senso s
A icle
De ec ion o A ial Fib illa ion Episodes in
Long-Te m Hea Rhy hm Signals Using a Suppo
Vec o Machine
Robe Czabanski 1, K zysz o Ho oba 2,*, Janusz W obel 2, Adam Ma onia 2,
Radek Ma inek 3, Tomasz Kupka 2, Michal Jezewski 1, Radana Kahanko a 3,
Janusz Jezewski 2and Jacek M. Leski 1
1Depa men o Cybe ne ics, Nano echnology and Da a P ocessing, Silesian Uni e si y o Technology,
PL44100 Gliwice, Poland; [email p o ec ed] (R.C.); [email p o ec ed] (M.J.);
[email p o ec ed] (J.L.)
2
Łukasiewicz Resea ch Ne wo k–Ins i u e o Medical Technology and Equipmen , PL 41800 Zab ze, Poland;
[email p o ec ed] (J.W.); [email p o ec ed] (A.M.); [email p o ec ed] (T.K.);
[email p o ec ed] (J.J.)
3Depa men o Cybe ne ics and Biomedical Enginee ing, VSB–Technical Uni e si y o Os a a,
708 00 Os a a-Po uba, Czech Republic; [email p o ec ed] (R.M.); [email p o ec ed] (R.K.)
*Co espondence: k zysz o .ho [email p o ec ed]
Recei ed: 19 Decembe 2019; Accep ed: 27 Janua y 2020; Published: 30 Janua y 2020


Abs ac :
A ial ib illa ion (AF) is a se ious hea a hy hmia leading o a signi ican inc ease o he
isk o occu ence o ischemic s oke. Clinically, he AF episode is ecognized in an elec oca diog am.
Howe e , de ec ion o asymp oma ic AF, which equi es a long- e m moni o ing, is mo e e icien
when based on i egula i y o bea - o-bea in e als es ima ed by he hea a e (HR) ea u es.
Au oma ed classi ica ion o hea bea s in o AF and non-AF by means o he Lag angian Suppo
Vec o Machine has been p oposed. The classi ie inpu ec o consis ed o six een ea u es, including
ou coe icien s e y sensi i e o bea - o-bea hea changes, aken om he e al hea a e analysis
in pe ina al medicine. E ec i eness o he p oposed classi ie has been e i ied on he MIT-BIH
A ial Fib illa ion Da abase. Designing o he LSVM classi ie using e y la ge numbe o ea u e
ec o s equi es ex eme compu a ional e o s. The e o e, an o iginal app oach has been p oposed
o de e mine a aining se o he smalles possible size ha s ill would gua an ee a high quali y
o AF de ec ion. I enables o ob ain sa is ac o y esul s using only 1.39% o all hea bea s as he
aining da a. Pos -p ocessing s age based on agg ega ion o classi ied hea bea s in o AF episodes
has been applied o p o ide mo e eliable in o ma ion on pa ien isk. Resul s ob ained du ing he
es ing phase showed he sensi i i y o 98.94%, posi i e p edic i e alue o 98.39%, and classi ica ion
accu acy o 98.86%.
Keywo ds:
suppo ec o machine (SVM); hea a e a iabili y (HRV); HRV ea u es; a ial
ib illa ion (AF); AF de ec ion
1. In oduc ion
A ial ib illa ion (AF) is he mos common hea a hy hmia, which occu s when he a ia con ac s
quickly and i egula ly a a es o 400 o 600 pe minu e. These con ac ions a e independen om
en icles, which hemsel es ope a e a much lowe a e. AF symp oms o en include palpi a ions,
i egula hea bea , sho ness o b ea h, ches pains and o he s, bu hey can be also asymp oma ic
and is hen called silen AF. The equency o AF occu ence is s ic ly co ela ed wi h he pa ien ’s
age [
1
,
2
]. The p ognosis indica es ha he AF occu ence wi hin he pe iod o he nex 20–30 yea s will
Senso s 2020,20, 765; doi:10.3390/s20030765 www.mdpi.com/jou nal/senso s
Senso s 2020,20, 765 2 o 24
double, mainly due o he longe li e span o he popula ion. The AF de ec ion is impo an , since his
hea a hy hmia is a well-known isk ac o o occu ence o ischemic s oke, e en six imes highe
han among pa ien s wi hou he a hy hmia [3].
Figu e 1p esen s he ECG signals om he MIT-BIH A ial Fib illa ion da abase (MIT-BIH AF)
published on PhysioNe [
4
–
6
], comp ising bo h segmen s wi h he AF episodes and non-AF segmen s.
AF episodes occu i egula ly and may las om a ew hea bea s o hou s, which signi ican ly
hinde he possibili y o diagnose he silen AF by means o occasionally pe o med ambula o y
ECG eco dings. I implies ha he longe he eco ding, he highe chance o de ec he silen AF
episodes [
7
,
8
]. The mos e icien echniques o long- e m moni o ing a e: Hol e moni o , con inuous
eleme y [
9
–
12
], o implemen able de ices wi h in e nal memo y [
13
–
15
]. Howe e , isual analysis
o long 24-h eco ding equi es a lo o ime and e o s om he ca diologis s, hus he me hods o
au oma ed de ec ion o a ial ib illa ion a e needed o imp o e he objec i i y o in e p e a ion. When
based on ECG, he e icien au oma ed AF de ec ion equi es a high quali y signal. I may no be
ensu ed by he long- e m moni o ing echniques which usually comp ise pe iods o daily physical
ac i i y o he pa ien which dis o he ECG signal.
Senso s 2020, 20, 765 2 o 24
is impo an , since his hea a hy hmia is a well-known isk ac o o occu ence o ischemic
s oke, e en six imes highe han among pa ien s wi hou he a hy hmia [3].
