A no el u ban mobili y classi ica ion app oach based on con olu ional
neu al ne wo ks and mobili y- o-image encoding
Peppino Fazio
a,b,
⇑
, Mi alem Mehic
b,c
, Mi osla Voznak
b
a
DSMN, Ca’ Fosca i Uni e si y o Venice, Via To ino 155, 30172 Mes e, VE, I aly
b
VSB – Technical Uni e si y o Os a a, 17. lis opadu 2172/15, 70800 Os a a, Czechia
c
Depa men o Telecommunica ions, Facul y o Elec ical Enginee ing, Uni e si y o Sa aje o, Zmaja od Bosne bb, 71000 Sa aje o, Bosnia and He zego ina
a icle in o
A icle his o y:
Recei ed 21 No embe 2022
Re ised 22 Ma ch 2023
Accep ed 13 Ap il 2023
A ailable online 27 Ap il 2023
Keywo ds:
Con olu ional neu al ne wo ks
Da a-2-image con e sion
Machine lea ning
Mobili y classi ica ion
Pa e n p edic ion
abs ac
O e he las ew decades, he classi ica ion and p edic ion o mobili y ajec o ies in dynamic ne wo ks
ha e become majo esea ch opics. Swi ching o mobili y a eas (hand-o e ) in mode n cellula ne wo ks
is equen due o es ic ed co e age a ea and node speeds (u ban, highway, e c.). Accu a e managemen
o hand-o e e en s is highly desi able o imp o e he sys em’s quali y o se ice. We ha e exploi ed he
high accu acy o machine lea ning o classi y use mobili y om mobili y aces which we encoded in o
images. The me hod deli e s high pe o mance in mobili y classi ica ion/p edic ion (exceeding 95%) and
a oids he need o s udy and implemen a dedica ed neu al ne wo k s uc u e. The echnique equi es
he con e sion o mobili y aces in o image s uc u es and he subsequen applica ion o a con olu ional
neu al ne wo k. We p opose a no el app oach o classi ying mobili y ha in ol es da a- o-image encod-
ing and machine lea ning o image classi ica ion. Nume ous simula ions we e pe o med o demons a e
he bene i s o he p oposed echnique and o illus a e he a iance in he accu acy o he unc ions o
many encoding/classi ica ion pa ame e s. The wo k ep esen s a i s p elimina y s ep owa ds a new
mobili y p edic ion app oach. We demons a e ha i is possible o achie e a e y high le el o p edic ion
accu acy wi h low compu a ional complexi y, exploi ing he s eng h o neu al ne wo ks in image
ecogni ion.
Ó2023 The Au ho (s). Published by Else ie B.V. on behal o King Saud Uni e si y. 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/).
1. In oduc ion
The ad en o 5G echnology and ela ed s udies conce ning i s
po en ial la ency and bandwid h pe o mance (Liu e al., 2020)in
mobile ne wo ks ha e demons a ed ha i is possible o a ain a
good le el o Quali y o Se ice (QoS), especially i p edic i e
app oaches a e in eg a ed in o he sys em (Fazio e al., 2017;
Fazio e al., 2023) a e co ec ly modeling a ic lows (K ome
e al., 2020; K ome e al., 2018; De Rango e al., 2005). Machine
and deep lea ning applica ions (Ma in e al., 2021; Singh e al.,
2021; Xu e al., 2021) ha e also s eeply p oli e a ed in he las
ew yea s and added eno mous alue o he so wa e which can
exploi hem. In he cu en wo k, we especially highligh he pos-
sibili y o using well-known Con olu ional Neu al Ne wo ks
(CNNs) (Khan e al., 2018) o classi y mobili y a e ansposing
he mobili y da a in o sui able mobili y images (ins ead o eal-
wo ld images). Ou wo k does no p opose a new neu al ne wo k
laye scheme o image classi ica ion me hod. S ill, we demons a e
he s eng h o CNNs (Luo e al., 2018) in hei accu acy and how
hey can be applied o classi ying/p edic ing mobili y. Neu al-
based image classi ica ion algo i hms a e known o achie e an
accu acy o 95–98 %whe eas mobili y classi ica ion o p edic ion
schemes such as hose desc ibed in Jin e al. (2001), Gaiduchenko
and G i syk (2019),Fazio e al. (2017), Zhang e al. (2018) can
ob ain, o he bes o ou knowledge, a maximum accu acy o abou
85–87 %, which is well below 90 %.Fig. 1 shows a gene ic e e -
ence scena io: mobile hos s a e ee o mo e in any geog aphical
a ea, each one co e ed by a 5G mic o/ em o-cell. Fo example,
o he black pa h, a mobili y p edic i e app oach can be in eg a ed
wi h 5G a chi ec u e, in o de o ese e esou ces (bandwid h
channels) in-ad ance, a oiding se ice dis up ions o he mobile
hos (da ke cells). The encoding can be made locally, on- he- ly,
h ps://doi.o g/10.1016/j.jksuci.2023.101561
1319-1578/Ó2023 The Au ho (s). Published by Else ie B.V. on behal o King Saud Uni e si y.
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/).
⇑
Co esponding au ho .
E-mail add esses: [email p o ec ed] (P. Fazio), [email p o ec ed]
(M. Mehic), [email p o ec ed] (M. Voznak).
Pee e iew unde esponsibili y o King Saud Uni e si y.
