulamis, A. Doulamis, E. P o opapadakis, Deep lea ning
o compu e ision: A b ie e iew, Compu . In ell. Neu osci. 2018 (2018).
[10] L.C. Yan, B. Yoshua, H. Geo ey, Deep lea ning, Na u e 521 (7553) (2015)
436–444.
[11] Y. Belinko , J. Glass, A cha ac e -le el con olu ional neu al ne wo k o
dis inguishing simila languages and dialec s, 2016, a Xi p ep in a Xi :
1609.07568.
[12] S. Shon, A. Ali, J. Glass, Con olu ional neu al ne wo ks and language
embeddings o end- o-end dialec ecogni ion, 2018, a Xi p ep in a Xi :
1803.04567.
[13] M. Ali, Cha ac e le el con olu ional neu al ne wo k o Ge man dialec
iden i ica ion, in: P oceedings o he Fi h Wo kshop on NLP o Simila
Languages, Va ie ies and Dialec s (Va Dial 2018), 2018, pp. 172–177.
[14] A.A. Helmy, A mul ilingual encoding me hod o ex classi ica ion and
dialec iden i ica ion using con olu ional neu al ne wo k, 2019, a Xi
p ep in a Xi :1903.07588.
[15] N. Vasconcelos, A. Lippman, A uni ying iew o image simila i y, in: P o-
ceedings 15 h In e na ional Con e ence on Pa e n Recogni ion. ICPR-2000,
Vol. 1, IEEE, 2000, pp. 38–41.
[16] R. Shanmugamani, Deep Lea ning o Compu e Vision: Expe Techniques
o T ain Ad anced Neu al Ne wo ks using Tenso Flow and Ke as, Pack
Publishing L d, 2018.
[17] D.G. Lowe, Objec ecogni ion om local scale-in a ian ea u es, in:
P oceedings o he Se en h IEEE In e na ional Con e ence on Compu e
Vision, Vol. 2, Ieee, 1999, pp. 1150–1157.
[18] T. Lindebe g, Image ma ching using gene alized scale-space in e es poin s,
J. Ma h. Imaging Vision 52 (1) (2015) 3–36.
[19] Y. Qin, H. Xu, H. Chen, Image ea u e poin s ma ching ia imp o ed ORB,
in: 2014 IEEE In e na ional Con e ence on P og ess in In o ma ics and
Compu ing, IEEE, 2014, pp. 204–208.
[20] A. Kee hi Nayani, C. Sekha , M. S ini asa Rao, K. Venka a Rao, Enhancing
image esolu ion and denoising using au oencode , in: Da a Analy ics and
Managemen , Sp inge , 2021, pp. 649–659.
[21] S. Lange, M. Riedmille , Deep au o-encode neu al ne wo ks in ein o ce-
men lea ning, in: The 2010 In e na ional Join Con e ence on Neu al
Ne wo ks, IJCNN, IEEE, 2010, pp. 1–8.
[22] Y. Wang, H. Yao, S. Zhao, Au o-encode based dimensionali y educ ion,
Neu ocompu ing 184 (2016) 232–242.
[23] L. Badino, C. Cane a i, L. Fadiga, G. Me a, An au o-encode based app oach
o unsupe ised lea ning o subwo d uni s, in: 2014 IEEE In e na ional
Con e ence on Acous ics, Speech and Signal P ocessing, ICASSP, IEEE, 2014,
pp. 7634–7638.
[24] C. Zhou, R.C. Pa en o h, Anomaly de ec ion wi h obus deep au oencode s,
in: P oceedings o he 23 d ACM SIGKDD In e na ional Con e ence on
Knowledge Disco e y and Da a Mining, 2017, pp. 665–674.
[25] S.M. E ani, S. Rajasega a , S. Ka unaseke a, C. Leckie, High-dimensional
and la ge-scale anomaly de ec ion using a linea one-class SVM wi h deep
lea ning, Pa e n Recogni . 58 (2016) 121–134.
[26] V. Singh, K.R. Kuma , K. Eswa an, Lea ning disc imina i e ea u es using
encode -decode ype deep neu al ne s, 2016, a Xi p ep in a Xi :1607.
01354.
[27] Y. Zhao, P. Yu, S. Mahapa a, Q. Su, C. Chen, Imp o e a ia ional au-
oencode o ex gene a ionwi h disc e e la en bo leneck, 2020, a Xi
p ep in a Xi :2004.10603.
[28] J. Benes y, J. Chen, Y. Huang, I. Cohen, Pea son co ela ion coe icien , in:
Noise Reduc ion in Speech P ocessing, Sp inge , 2009, pp. 1–4.
[29] S. Boslaugh, S a is ics in a Nu shell, O’Reilly Media, Inc., 1005 G a ens ein
Highway No h, Sebas opol, CA 95472, 2013.
[30] U. Ruby, V. Yendapalli, Bina y c oss en opy wi h deep lea ning echnique
o image classi ica ion, In . J. Ad . T ends Compu . Sci. Eng. 9 (10) (2020).
17