Figu e 1 p esen s he ECG signals om he MIT-BIH A ial Fib illa ion da abase (MIT-BIH AF)
published on PhysioNe [4–6], comp ising bo h segmen s wi h he AF episodes and non-AF
segmen s. AF episodes occu i egula ly and may las om a ew hea bea s o hou s, which
signi ican ly hinde he possibili y o diagnose he silen AF by means o occasionally pe o med
ambula o y ECG eco dings. I implies ha he longe he eco ding, he highe chance o de ec he
silen AF episodes [7,8]. The mos e icien echniques o long- e m moni o ing a e: Hol e moni o ,
con inuous eleme y [9–12], o implemen able de ices wi h in e nal memo y [13–15]. Howe e ,
isual analysis o long 24-h eco ding equi es a lo o ime and e o s om he ca diologis s, hus
he me hods o au oma ed de ec ion o a ial ib illa ion a e needed o imp o e he objec i i y o
in e p e a ion. When based on ECG, he e icien au oma ed AF de ec ion equi es a high quali y
signal. I may no be ensu ed by he long- e m moni o ing echniques which usually comp ise
pe iods o daily physical ac i i y o he pa ien which dis o he ECG signal.
Figu e 1. ECG signals (04043 and 04045) aken om he MIT-BIH AF da abase, wi h ecognized
segmen s o a ial ib illa ion and he non-AF ones.
The AF episode is mani es ed in ECG by signi ican changes o du a ion o he bea - o-bea (RR)
in e als [16–19], see Figu e 1. Howe e , he RR in e als i egula i y caused by AF occu ences is
much mo e easy o obse e a e con e ing RR in e als in o he ins an aneous hea a e (HR)
signal (Figu e 2). The p esen ed HR signals con i m ha AF episodes occu e y acciden ally, and
hey can las a ew seconds (signal 04048), bu also expand o long las ing episodes (signal 04936).
In he ligh o abo e ac s an e icien au oma ed me hod o AF de ec ion should be based on
es ima ion o RR i egula i y o equi alen i.e., HR i egula i y obse ed in long- e m eco ding
[20,21]. Mo eo e , such app oach enables o in ol e he a ious eco ding me hods which can
p o ide signals in which he hea bea s can be de ec ed. Beside elec oca diog am, such signals
include pho ople hysmog am [22–24] o seismoca diog am [25]. Using a pho oelec ic senso is
a ac i e in case o home eleca e as long- e m eco ding should be accomplished by
ins umen a ions being minimally oublesome and incon enien o he pa ien [26,27]. I may be a
sma moni o in a o m o a w is b acele wi h a specialized e lec i e op ical senso o pe o m he
hea a e moni o ing using he me hod p e iously de eloped by he au ho s [28].
The gene al concep o he me hods mos commonly used o au oma ed de ec ion o AF
episodes elies on de e mina ion o ea u es es ima ing he RR in e al changes, and hen applica ion
o he s a is ical analysis o mo e ad anced classi ie o di e en ia e be ween AF episode and no mal
sinus hy hm segmen s, basing on he in o ma ion on RR i egula i y. The ea u e se is composed
mos commonly o di e en s a is ical measu es (mean o median HR, oo mean squa e o
successi e RR di e ences, u ning poin a io). I can also include no malized RR in e als [29,30] o
no malized RR di e ences [31], Shannon en opy [19] o coe icien o sample en opy [15,32]. O he
Figu e 1.
ECG signals (04043 and 04045) aken om he MIT-BIH AF da abase, wi h ecognized
segmen s o a ial ib illa ion and he non-AF ones.
The AF episode is mani es ed in ECG by signi ican changes o du a ion o he bea - o-bea (RR)
in e als [
16
–
19
], see Figu e 1. Howe e , he RR in e als i egula i y caused by AF occu ences is
much mo e easy o obse e a e con e ing RR in e als in o he ins an aneous hea a e (HR) signal
(Figu e 2). The p esen ed HR signals con i m ha AF episodes occu e y acciden ally, and hey can
las a ew seconds (signal 04048), bu also expand o long las ing episodes (signal 04936).
In he ligh o abo e ac s an e icien au oma ed me hod o AF de ec ion should be based on
es ima ion o RR i egula i y o equi alen i.e., HR i egula i y obse ed in long- e m eco ding [
20
,
21
].
Mo eo e , such app oach enables o in ol e he a ious eco ding me hods which can p o ide
signals in which he hea bea s can be de ec ed. Beside elec oca diog am, such signals include
pho ople hysmog am [
22
–
24
] o seismoca diog am [
25
]. Using a pho oelec ic senso is a ac i e
in case o home eleca e as long- e m eco ding should be accomplished by ins umen a ions being
minimally oublesome and incon enien o he pa ien [
26
,
27
]. I may be a sma moni o in a o m o
a w is b acele wi h a specialized e lec i e op ical senso o pe o m he hea a e moni o ing using
he me hod p e iously de eloped by he au ho s [28].
The gene al concep o he me hods mos commonly used o au oma ed de ec ion o AF episodes
elies on de e mina ion o ea u es es ima ing he RR in e al changes, and hen applica ion o he
s a is ical analysis o mo e ad anced classi ie o di e en ia e be ween AF episode and no mal sinus
hy hm segmen s, basing on he in o ma ion on RR i egula i y. The ea u e se is composed mos
commonly o di e en s a is ical measu es (mean o median HR, oo mean squa e o successi e RR
Senso s 2020,20, 765 3 o 24
di e ences, u ning poin a io). I can also include no malized RR in e als [
29
,
30
] o no malized RR
di e ences [
31
], Shannon en opy [
19
] o coe icien o sample en opy [
15
,
32
]. O he o m o p esen
he RR i egula i y a e: he densi y his og am o he di e ence be ween successi e RR in e als [
33
,
34
],
map ha plo s RR in e als e sus change o RR in e als [
35
], mapping he RR-in e al ime se ies o
bina y symbolic sequences [36,37] o Ma ko sco e o RR in e al [16].
Senso s 2020, 20, 765 3 o 24
o m o p esen he RR i egula i y a e: he densi y his og am o he di e ence be ween successi e
RR in e als [33,34], map ha plo s RR in e als e sus change o RR in e als [35], mapping he
RR-in e al ime se ies o bina y symbolic sequences [36,37] o Ma ko sco e o RR in e al [16].
Figu e 2. Two HR signals exp essed in bea s pe minu e (bpm) wi h clinically ecognized AF
segmen s o di e en cha ac e is ics o HR changes in ela ion o no mal sinus hy hm (non-AF). The
AF segmen s a e ma ked using he expe s’ anno a ions p o ided o pa icula eco ds in he
MIT-BIH AF da abase.