P oduc ion and hos ing by Else ie
Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
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Compu e and In o ma ion Sciences
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o emo ely, by a dedica ed se e , while he emo e CNN ecei es
he images and he ela ed belonging cell, ha ing he possibili y o
be ained and, hen, alida ed. S a ing om his obse a ion, a
new me hod o con e ing mobili y-da a in o image-da a is p o-
posed; in pa icula , he main con ibu ions o he cu en wo k
can be summa ised as:
A p oposed inno a i e me hod o encoding mobili y da a in o
images, aking in o accoun he en opy me ic (F ank and
F ank, 2020), o assis he CNN in eaching a be e alida ion
accu acy;
No need o he design and implemen a ion o a new neu al ne -
wo k: he mos s aigh o wa d CNN s uc u es a e aken in o
accoun (we do no design a new laye ing s uc u e, we demon-
s a e how i can pe o m in i s simples con igu a ion);
E alua ion o CNN pe o mance in he unc ion o encoding
pa ame e s such as sampling equency, encoding algo i hm,
image size, e c.;
Base s a ion capabili y o ecognizing he geog aphical a ea
whe e a mobile hos is mo ing wi hou he aid o GPS o o he
posi ioning de ices. Mobile nodes and base s a ions can apply
Angle-o -A i al (AoA), P oximi y, T ila e a ion, o Time Di e -
ence o A i al (TDoA) me hods. Ou encoding scheme unc ions
wi h no malized mobili y da a so he ained CNN ecognizes
he mobili y egion wi hou accu a e GPS da a.
The emainde o he pape is s uc u ed as ollows: Sec ion 2
in oduces some ecen wo ks which examine mobili y classi ica-
ion and p edic ion; Sec ion 3desc ibes he main p oposed algo-
i hm, speci ying su icien de ail ega ding he encoding
app oach; Sec ion 4desc ibes in de ail he main esul s ob ained
h ough he p oposed app oach; Sec ion 5concludes he pape ,
ema king on he main ad an ages o he p oposed algo i hm.
2. Rela ed wo k
This sec ion e iews he main li e a u e con ibu ions conce n-
ing mobili y classi ica ion, p edic ion, and image ecogni ion. We
examined he exis ing li e a u e and ound ha no s udies ha e
in eg a ed hese ea u es and exploi ed he s eng h o image-
classi ica ion CNNs o sugges ed me hods o encoding mobili y
aces in images. We ho oughly e iew he mos signi ican wo ks
ela ed o ou p oposal. In pa icula , ehicle ajec o y is consid-
e ed as a ime se ies (coo dina es, speeds, and ehicle pa ame e s
a e ime-dependen ). The g ea pe o mance o CNNs (Ka im e al.,
2019) is exploi ed o mul i a ia e ime se ies classi ica ion: he
au ho s in oduced mul iple con olu ional laye s o ea u es
ex ac ion, showing he classi ica ion accu acy o he p oposed
me hod in he unc ion o he da ase noise and ob aining an accu-
acy ha anges om 30%and 100%. The au ho s o Asad e al.
(2020) ocused on a ele s p o iling in ain s a ions o analyze
how humans beha e acco ding o hei age ( wo age classes a e
conside ed: 16–59 and 60-and-o e ) du ing he Co id-19 disease
pandemic. In pa icula , he au ho s employed six di e en classi-
ie s (Logis ic Reg ession, Mul i-laye Pe cep on, Suppo Vec o
Machine, Random Fo es , K-nea es Neighbou , and Decision T ee)
o es ablish au oma ion in in elligen decisions while lea ning
om his o y and adap ing o he es ing en i onmen . Gi en he
desc ibed da ase (London Unde g ound and O e g ound - LUO),
he p oposed idea can moni o po en ial con ac s/p oximi y a el-
e s and ad ise hem o sa egua d ulne able age-g oup a ele s.
Simula ion esul s eached an accu acy o abou 82%and 86% o
he wo age classes.
The impo ance o mobili y p edic ion is s a ed by se e al li e -
a u e con ibu ions, such as he ones in Fazio e al. (2017), Zhang
e al. (2018), whe e he au ho s su ey he main con ibu ions, also
in e ms o di e en me hodologies and app oaches, in he wo ld
o mobili y p edic ion. I has been s udied o decades, and he e
is a wide a ie y o p edic i e models (Kalman il e s, Ma ko
chains, Neu al Ne wo ks, Au o Reg essi e, e c.). In he men ioned
wo ks, he au ho s compa e he di e en app oaches, showing
he po en iali ies o each p edic o . I is also unde lined ha he
eached accu acy is gene ally below 90%. The wo k in Wang
e al. (2021) p oposes an inno a i e a en ional Ma ko model,
conside ing he long- e m co ela ion wi h his o ical ajec o ies
and con ex in o ma ion and p edic ing u u e hos posi ions. The
au ho s conside ed an ex ensi e da ase (mo e han 20000 use s),
ob aining an imp o emen o he classical machine lea ning
app oaches (such as he Hidden Ma ko Model - HMM, Recu en
Neu al Ne wo k - RNN, F iendship, and Mobili y - MF, e c.), wi h a
as e execu ion ime.
Fo many yea s, machine lea ning and neu al ne wo ks ha e
been widely used in image ecogni ion. The con olu ional laye
o CNNs can disco e some hidden ea u es o he inpu images
while he subsequen laye s p oduce he co ec ou pu . The wo k
in Chen e al. (2019) ex ends he well-known LeCun’s CNN (Lecun
e al., 1998), adding con olu ional and pooling laye s and p opos-
ing a Mul i-Con olu ion NN (MCNN). The au ho s es ed he new
CNN on he Ca s s. Dogs (Dogs s Ca s da ase , 2023), Ci a -10
(K izhe sky, 2023), and Fe 2013 (Facial Exp ession Recogni ion
da ase , 2013) da ase s, showing ha he p oposed MCNN ou pe -
o ms he classical one in e ms o complex- ex u e ea u es ecog-
ni ion. The au ho s o Tiwa i e al. (2020) p oposed he Visual
Geome y G oup 16 (VGG16) model o classi y images in o wo
addi ional ca ego ies ins ead o pe o ming ea u e ex ac ion o
segmen a ion. VGG16 o e s an accu acy o 99%, and images a e
u he ca ego ized in o addi ional sub-ca ego ies. The pape (Xu
e al., 2020) is ela ed o he comp essed-domain image classi ica-
ion: images a e conside ed be o e encoding in he desi ed o ma
( he econs uc ion s ep is bypassed), and he aining is made
wi h a dynamic Measu emen Ra e (MR) by selec ing he needed
MR wi h he help o a sensing ma ix. The au ho s es ed hei p o-
posal on a massi e se o da ase s (e.g. Ci a -10 (K izhe sky, 2023),
and Coil-100 (Nene e al., 2023)), and he pe o mance has been
e y sa is ac o y, also in e ms o noise obus ness.
Taking in o accoun he main esul s discussed abo e, we will
illus a e, in he nex sec ion, ou p oposal, o design a new mobil-
i y classi ica ion algo i hm based on CNNs and mobili y- o-image
encoding.
3. Mobili y classi ica ion h ough CNNs imaging
This sec ion is dedica ed o ou main p oposal. Fi s o all, we
will in oduce he main issue. Then we will gi e an in-dep h o e -
iew o mobili y encoding and he ype o used CNN. We a e no
p oposing a new CNN s uc u e bu a new app oach o mobili y
classi ica ion, which can exploi he high accu acy o CNNs in
image classi ica ion. In addi ion, we a e no conside ing any pa ic-
ula kind o node (a ehicle, a human, a mobile senso , an
Unmanned Ae ial Vehicle, e c.), so he app oach is comple ely gen-
e al (simula ion esul s will be specialized o a pa icula case).
Fig. 2 illus a es he main s eps o ou p oposed idea h ough
Da a-Flow Diag am s uc u es. As shown in igu e (a), mobili y
aces a e gene a ed o all he conside ed geog aphical a eas
based on eal maps and eal a ic beha io s; hen, we p opose
wo possible algo i hms o con e ing he c ea ed da a in o ma i-
ces and, in he end, in o images. In his way, each pa h o a mobile
use is s o ed as a se o images, so he use s mo ing in o he same
a ea c ea e images belonging o he same class. Then (b), a classical
CNN is ained based on he p e iously gene a ed se o images; we
ca ied ou se e al simula ions o a oid o e - i ing and ind he
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
2
bes ade-o be ween he subse o he images o aining and
he subse o he images o alida ion. Once he CNN has been
ained (c), each new mobile ace can be classi ied adequa ely, gi -
ing he CNN a sho po ion o he ace as inpu . All he implemen-
a ion de ails a e gi en in he ollowing subsec ions and as
simula ion esul s.
3.1. The gene al model o mobili y classi ica ion
We a e conside ing a gene al se o Mobili y A eas (e.g., a squa e
a ea on he Ea h’s su ace, a po ion o he sky, a olume in he
sea/ocean, e c.) MAs ¼ma
1
;ma
2
;...;ma
n
g
, wi h jMAsj¼n. Each
ma
i
2MAs, can be adjacen o ano he ma
j
2MAs, wi h i–jand
i;j¼1;...;n, o i can be loca ed in a comple ely di e en pa o
he Ea h/sky.
Le us indica e wi h V he se o mobile nodes which a e mo ing
in o MAs: we assume ha V¼
1
;...;
m
g
and jVj¼m. So, ou
sys em has nmobili y a eas and mmobile nodes. Each
k
2V
mo es in o only one ma
i
2MAs, so we can use he no a ion
k;i
o indica e he k h mobile node is mo ing in ma
i
2MAs.
Unde hese assump ions, we canno ha e
k;i
and
k;j
a he same
ime.
Wi hou loss o gene ali y, we assume ha each mobile node
mo es in a 3D en i onmen , so each ma
i
2MAs is cha ac e ized
by a cen e c
i
¼cx
i
;cy
i
;cz
i
ðÞand an ex ension adius
i
, ha is
ma
i
¼c
i
;
i
ðÞ, wi h cx
i
;cy
i
;cz
i
2R. So, each ma
i
2MAs can be ep e-
sen ed as a sphe e (o a ci cle in 2D mobili y). Ou model is alid i
a cube o a squa e is conside ed.
Each node
k;i
, by i s mobili y in ma
i
, c ea es a pa e n
P
k
¼
x
k
;
y
k
;
z
k