In he simples app oach o AF classi ica ion he Recei e Ope a ing Cha ac e is ics (ROC)
cu e has been used o ind he op imal h eshold alues o he inpu ea u es p o iding he bes
classi ica ion pe o mance [30,35,36,38]. The s a is ical es (Kolmogo o -Smi no ) was used in [33]
o check i he densi y his og ams o he es da a di e om he s anda d densi y ones p epa ed as a
empla e o AF episodes. In o de o di e en ia e be ween AF and non-AF pa e ns he a ious
classi ica ion me hods ha e been applied: Neyman-Pea son de ec o [31], Random Fo es (RF)
model and k-nea es neighbo s classi ie [32], Suppo Vec o Machine (SVM) wi h p omising esul s
epo ed in [39–41], as well as a i icial neu al ne wo k [42], also wi h in e al ansi ion ma ices as
an inpu [43].
In [39] SVM app oach was used o classi ica ion o he 30-s segmen s o ECG and 300-bea
sequences o RR in e als. Two pa ame e s o S a iona y Wa ele T ans o m (peak- o-a e age
powe a io and log-ene gy en opy) we e used o aw ECG-based app oach, while i e ea u es
we e ex ac ed om HR signal. The e iciency o AF de ec ion achie ed by he ea u e-based
classi ica ion o he RR sequences was es ed agains he algo i hm based on aw ECG. Highe
sensi i i y was ensu ed by he HR-based app oach, while ECG-based algo i hm p o ided imp o ed
speci ici y and classi ica ion accu acy. The classi ie based on SVM wi h adial basis unc ion was
p oposed in [40], wi h wo ea u es as he inpu s: he a e age o RR di e ences and he s anda d
de ia ion o di e ences in a de ined du a ion. The same SVM classi ie was employed in [41]. The
inpu se comp ised mo e RR in e al ea u es: median hea a e, minimum RR in e al, mean RR
in e al, a ious en opy measu es, and di e ence i egula i y measu e.
The ea u es es ima ing he RR a iabili y a e calcula ed in a sliding window comp ising an
es ablished numbe o consecu i e RR in e als (o HR alues). Since he e is no s anda d o he
window leng h, many wo ks ha e aimed o ind he op imal leng h, p o iding he bes classi ica ion
pe o mance. Some wo ks assumed ha AF episodes o less han 30 s du a ion a e no clinically
signi ican , which led o highe op imal numbe o hea bea s: 100 [33], 128 [35] and 150 [37]. O he
au ho s claim ha longe windows end o miss sho AF episodes, and hus hey applied
signi ican ly sho e windows: 30 [32], 12 [15] o e en 8 bea s [44]. I is ob ious ha di e en
Figu e 2.
Two HR signals exp essed in bea s pe minu e (bpm) wi h clinically ecognized AF segmen s
o di e en cha ac e is ics o HR changes in ela ion o no mal sinus hy hm (non-AF). The AF segmen s
a e ma ked using he expe s’ anno a ions p o ided o pa icula eco ds in he MIT-BIH AF da abase.
In he simples app oach o AF classi ica ion he Recei e Ope a ing Cha ac e is ics (ROC) cu e
has been used o ind he op imal h eshold alues o he inpu ea u es p o iding he bes classi ica ion
pe o mance [
30
,
35
,
36
,
38
]. The s a is ical es (Kolmogo o -Smi no ) was used in [
33
] o check i he
densi y his og ams o he es da a di e om he s anda d densi y ones p epa ed as a empla e o AF
episodes. In o de o di e en ia e be ween AF and non-AF pa e ns he a ious classi ica ion me hods
ha e been applied: Neyman-Pea son de ec o [
31
], Random Fo es (RF) model and k-nea es neighbo s
classi ie [
32
], Suppo Vec o Machine (SVM) wi h p omising esul s epo ed in [
39
–
41
], as well as
a i icial neu al ne wo k [42], also wi h in e al ansi ion ma ices as an inpu [43].
In [
39
] SVM app oach was used o classi ica ion o he 30-s segmen s o ECG and 300-bea
sequences o RR in e als. Two pa ame e s o S a iona y Wa ele T ans o m (peak- o-a e age powe
a io and log-ene gy en opy) we e used o aw ECG-based app oach, while i e ea u es we e
ex ac ed om HR signal. The e iciency o AF de ec ion achie ed by he ea u e-based classi ica ion
o he RR sequences was es ed agains he algo i hm based on aw ECG. Highe sensi i i y was
ensu ed by he HR-based app oach, while ECG-based algo i hm p o ided imp o ed speci ici y and
classi ica ion accu acy. The classi ie based on SVM wi h adial basis unc ion was p oposed in [
40
],
wi h wo ea u es as he inpu s: he a e age o RR di e ences and he s anda d de ia ion o di e ences
in a de ined du a ion. The same SVM classi ie was employed in [
41
]. The inpu se comp ised mo e
RR in e al ea u es: median hea a e, minimum RR in e al, mean RR in e al, a ious en opy
measu es, and di e ence i egula i y measu e.
The ea u es es ima ing he RR a iabili y a e calcula ed in a sliding window comp ising an
es ablished numbe o consecu i e RR in e als (o HR alues). Since he e is no s anda d o he
window leng h, many wo ks ha e aimed o ind he op imal leng h, p o iding he bes classi ica ion
pe o mance. Some wo ks assumed ha AF episodes o less han 30 s du a ion a e no clinically
signi ican , which led o highe op imal numbe o hea bea s: 100 [
33
], 128 [
35
] and 150 [
37
]. O he
au ho s claim ha longe windows end o miss sho AF episodes, and hus hey applied signi ican ly
Senso s 2020,20, 765 4 o 24
sho e windows: 30 [
32
], 12 [
15
] o e en 8 bea s [
44
]. I is ob ious ha di e en window leng h
epo ed as he op imal alue depends on he me hod used o au oma ed AF de ec ion. Ano he
impo an aspec o using he sliding window o AF de ec ion is how many bea s i is shi ed. Shi ing
he window e e y hea bea esul s in one bea esolu ion o he AF classi ica ion. Then each hea bea
(RR in e al), usually co esponding o he middle o he window, is classi ied as AF o non-AF. In such
case, de e mina ion o classi ica ion pe o mance is e iden as each au oma ically classi ied bea can be
ela ed o he e e ence one, basing on he expe anno a ions. O he wise, addi ional condi ion has o
be applied— he window is labeled as AF episode only i he numbe o clinically anno a ed AF bea s
wi hin he window exceeds a p ede ined h eshold, usually 0.5 like in [
35
,
45
]. Howe e , i is ob ious
ha he h eshold alue a ec s he classi ica ion pe o mance. The h eshold has been included in o
he inpu ea u e se and uned o op imum sensi i i y and speci ici y in [
38
]. Howe e , i should be
no ed ha in such app oach, he e e ence in o ma ion is modi ied o achie e he bes classi ica ion
pe o mance o he au oma ed me hod es ed, which seems o be a he doub ul.