, whe e ¼1;2;...is he disc e e ime index,
wi h
l

l1
ðÞ¼T, he sampling pe iod ( he pe iod a which
mobili y posi ion is sampled and s o ed). We can e e o P
k
also
by he no a ion P
k
¼
x
1
k
;
y
1
k
;
z
1
k

;
x
2
k
;
y
2
k
;
z
2
k

;...;

x
k
;
y
k
;
z
k

;...g, gi en ha i is composed by a sequence o i-
ple s (in he gene al case o 3D space). An o de ed subse o P
k
;p
0
k
,
o leng h pis de ined as p
0
k
#P
k
:
Fig. 1. An example o 5G cellula co e age and use s ajec o ies encoded in o images, able o ain a emo e se e and i s CNN.
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
3
p
0
k
¼x
1
;y
1
;z
1
ðÞ;x
2
;y
2
;z
2
ðÞ;...;x
p
;y
p
;z
p

i 9
0
j...
x
1
;y
1
;z
1
ðÞ
¼
x
0
k
;
y
0
k
;
z
0
k

;...
x
2
;y
2
;z
2
ðÞ¼
x
0
þ1
k
;
y
0
þ1
k
;
z
0
þ1
k

;...
x
p
;y
p
;z
p

¼
x
0
þp
k
;
y
0
þp
k
;
z
0
þp
k

:
ð1Þ
So, unde he assump ions abo e, i we e e o
k;i
, i means ha :
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
cx
i

x
k

2
þcy
i

y
k

2
þcz
i

z
k

2
hi
6
i
8 2N:ð2Þ
Eq. 2indica es ha each poin o he mobili y pa e n o
k
is
bounded o he ex ension a ea (o olume) o ma
i
.
The goal o ou en i e a icle is: gi en an o de ed subse p
0
k
(ex ac ed om P
k
), a CNN should classi y i by e u ning he
ma
i
in which node
k
is mo ing.
To each his aim, i s o all, we p opose a mobili y- o-image
encoding scheme, and hen, he CNNs a e ained and alida ed
by he ob ained encoded da ase s.
3.2. Mobili y o ma ix encoding: MME, an al e na i e o aw da a
ep esen a ion
Based on he de ini ions abo e, we will p opose a new way o
encode mobili y da a in o lossless images (basically, a ma ix is
ob ained, hen s o ed as an image h ough a p ope lossless codec).
Le us s a wi h a mobili y pa e n subse
p
0
k
¼
x
k
;
y
k
;
z
k

j 2
0
;
0
þp
½

. As ea lie de ined, i is a
se o iple s x;y;zðÞ(in he gene al case o a 3D mobili y). We
can e alua e he ela ed speed s
0
k
o node
k
du ing he ime ange
0
;
0
þp½as:
s
0
k
¼
1
T

x
0
þlþ1
k

x
0
þl
k
;
y
0
þlþ1
k

y
0
þl
k
;...
z
0
þlþ1
k

z
0
þl
k
no
;
ð3Þ
wi h l¼0;1;...;p1, and sx
0
k
¼ x
0
þlþ1
k
 x
0
þl
k

;
sy
0
k
¼ y
0
þlþ1
k
 y
0
þl
k

;sz
0
k
¼ z
0
þlþ1
k
 z
0
þl
k

. The leng h o s
0
k
will be p1.
We can also e alua e he accele a ion/decele a ion a
0
k
o node
k
du ing he ime ange
0
;
0
þp½as:
a
0
k
¼
1
T
sx
0
þqþ1
k
sx
0
þq
k
;sy
0
þqþ1
k
sy
0
þq
k
;...sz
0
þqþ1
k
sz
0
þq
k
no
;ð4Þ
wi h q¼0;1;...;p2, and ax
0
k
¼sx
0
þqþ1
k
sx
0
þq
k