In o de o a oid sho alse posi i e AF episodes o sho a i ac o classi ied AF he
pos -p ocessing co ec ion was applied, like dedica ed mechanism called AF ala m enhance [
16
]. I is
he hys e esis coun e ha begins (o ends) an episode i es ablished numbe o consecu i e analyzed
RR segmen s ha e been classi ied as AF (o non-AF). O he pos -p ocessing me hod was based on
median il e ing [45].
In [
16
], a e combining R-R in e al Ma ko sco e wi h wo P-wa e measu emen s: he loca ion
exp essed by P-R in e al du a ion, and he mo phology de ined as simila i y be ween wo consecu i e
P-wa es, he sensi i i y did no change, whe eas speci ici y and posi i e p edic i e alues inc eased sligh ly.
A no el deep lea ning has been adop ed o au oma ed de ec ion o AF in he long- e m ECG
eco dings. This classi ie lea ns di ec ly om he RR in e als and he e o e he e is no need o ex ac
he ea u es. The model based on deep Recu en Neu al Ne wo k (RNN) wi h Long Sho -Te m
Memo y (LSTM) was used in [
46
], and combining wi h he Con olu ional- and Recu en -Neu al
Ne wo ks o ex ac high le el ea u es was p oposed in [
45
]. Al hough a high classi ica ion pe o mance
has been epo ed, he compu a ional complexi y o deep lea ning model is much highe han adi ional
ea u e-based classi ie . In his pape , we desc ibe he me hod o au oma ed AF de ec ion which
assigns he ec o o pa ame e s quan i a i ely desc ibing he HR signal in o wo classes ep esen ing
he absence o p esence o a ial ib illa ion. As es ima ion o HR a iabili y is also impo an pa o he
Fe al Hea Ra e (FHR) analysis [
47
–
49
], he indices widely used o FHR a iabili y desc ip ion ha e
been conside ed as po en ially use ul o AF de ec ion. The de ec ion me hod p esen ed in his pape
was de i ed om he machine lea ning p inciples. Ou classi ica ion ou ine was pe o med by means
o he Lag angian Suppo Vec o Machine (LSVM) [
50
]— he s a e-o - he-a classi ie based on he
linea ly con e gen lea ning algo i hm. The e icien LSVM lea ning p ocedu e was ob ained om he
e o mula ion o he Quad a ic P og aming (QP) op imiza ion p oblem o he Suppo Vec o Machine
(SVM) [
51
]. Addi ional agg ega ion s age has been applied o p o ide mo e eliable in o ma ion on
isk o he pa ien . The pe o mance o he p oposed AF de ec ion me hod was examined using he
MIT-BIH A ial Fib illa ion da abase, which includes 25 en-hou long ECG eco dings.
2. Ma e ials and Me hods
Au oma ed de ec ion o he a ial ib illa ion episodes p oposed in his wo k s a s wi h ex ac ion
o six een HR i egula i y ea u es composing he classi ie inpu ec o . Then he LSVM classi ie is
applied o ma k a gi en hea bea as AF o non-AF one. Final s ep is agg ega ion o he classi ied bea s
in o AF episodes.
2.1. HR I egula i y Fea u es
Conside ing on-line de ec ion o AF and limi ed compu a ional powe o he de eloped mobile
moni o , we applied a simple linea classi ie which ecognizes he AF hea bea s basing on easily
accessible in o ma ion abou hea hy hm and HR ea u es [
52
,
53
]. Apa om he HR alue, o he
Senso s 2020,20, 765 5 o 24
ou inpu ea u es ha e been selec ed in a se ies o p elimina y in es iga ions ca ied ou among
la ge ea u e se [
54
]. Ha ing he in o ma ion on hea bea s de ec ed, he ins an aneous hea a e
alues HRi(exp essed in bea s pe minu e) a e calcula ed acco ding o he o mula:
HRi[bpm]=60000
RRi[ms], (1)
whe e: RRiis he i- h in e al be ween wo consecu i e hea bea s exp essed in milliseconds.
Nex , he ea u es a e de e mined in symme ical mo ing window comp ising 21 o HRi alues:
•MEDi=median{HRi−k,. . . ,HRi+k};
•MADi=median{xi−k,. . . ,xi+k}, whe e xi= |HRi−MEDi|;
•QNTi— ep esen s he quan ile o o de 0.7 es ima ed o e 21 alues o hea a e;
•
PRP
i
—is he a io o numbe o HR alues be ween h esholds le el o 120 o 160 bpm, o
o al numbe .
whe e: iis he numbe o consecu i e hea bea s o be classi ied, and k=1. . . 10.
The alues o he addi ional pa ame e s: window wid h Nse o 21, quan ile o de se o 0.7 and
HR h esholds o 120 and 160 we e de e mined as a esul o p e iously pe o med expe imen s [54].