;ay
0
k
¼
sy
0
þqþ1
k
sy
0
þq
k
Þ;az
0
k
¼sz
0
þqþ1
k
sz
0
þq
k

. The leng h o a
0
k
will be
p2.
In he ollowing, we will use he sho e no a ions o p
0
k
;s
0
k
and
a
0
k
. In he case o Raw Mobili y Da a (RMD) ep esen a ion, he
in o ma ion is con e ed om a ec o o a ma ix o ma . Th ee
ma ices a e ob ained o p
0
k
;s
0
k
and a
0
k
. Wi hou loss o gene ali y,
we assume ha , o RMD, pis a squa e alue, so i is easy o de ine
¼ffiffiffi
p
p. Fo speed and accele a ion ec o s, he missing elemen s (1
and 2, espec i ely) can be padded du ing he ma ix cons uc ion
(we assume ha , o example, he alues a e eplaced by ze os).
Ma ix dimensions a e x3 , because columns a e dedica ed o
each coo dina e.
Fig. 2. The Da a-Flow Diag ams o he h ee s eps p o ided in ou p oposal.
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
4
Algo i hm 1 ep esen s jus a da a-s uc u e ans o ma ion
wi h a compu a ional complexi y h
2

. I is applied o posi ion,
speed, and accele a ion ec o s, accep ing as inpu he ec o
ec
0
k
con aining posi ion, speed, o accele a ion mobili y in o ma-
ion (speci ied in he inpu pa ame e ype) ela ed o mobile hos
k
, ha is one o he e ms in Eq. 5. Fi s ly, he algo i hm e alua es
he igh ma ix dimension . Then i execu es wo nes ed Fo
cycles o ill up he ows and columns o he ou pu ma ix M
0
k
,
which has been ini ially se o he null ma ix and no malized in
he ange 0;1½a he end. Inside he nes ed loops, he no a ion
ec
0
k
c;ind
ðÞ, wi h c= 1,2,3 e e s o he x;yand zcomponen s o
he
ec
0
k
cðÞ iple .
Le us see how he aw da a can be e ec i ely encoded while
pu ing i in o a ma ix s uc u e. We can s a o build h ee sep-
a a e ma ices om he h ee ec o s. A sp eading ac o s is
de ined, and each ma ix will be squa e: se ing ¼ps ðÞ, hen
he dimensions will be x . All he elemen s o p
0
k
;s
0
k
and a
0
k
a e
ini ially e-scaled ( s) be ween 0 and 1 ( hey can also con ain neg-
a i e alues), so we can w i e:
p
0
k
¼ s p
0
k

;s
0
k
¼ s s
0
k

;a
0
k
¼ s a
0
k

:ð5Þ
The s ope a ion di ides all he elemen s o a ec o by he maxi-
mum one i he e a e no nega i e alues; o he wise, he absolu e
alue o he lowes nega i e elemen is added o each alue be o e
selec ing he maximum and no malizing he elemen s. Then he
s uc u e o he ma ices is de ined as ollows. Fi s o all, he x
ma ices Mp
0
k
;Ms
0
k
and Ma
0
k
a e c ea ed as emp y ma ices, ha
is, each elemen is equal o ze o.
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
5

Fo all o hem, he xcomponen is encoded as a sequence o
columns om op o bo om, he ycomponen is encoded as col-
umns om he bo om o he op, and he zcomponen is encoded
as ows, om le o igh . The idea is o associa e a ow o a col-
umn o ”ones” which is p opo ional o he con en o p
0
k
;s
0
k
;a
0
k
.
We unde line ha ou p oposal is only one o he possible ways
o ill he ma ices: Howe e , by knowing which kind o esul s can
be ob ained, one can ind di e en ways o c ea e images. So, he
Algo i hm 2 speci ies how he h ee ma ices a e illed up; we illus-
a e he algo i hm o he gene ic ma ix M. Bo h RMD and MME
algo i hms a e execu ed o :
Posi ion p
0
k
:Mp
0
k

¼MME p
0
k
;s ;p;
’posi ion
0
Þ;o Mp
0
k

¼
RMD p
0
k
;
0
posi ion
0

;
Speed s
0
k
:Ms
0
k

¼MME s
0
k
;s ;p;
’speed
0
Þ;o Ms
0
k

¼RMD s
0
k
;