Fo he new classi ica ion me hod, he inpu ec o has been signi ican ly expanded. I addi ionally
comp ises se en measu es ob ained om classical analysis o HR a iabili y used in adul s’
elec oca diog aphy. This analysis includes exclusi ely sinus exci a ion, i.e., gene a ed by he
sinus-a ial node. Thus, i conce ns only sinus hy hm a iabili y, and any o he ypes o exci a ion a e
excluded and eplaced wi h a i icially gene a ed bea s. Co ec ed in his way he se ies o changes in he
subsequen RR in e als become he basis o he de e mina ion o hea a e a iabili y measu es. The
mos commonly used quan i a i e analysis me hods can be di ided in o ime, equency, ime- equency
and non-linea me hods. In he p esen ed wo k, he indices desc ibing he HR a iabili y we e used
in an unusual way as a se o ea u es allowing he de ec ion o a ial ib illa ion episodes. The ou
selec ed ea u es, ob ained in s a is ical analysis in ime domain wi hin he same mo ing window, a e
as ollows:
•The mean hea a e:
HR[bpm]=1
N
N
X
i=1
HRi. (2)
•S anda d de ia ion o ins an aneous hea a e alues:
STD_HR [bpm]=
u
1
N−1
N
X
i=1HR −HRi2. (3)
•
Roo Mean Squa e o Successi e Di e ences (RMSSD) which measu es he a iabili y wi hin a
da a se —RR in e als—acco ding o he ollowing equa ion:
RMSSD[ms]=
u
1
N−1
N−1
X
i=1
(RRi+1−RRi)2. (4)
•
Pe cen age o di e ences be ween he RR in e als ha exceed he alue o 50 ms, deno ed as
pNN50 [%]:
pNN50 =PN−1
i=1Ai
N−1∗100%, (5)

Senso s 2020,20, 765 6 o 24
whe e:
Ai=(1 when RRi+1−RRi>50
0 when RRi+1−RRi≤50 (6)
In addi ion, h ee non-linea ea u es o HRV analysis we e applied in he o m o :
•
Poinca e g aph, which is a g aphical ep esen a ion o he cu en in e al RR
i
plo ed agains
subsequen one RR
i+1
. Using he ellipse i ing echnique, in each mo ing window comp ising
21 hea bea s, wo s anda d de ia ions a e de e mined om he poin s: pe pendicula o he
eg ession line (SD1) and along he line (SD2). The SD1 desc ibes he sho - e m a iabili y o he
hea hy hm, while he SD2 e e s o he long- e m HR a iabili y.
•
Tu ning Poin s Ra io (TPR) measu es he andomness o luc ua ions wi hin a da a se , by
calcula ing he a io o he numbe o u ning poin s o he maximum numbe o possible u ning
poin s. Tu ning poin is ound i bo h he p eceding and succeeding poin s a e ei he g ea e o
lowe . I is expec ed in andom da a se o a bi a y leng h N, ha he numbe o possible u ning
poin s is (2N−4)/3, wi h a s anda d de ia ion o p(16N−29)/90.
A sepa a e g oup o ea u es used o he de ec ion o AF episodes a e pa ame e s commonly
used in e al hea a e analysis [
55
,
56
]. I u ns ou ha in pe ina al medicine qui e di e en ea u es
a e used o desc ibe he FHR a iabili y, mainly sho - e m (bea - o-bea ) [
57
]. Fo he de ec ion o
AF episodes, ou widely known sho - e m coe icien s (indices) ha e been selec ed [
58
,
59
]. They
a e cha ac e ized by high sensi i i y o changes in subsequen alues o RR in e als and hus hey
po en ially may be use ul o AF de ec ion [60–62]:
•
The Yeh’s index (DI_Yeh) whose de e mina ion s a s wi h calcula ion o he auxilia y alues d
i
ep esen ing he a io o he di e ence be ween wo successi e RR in e als o hei sum:
di=RRi−RRi+1
RRi+RRi+1
. (7)
Then, o he analyzed signal agmen , he DI_Yeh index is de ined as he s anda d de ia ion
om he ob ained coe icien s di:
DI_Yeh [ms]=
u
1
N−2
N−1
X
i=1di−d2, (8)
whe e: d =1
N−1
N−1
P
i=1
di,N—numbe o bea s se o 21.
•
The Zugaib’s a iabili y index (STV_Zug) has been de ined as an a e age o he absolu e alues
o he di e ences be ween successi e Di alues and hei median alue:
STV_Zug[ms]=1
N−1
N−1
X
i=1
|Di−Med|, (9)
whe e: Med—median alue o he D
i
se ies, N—numbe o bea s se o 21. The D
i
alue ep esen s
he a io o he absolu e alue o he di e ence be ween he hea in e als RR o hei sum:
Di=RRi+1−RRi
RRi+1+RRi
, (10)
Senso s 2020,20, 765 7 o 24
•
The Huey’s index (STV_Huey) was de ined as he sum o absolu e alues o di e ences o
subsequen ins an aneous HR alues o which he sign o di e ence was changed:
STV_Huey [bpm]=
N−1
X
i=2
k·HRi+1−HRi. (11)
whe e:
k=(1 o (HRi−1−HRi)·(HRi−HRi+1)<0
0 o (HRi−1−HRi)·(HRi−HRi+1)≥0. (12)
•
The de ini ion o de Haan’s index (STI_Haan) is based on a pola coo dina e sys em whose bo h
axes e e o RR in e als exp essed in milliseconds, and poin s ep esen he pai s o subsequen
in e als (RR
i−1
, RR
i
), as shown in Figu e 3. STI_Haan is de e mined as he in e qua ile ange o
he angles
ϕi
be ween he lines connec ing he poin wi h o igin o he coo dina e sys em, and he
X axis, designa ed o subsequen pe iods RRi:
STI_Haan =IQR(ϕi), (13)
whe e: i =1, 2 . . . N,N—numbe o bea s.
Senso s 2020, 20, 765 7 o 24
• The de ini ion o de Haan’s index (STI_Haan) is based on a pola coo dina e sys em whose bo h
axes e e o RR in e als exp essed in milliseconds, and poin s ep esen he pai s o
subsequen in e als (RRi-1, RRi), as shown in Figu e 3. STI_Haan is de e mined as he
in e qua ile ange o he angles ϕi be ween he lines connec ing he poin wi h o igin o he
coo dina e sys em, and he X axis, designa ed o subsequen pe iods RRi:
STI_Haan=IQR(), (13)
whe e: i = 1, 2…N,N – numbe o bea s.
Figu e 3. Dis ibu ion o successi e RRi in e als in he pola coo dina e sys em, illus a ing
he de ini ions o he de Haan’s index desc ibing he sho - e m HR a iabili y.