’speed
0
Þ;
Accele a ion a
0
k
:Ma
0
k

¼MME a
0
k
;s ;p;
’accel
0
Þ;o
Ma
0
k

¼RMD a
0
k
;
’accel
0
Þ;
Re e ing o Algo i hm 2, i accep s as inpu he no malized ec-
o
ec
0
k
con aining posi ion, speed o accele a ion mobili y in o -
ma ion (speci ied in he inpu pa ame e ype) ela ed o mobile
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
6
hos
k
, ha is one o he e ms in Eq. 5; he leng h o he subse p
and he sp eading ac o s a e also gi en as inpu . The alues o s
indica e he numbe o columns assigned o each componen (a
leas i should be se o 3).
Fi s ly, he MME e alua es he ma ix dimension as de ined
ea lie and c ea es he emp y ma ix M
0
k
. Then i compu es he
igh dimension o he inpu ec o : om he de ini ions o Eqs.
(3) and (4), we know ha o speed and accele a ion ec o s, he
leng hs a e p1 and p2 espec i ely. A his poin he algo i hm
execu es he i s cycle (h a iable), conside ing o he xcompo-
nen s he columns (index
x
)1,1+s , 1+2 s , and so on, o he y
componen s he columns (index
y
), 3, 3 + s , 3+2 s , and so on, while
o he zcomponen s he ows (index
z
)1,1+s , 1+2 s , and so on.
A his poin , each ow/column is illed wi h se e al ones, which is
p opo ional o he con en o he elemen s o
ec
0
k
c;hðÞ. Fo he z
componen , du ing he hi d in e nal cycle, i he gene ic ma ix
elemen M
0
k
index
z
; ðÞhas al eady been modi ied by he wo p e i-
ous cycles ( o he xand ycomponen s), no u he ac ions a e
made.
Recalling ha he elemen s o
ec
0
k
a e no malized om 0 o 1,
hen he e m b
ec
0
k
c;hðÞ ewill be bounded o he maximum size
o M
0
k
. The symbol be indica es he ounding ope a ion ( he nea es
in ege is chosen). Compu a ional complexi y is accep able
because he ini ial ope a ions ha e cons an complexi y (negligi-
ble), he p ima y cycle is execu ed OpðÞ imes. In con as , he
in e nal cycles a e execu ed O
ðÞ imes, so we can w i e ha he
o e all compu a ional complexi y is Op3 ðÞ=Op3ps ðÞ
which is bounded by Op
3