2.2. LSVM Classi ie
The p oposed me hod o au oma ed ecogni ion o AF episodes is based on a machine lea ning
app oach. To achie e high accu acy o AF de ec ion, we applied he classi ica ion ou ine ha
o igina es om he S a is ical Lea ning Theo y (SLT) [63]. The SLT is he base o he machine
lea ning me hods which a e cha ac e ized by a high gene aliza ion abili y, meaning he high
e iciency when e alua ing p e iously unknown da a i.e., da a ha ha e no been used when
designing he classi ie (also called as classi ie aining o lea ning). One o he majo achie emen s
o SLT is he S uc u al Risk Minimiza ion (SRM) p inciple, which s a es ha he quali y o machine
lea ning depends bo h on he empi ical da a and he complexi y o he model. The mos -known
p ac ical implemen a ion o he SRM is he Suppo Vec o Machine (SVM) me hodology [51,64,65].
The SVM allows o inding he hype plane in he inpu ea u e space which di ides he conside ed
classes wi h he wides ma gin o sepa a ion. The inpu da a ha a e used o de ine he ma gin a e
called he suppo ec o s. The o iginal SVM algo i hm was o mula ed as a linea ly cons ained
quad a ic op imiza ion p oblem. Consequen ly, he lea ning p ocedu e o high compu a ional
complexi y was ob ained [66–68]. As he low compu a ional cos o he de ec ion me hod is o ou
special in e es , in he p oposed solu ion he Lag angian Suppo Vec o Machine (LSVM) [50] was
applied. I s lea ning eplaces he quad a ic p og amming wi h he linea ly con e gen i e a i e
algo i hm which esul s in signi ican educ ion o he compu a ional complexi y and highe
e iciency when compa ed o he o iginal SVM [50].
Le us conside a aining se ℒ, which con ains NTRN ec o s (1),(2),⋯,()∈ℝ o
pa ame e s quan i a i ely desc ibing he HR signal, and he co esponding ou pu alue
(1),(2),⋯,()∈󰇝−1,1󰇞 de ining he absence (non-AF) ()=−1 o he p esence
()=1 o he AF episode. The linea SVM classi ica ion p oblem o ℒ can be o mula ed as he
cons ained minimiza ion: min
ℝ
×
ℝ


(,)=
2+, (14)
subjec o he condi ion: (−)+≥, (15)
Figu e 3.
Dis ibu ion o successi e RR
i
in e als in he pola coo dina e sys em, illus a ing he
de ini ions o he de Haan’s index desc ibing he sho - e m HR a iabili y.
2.2. LSVM Classi ie
The p oposed me hod o au oma ed ecogni ion o AF episodes is based on a machine lea ning
app oach. To achie e high accu acy o AF de ec ion, we applied he classi ica ion ou ine ha o igina es
om he S a is ical Lea ning Theo y (SLT) [
63
]. The SLT is he base o he machine lea ning me hods
which a e cha ac e ized by a high gene aliza ion abili y, meaning he high e iciency when e alua ing
p e iously unknown da a i.e., da a ha ha e no been used when designing he classi ie (also called as
classi ie aining o lea ning). One o he majo achie emen s o SLT is he S uc u al Risk Minimiza ion
(SRM) p inciple, which s a es ha he quali y o machine lea ning depends bo h on he empi ical da a
and he complexi y o he model. The mos -known p ac ical implemen a ion o he SRM is he Suppo
Vec o Machine (SVM) me hodology [
51
,
64
,
65
]. The SVM allows o inding he hype plane in he inpu
ea u e space which di ides he conside ed classes wi h he wides ma gin o sepa a ion. The inpu
da a ha a e used o de ine he ma gin a e called he suppo ec o s. The o iginal SVM algo i hm
was o mula ed as a linea ly cons ained quad a ic op imiza ion p oblem. Consequen ly, he lea ning
p ocedu e o high compu a ional complexi y was ob ained [
66
–
68
]. As he low compu a ional cos o
he de ec ion me hod is o ou special in e es , in he p oposed solu ion he Lag angian Suppo Vec o
Machine (LSVM) [
50
] was applied. I s lea ning eplaces he quad a ic p og amming wi h he linea ly
con e gen i e a i e algo i hm which esul s in signi ican educ ion o he compu a ional complexi y
and highe e iciency when compa ed o he o iginal SVM [50].
Senso s 2020,20, 765 8 o 24
Le us conside a aining se
L
, which con ains N
TRN
ec o s
x0(1)
,
x0(2)
,
· · ·
,
x0(NTRN)∈
R
o pa ame e s quan i a i ely desc ibing he HR signal, and he co esponding ou pu alue
y0(1)
,
y0(2)
,
· · ·
,
y0(NTRN)∈{−1, 1}
de ining he absence (non-AF)
y0(n)=−
1 o he p esence
y0(n)=
1 o he AF episode. The linea SVM classi ica ion p oblem o
L
can be o mula ed as he
cons ained minimiza ion:
min
RN×RN SVM(w,ξ)=wTw
2+γ1Tξ, (14)
subjec o he condi ion:
D(X0w−1w0)+ξ≥1, (15)
and:
ξ≥0, (16)
whe e w∈R and w0∈Ra e he pa ame e s o wo bounding planes:
(xTw−w0= +1,
xTw−w0=−1. (17)
sepa a ing he aining da a wi h he ma gin
2
kwk
,
γ≥
0 is a cons an ha con ols he ade-o be ween
model simplici y and model ma ching o he aining da a,
1∈RN
deno es he ec o wi h all en ies
equal o one,
ξ∈RN
is he ec o o he slack (e o ) a iables, ha allow he classes o be bounded
wi h he maximum “so ” ma gin i.e., wi h he minimum sum o de ia ions o aining e o s and
maximum ma gin o he co ec ly classi ied ec o s,
D=diag(y0(1),y0(2),· · · ,y0(N)) ∈RN×N
is
a diagonal ma ix wi h class labels along i s diagonal,
X0="xT
0(1).
.
.xT
0(2).
.
.· · · .
.
.xT
0(N)#T
∈RN×
is he
ma ix o aining inpu da a.