and pdoes no depend on he leng h
o he o e all pa e n. A his poin , i is use ul o make an example
o how he ma ices a e c ea ed om eal alues wi h MME (RMD
is mo e in ui i e since i is only a con e sion be ween ec o s and
ma ices). Le pbe equal o 4, s be equal o 4 and p
0
k
be
12:735;87:675;10:22ðÞ;18:143;79:884;ð11:31Þ;25:750;71:943;ð
12:7Þ;30:564;63:345;11:8ðÞg, wi h jp
0
k
j¼p¼4. By applying
Eqs. (3) and (4) hen we will ha e s
0
k
=
5:408;7:791;1:09ðÞ;7:607;7:941;1:39ðÞ;4:814;8:598;0:9ðÞ;g,
wi h js
0
k
j¼p1¼3 and a
0
k
= 2:199;0:15;0:3
ðÞ
;
2:793;ð0:657;2:29Þg, wi h ja
0
k
j¼p2¼2. A his poin , by
he inpu alue o s , we will ha e =4 4¼16, so he h ee ma ices
will ha e dimensions o 16 x 16. The no malized ec o s will be:
p
0
k
: 0:145;1;0:116ðÞ;0:207;0:911;0:129ðÞ;0:294;0:820;ð
0:145Þ;0:349;0:722;0:134ðÞg;
s
0
k
= 0:864;0:04978;0:598ðÞÞ;1;0:040;0:616ðÞ;0:827;0;0:475ðÞg;
a
0
k
= 1;0:529;0:619ðÞ;0;0:427;0:101ðÞg.
The MME is applied o each no malized ec o a his poin , and
he ma ices illus a ed in Fig. 3 a e ob ained.
F om Fig. 3, i can be seen how he xcomponen s a e added by
he uni a y elemen s om op o bo om ( ed colo ) in he columns
indexed as in he MME (indexes 1, 5, 9, 13), he uni a y elemen s
om he bo om add he ycomponen s o he op (g een colo )
in he columns indexed as in he MME (3, 7, 11, 15) and he z
Fig. 3. An example o he h ee ma ices as ou pu o MME.
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
7
componen s a e added by he uni a y elemen s om le o igh
(da k blue colo ) in he ows indexed as in he MME (1, 5, 9, 13).
O ange alues ep esen he p esence o mo e componen s in he
same ma ix elemen s: e.g., he elemen Mp
0
k
1;1ðÞis gene a ed
by bo h he xcomponen and zcomponen .
The ollowing (and las ) s ep is o encode he ma ices in o an
image: o his aim, we associa e he Mp
0
k
ma ix o he RED image
channel, he Ms
0
k
ma ix o he GREEN image channel and he Ma
0
k
ma ix o he BLUE image channel, a e mul iplying each ma ix
by 2
8
-1 (we a e conside ing 8-bi s esolu ion pe laye ), indepen-
den ly om RMD o MME. We did no ca e abou in es iga ing
he pa icula image o ma . S ill, we ocused on a lossless encod-
ing, such as he Po able Ne wo k G aphics (PNG) (The Po able
Ne wo k G aphics speci ica ion, 2023), o a oid he c ea ion o a i-
ac s (JPG o ma , o example, is no sui able o ou app oach).
In pa icula , we chose he RGB 24bi o ma o PNG, so each
elemen in each ma ix is ep esen ed by 8 bi s (256 le els): a
de ail o he h ee ma ices o Fig. 3 in a isual ep esen a ion is
gi en in Fig. 4 (please, no e ha he images ha e been magni ied,
because he wid h o each ow/column is 1 pixel).
3.3. The image en opy: A possible e alua ion me ic
I is known om he li e a u e ha he en opy concep plays a
i al ole in image classi ica ion (Gowd a e al., 2020). The classical
me ic used o e alua e he goodness o a slicing ecogni ion and
classi ica ion is he Maximum En opy (ME): he majo i y o classi-
ica ion/ ecogni ion machine lea ning app oaches y o di ide big
images in o smalle ones, inding he slices which a e cha ac e ized
by he highes ME (i.e., he maximum le el o in o ma ion, he
mos isually ep esen a i e po ions o he image), which can be
used o aining he CNN, whose con olu ion ope a ions can dis-
co e and ex ac he hidden in o ma ion. En opy, independen ly
om Ha ley’s (Ha ley, 1928) o Shannon’s (Shannon, 1953) de i-
ni ions, ep esen s he amoun o in o ma ion con ained in he
image o be classi ied and he deg ee o andomness o he pixel
alues. I is in ended ha he mo e in o ma ion is included in
he image, he highe will be bo h he en opy and, also, he s uc-
u al complexi y o he CNN: gene ally, mo e han one con olu ion
laye is needed o ex ac he igh ea u es om da a. In ou expe -
imen s, we e alua e he colo image en opy as ollows (assuming
ha is he numbe o image pixels and 8-bi alues ep esen
each colo channel):
EIm½¼
1
3E
c
Im
RED
ðÞþE
c
Im
GREEN
ðÞþE
c
Im
BLUE
ðÞ½;ð6Þ
ha is he a e age o he en opy o each colo channel E
c
de ined
as:
E
c
Im
ch
½
¼X
2
8
1
pix
ch
¼0
pIm
ch
;pix
ch
ðÞ
log
2
pIm
ch
;pix
ch
ðÞ½
;ð7Þ
wi h:
pIm
ch
;pix
ch
ðÞ¼
coun Im
ch
;pix
ch
ðÞ
ð8Þ
wi h he unc ion coun In
ch
;pix
ch
ðÞcoun ing he numbe o imes a
pixel in Im
ch
assumes he alue pix
ch
. The ocus o ou wo k is no
ela ed o he p oposal o a new CNN s uc u e bu only o show
ha good esul s can be achie ed in mobili y classi ica ion wi h a
no el app oach. Fo hese easons, we a e p oposing a new MME
algo i hm o main ain he CNN complexi y as low as possible, so
images will be cha ac e ized by ela i ely low en opy alues.
As s a ed in he p e ious sub-sec ion, he p oposed MME is jus
one o he possible algo i hms o da a- o-image encoding. In his
wo k, we show, o he i s ime, ha his app oach is sui able
o mobili y classi ica ion. The easies way o encode mobili y in o
an image is o pu he aw da a di ec ly in o a ma ix and hen
encode i as an image. Bu his las app oach has se e al
d awbacks:
Ve y iny images will be gene a ed: e e y CNN, as shown in he
nume ical esul s sec ion, needs a minimum image size o ec-