In con as o SVM, he Lag ange suppo ec o machine maximizes he ma gin be ween he
sepa a ing planes wi h espec o bo h o ien a ion (
w
) and loca ion o he planes (
w0
). Mo eo e , in he
LSVM c i e ion unc ion he sum o he slack a iables
1Tξ
(14) is eplaced wi h he sum o squa es
ξTξ
making he cons ain (16) edundan . Consequen ly, he linea LSVM is de ined as minimiza ion
p oblem o he unc ional:
min
R ×R×RN pLSVM(w,b,ξ)=1
2wTw+w2
0+γ
2ξTξ, (18)
subjec o he cons ain (17). Mo eo e , he dual p oblem o (20):
min
RN
+
dLSVM(λ)=1
2λTQλ−1Tλ, (19)
whe e:
Q=I
γ+HHT∈RN×N
,
H=D"X0
.
.
.−1#∈RN×( +1)
and
I∈RN×N
is he iden i y ma ix, has he
non-nega i i y cons ain only λ∈RN
+.
The solu ion can be de e mined based on he Ka ush-Kuhn-Tucke necessa y and su icien
op imali y condi ions [
50
]. This leads o a linea ly con e gen i e a i e scheme which cons i u es he
LSVM me hod:
λ(k+1)=Q−11+Qλ(k)−1−αλ(k)+, (20)
whe e: kis he i e a ion index and
Qλ(k)−1−αλ(k)+∈RN
is he ec o wi h all o i s nega i e
componen s se o ze o.
Senso s 2020,20, 765 9 o 24
The abo e algo i hm is con e gen o any s a ing poin i :
0<α< 2
γ. (21)
The pa ame e s o he bounding planes ha sepa a e he classes can be eco e ed om he solu ion
o he dual p oblem by using he ollowing o mulas:











w=X0TDλ,
w0=−1TDλ,
ξ=λ
γ.
(22)
The LSVM app oach educes signi ican ly he ime necessa y o pe o m calcula ions o he
op imal (w,w0)while p ese ing high classi ica ion e iciency o he o iginal SVM lea ning.
The basic LSVM is a linea classi ie , hus o handle he non-linea ly sepa able da a he so-called
“ke nel ick” is equi ed. I is based on he p emise ha he complex non-linea classi ica ion p oblem
will be linea ly sepa able in some ea u e space o highe dimensionali y and in ol es he non-linea
ans o ma ion o inpu da a in he high-dimensional space. The linea sepa a ing plane
xTw−w0=
0
is hen eplaced by he non-linea su ace:
KxT
e,XT
0eDλ=0, (23)
whe e: xe="xT.
.
.−1#T
,X0e="X0
.
.
.−1#, and Kis he ke nel unc ion. Rede ini ion o he dual p oblem
(19) by using:
Q=I
γ+DKX0e,XT
0eD, (24)
which makes he LSVM i e a i e schema (20) alid o any posi i e semide ini e ke nel
K
[
50
]. In he
p oposed app oach we used he adial (Gaussian) ke nel:
K(x,y)=exp−χkx−yk2, whe e χ > 0. (25)
2.3. Pe o mance E alua ion
The pe o mance (gene aliza ion abili y) o he AF classi ica ion was e alua ed by he classi ica ion
accu acy (CA), de ined as he pe cen age o co ec ly classi ied cases in he es ing se (da a which was
no used du ing classi ie aining). As he AF de ec ion p ocess is a kind o diagnos ic es gi ing
nega i e o posi i e esul s, we also measu ed he classi ica ion quali y using sensi i i y (Se), speci ici y
(Sp), posi i e (PPV) and nega i e (NPV) p edic i e alue, calcula ed o he es ing da a se using
a con usion ma ix. Since e alua ion o he classi ica ion e iciency is di icul when analyzing all he
p ognos ic measu es simul aneously, we calcula ed also he F-Sco e (FS), de ined as a ha monic mean
o Se and PPV:
FS [%]=2·Se·PPV
Se +PPV. (26)
2.4. Hea bea Agg ega ion
The agg ega ion o he classi ied hea bea s should lead o emo al o acciden al changes o
hea bea s a us, and hus o ob ain mo e eliable in o ma ion on AF episodes. This p ocess is con olled
by wo pa ame e s: he window wid h and pe cen age h eshold. Each hea bea s a us is alida ed
in symme ical window by checking i he numbe o he hea bea s wi h he same s a us exceeds
he pe cen age h eshold. We de ined he pe cen age h eshold o he AF s a us, as he numbe o
hea bea s classi ied as AF o he numbe o all bea s in he analyzed window. I he h eshold is
exceeded he AF s a us emains unchanged, o he wise is se o non-AF. The op imal alues o he
Senso s 2020,20, 765 16 o 24
o compa e ou esul s wi h hose epo ed ea lie . On his esea ch ma e ial he LSVM classi ie , ed wi h
six een ea u es desc ibing he hea a e a iabili y, ensu ed he sensi i i y 98.10%, speci ici y 97.50%,
posi i e p edic i e alue 96.67%, classi ica ion accu acy 97.75 and F-Sco e 97.38%. A e agg ega ion
s age hose pe o mance measu es inc eased o 98.94%, 98.80%, 98.39%, 98.86% and 98.66 espec i ely.
Especially, signi ican inc ease o he PPV alue was no ed a lowe numbe o alse AF de ec ions.
Ob ained pe o mance is highe han ha p o ided by p e iously de eloped classi ica ion me hod
based on linea classi ie , whe e Se =95.42% and PPV =94.97% [
53
]. Thus, he p oposed mo e ad anced
me hod has be e abili y o de ec he ue occu ences o AF and p o ides lowe numbe o alse
a hy hmias. I should be emphasized ha bo h in case o simple linea classi ie and ad anced LSVM
app oach he agg ega ion s age signi ican ly imp o es he e iciency o AF episodes de ec ion. Du ing
his s udy he HR ea u es ha e been de e mined in 21 bea s wide window [
54
]. Ne e heless, he
esul s ob ained so a by he au ho s a e be e han hose p o ided by o he au oma ed AF de ec ion
me hods epo ed ea lie , e alua ed using he MIT-BIH AF da abase (Table 6).