ognize he image and classi y i ; i we do no hink abou an e i-
cien encoding scheme, a huge numbe o samples is needed.
Conside he p e ious example: we had p= 4, which means
we ha e only ou iple s (4 alues o each coo dina e compo-
nen ). I also means ha we ob ain h ee alues o speed and
wo alues o accele a ion: we ha e nine di e en da a o each
componen , o a o al o 27 ma ix elemen s. Wi h an encoding
scheme (as MME), we ha e 3 
2
=768 ma ix elemen s, s a ing
om 27 da a poin s. So, a p ope ep esen a ion o he da a is
manda o y o build an adequa e aining se ;
F om an en opy poin o iew: i we ep esen he aw da a
di ec ly in o an image, he en opy alue will be high due o
he eno mous colo changes wi h high g anula i y (especially
i mobili y is ep esen ed by la and lon couples); he MME,
ins ead, as demons a ed la e , will educe he en opy sensibly.
Fo example, we show he di e ence be ween RMD and MME
encoding in e ms o en opy alues dis ibu ion. Fig. 5 shows an
example o he esul s ob ained by encoding 2D mobili y da a by
MME o jus lea ing he aw alues in o a single RGB ma ix
(RMD). RMD and MME images con ain 8192 and 7744 pixels,
espec i ely (compa able sizes). S ill, he RMD image is c ea ed
by exac ly 4096 samples (mobili y poin s, which a e doubled o
xand ycomponen s), while MME needs only 484 mobili y poin s
(wi h a gain o abou 88.1%).
We used 2500 2D mobili y pa e n subse s p ocessed wi h RMD
and MME o see an example o how he en opy is dis ibu ed. The
subse leng h phas been se o 22; Fig. 6 shows he massi e di e -
ence in e ms o en opy be ween RMD and MME encoded images:
o MME, he mean en opy is 1.22 J/K, while o RMD i is 4.26 J/K.
In he case o MME i is almos cons an (due o he p esence o
high black spaces), while o RMD i has a subs an ial oscilla o y
end. I is also in e es ing o see how he en opy is dis ibu ed:
Fig. 7 shows he pd (E) end. I con i ms wha was obse ed in
Fig. 6, a e y low de ia ion a ound he mean alue o MME, while
mo e sp ead alues o RMD. In he nume ical esul s sec ion, we
will show wha happens o En opy based on he pa ame e s
ela ed o image encoding. In he nex sec ion, ins ead, he CNN
model is deeply discussed.
Fig. 4. A isual ep esen a ion o Mp
0
k
;Ms
0
k
;Ma
0
k
( op) and he ela ed RGB laye s
(bo om).
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
8
3.4. The conside ed con olu ional neu al ne wo k
Ou wo k shows which pe o mance can o e a CNN-based
image classi ica ion model i ained on mobili y da a (p e iously
encoded in o images). So, ou aim does no ega d he p oposal
o a new CNN model bu a new way o using i in a di e en
esea ch con ex . So, in his sub-sec ion, we a e gi ing jus he
main desc ip ion o he used LeCun-like (Lecun e al., 1998) CNN
model. Using i s Machine Lea ning Toolbox, we used MATLAB
(MATLAB, 2021) o ou implemen a ion. In pa icula , we s uc-
u ed he CNN, ollowing LeCun’s p oposal, as ollows:
Inpu laye : i is designed o accep ing an image as inpu ; i is
c ea ed by de ining he size o he inpu image and he numbe
o i s laye s (3 in ou case: ed, g een, and blu); by de aul , in
MATLAB, he image inpu laye no malizes pixel alues by sub-
s ac ing hei mean alue; we can speci y pixel alues o be
no malized be ween 0 and 1;
Con olu ion laye : i applies sliding con olu ional il e s o he
2D inpu . The inpu is con ol ed by mo ing he speci ied il e s
along he 2D inpu (in ho izon al and e ical di ec ions) and
e alua ing he do p oduc o he weigh s and he inpu ;
Ba ch No maliza ion laye : i no malizes a da a ba ch ac oss
all obse a ions. I is gene ally used o speed up he aining
o he CNN, educing he sensi i i y o he beginning
unce ain y;
Rec i ied Linea Uni (ReLU) laye : i is one o he possible ac i-
a ion laye s and applies a h eshold ope a ion o i s inpu (in
simple wo ds, nega i e alues a e se o 0);
Fully Connec ed laye : i is a dense laye o neu ons and mul i-
plies he inpu by a weigh ma ix;
So Max laye : i applies a so max unc ion o he inpu . So -
max is a gene aliza ion o he logis ic unc ion, which can com-
p ess a k-leng h and a bi a y con en ec o o ano he k-
leng h ec o , wi h he sum o elemen s equal o 1;
Classi ica ion laye : i can ecei e an inpu and e u n he clas-
si ied ou pu (in ou case, he ma
i
2MAs).
Fig. 8 shows he comple e laye ing o he conside ed CNNs in
he MATLAB window, wi h he main used pa ame e s. Resul s
can be, o cou se, enhanced. S ill, in his pape , we a e in e es ed
nei he in in es iga ing he s uc u e o he CNN no in inc easing
i s complexi y (on he con a y, one o ou goals is o main ain he
CNN s uc u e as simple as possible).
Fo mo e de ails abou he possible CNN op imiza ion, please
e e o Bishop (2006).
Fig. 7. P obabili y Densi y Func ion o he en opy alues o Fig. 7.
Fig. 6. En opy end o RMD and MME images, wi h p= 22 and T= 1s.
Fig. 5. T ue images ob ained by using Raw Mobili y Da a (RMD), size 64 128, o
he MME algo i hm, size 88 88.
Fig. 8. The laye ing s uc u e o he simple CNN used in ou wo k.
P. Fazio, M. Mehic and M. Voznak Jou nal o King Saud Uni e si y – Compu e and In o ma ion Sciences 35 (2023) 101561
9