The mos ob ious ea u e o measu e he RR i egula i y seems o be he di e ence be ween
successi e in e als RR. In [
33
] he s anda d densi y his og am o RR di e ences was p epa ed as
a empla e—using he anno a ed AF episodes, and hen he simila i ies be ween he densi y his og ams
o he es da a and he s anda d densi y his og am we e es ima ed using he s anda d coe icien o
a ia ion (CV es ) and Kolmogo o -Smi no (K-S) s a is ical es . Fo he op imal h eshold o he es
ou pu ound by ROC, he K-S es showed Se =94.4%, Sp =97.2%, and PPV =96.1%, o he window
leng h o 100 in e als. De ec ion o AF episodes based on densi y his og am o RR di e ences was also
de eloped by Huang e al. [
74
]. The p oposed mo e ad anced analysis included wo s eps: AF e en
de ec ion using he del a RR in e al dis ibu ion di e ence cu e and AF e en classi ica ion. Using
he ROC cu es o de e mining he h eshold o he K-S es , he au ho s ha e achie ed he highe
Se and Sp (96.1% and 98.1%, espec i ely) o he MIT-BIH AF da abase. The algo i hm desc ibed
in [
34
] has been based on he ex ac ion o simple geome ic ea u es de e mined om he his og am o
RR p ema u i y, compu ed as he pe cen age a ia ion om he cu en hea a e and he di e ences
be ween wo successi e RR in e als. The ea u e se included: numbe o nonemp y bins, main
dis ibu ion wid h, di e ence be ween mean and median and geome ic es o bimodali y. The sco e
sys em was in oduced o inally classi y en-second segmen as non-AF o AF pe iod. Using he
MIT-BIH AF da abase, he RR p ema u i y algo i hm p o ided he sensi i i y o 91% and PPV o 92%,
while o he RR di e ences Se =92%, and PPV=78%. The map ha plo s RR in e als e sus RR
di e ences was p oposed in [
35
]. Fo e e ence, a window was labeled as ue AF episode i 1/2 o
in e als in he window we e anno a ed as AF. Th eshold alue o disc imina i e pa ame e —nonemp y
cell—was de e mined by ROC, and led o sensi i i y 95.8% and speci ici y 96.4% o he op imal
window leng h o 128 in e als.
Ano he linea ans o ma ion o RR in e als o di e en ia e be ween AF episodes and no mal
sinus hy hm was desc ibed in [
44
]. The p oposed algo i hm s a s wi h p ep ocessing (es ima ing
he RR end and il e ing he ec opic bea s), hen wo unc ions o measu e he RR i egula i y a e
calcula ed, and inally usion o hese signals is used o de ec ion o AF episodes elying on he ixed
h eshold. Based on he dis ibu ion o he usion signal ou pu o AF and non-AF bea s, he op imal
de ec ion h eshold wi h iden ical alues o sensi i i y and speci ici y was se . Using he MIT-BIH AF
he au ho s epo ed e y high alues o sensi i i y (97.1%) and speci ici y (98.3%). Fo ha app oach
a e y sho window o 8 bea s was ound as op imal. The au ho s unde line ha he p oposed me hod
can be ma ched o de ec e y sho episodes, bu i is a he expense o lowe speci ici y.
The nex app oach applying only RR in e al was based on he a iance o no malized RR in e als
o e en-second sliding window [
29
]. Acco ding o he au ho s, he no maliza ion imp o es he de ec ion
pe o mance. The au ho s used he mo phology independen QRS de ec o o compu e RR in e als and
a iance, and hen hey smoo hed he esul ing classi ica ions, using simple majo i y o ing scheme o e
600 bea windows, o u he obus ness. Howe e , he es s ca ied ou on he MIT-BIH AF da abase
showed ha he p oposed algo i hm has sensi i i y o 96% bu speci ici y only o 89%, which is su icien

Senso s 2020,20, 765 17 o 24
o AF sc eening only. The mo e ad anced no maliza ion o RR in e als by an a ine ans o ma ion
was p oposed in [
30
]. In e al i egula i y was ep esen ed by he spa seness o no malized in e al
p obabili y dis ibu ion which was measu ed by he no malized en opy calcula ed in he window.
The au ho s used h ee leng hs o he window (30, 50 and 70 bea s) o show hei in luence on he
no maliza ion. The ROC analysis enabled hem o ind he h eshold alue o he en opy classi ie
ou pu , ha ensu ed he ollowing alues o Se, Sp, PPV and CA: 96.39%, 96.38%, 95.19%, 96.38%.
Table 6.
An o e iew o published esul s o exis ing AF de ec ion me hods using he MIT-BIH A ial
Fib illa ion Da abase.
Me hod Fea u es Window Key Techniques Resul s
Se Sp PPV CA
Ta eno e al.
2001 [33]RR di e ence 100 bea s His og am, Kolmogo o -Smi no
es , ROC. 94.4 97.2 96.1 –
Huang e al.
2011 [74]RR di e ence 23 bea s His og am, SD analysis,
Kolmogo o -Smi no es . 96.1 98.1 – –
Pe ucci e al.
2005 [34]
RR di e ence, RR
p ema u i y 60 s Geome ic measu es o his og am,
Sco e sys em. 92 – 92 –
Lian e al.
2011 [35]
RR in e al, RR
di e ence 128 bea s Mapping RR in e als e sus RR
di e ences, h esholds. 95.8 96.4 – –
Pe enas e al.
2015 [44]RR in e al 8 bea s Th esholds 97.1 98.3 – –
Logan e al.
2005 [29]RR in e al 600 bea s Va iance o no malized RR in e al,
simple majo i y o ing. 96 89 – –
Islam e al.
2016 [30]RR in e al 70 bea s No maliza ion o RR in e als by an
a ine ans o ma ion. 96.39 96.38 95.19 96.38
Babaeizadeh.
e al. 2009 [16]
RR in e al P-wa e
measu emen s -S a iona y i s -o de Ma ko
p ocess, decision ee. 94 99 98 –
Zhou e al.
2014 [36]RR in e al 127 bea s
Mapping he RR sequence in o
symbolic one, Shannon en opy,
ROC.
96.89 98.25 97.62 97.67
Zhou e al.
2015 [75]RR in e al 127 bea s Online e sion o [36] 97.37 98.44 97.89 97.99
Cui e al. 2017
[37]RR in e al 150 bea s Mapping he RR sequence in o
symbolic one, dissimila i y index. 97.04 97.96 – 97.78
Dash e al.
2009 [38]RR di e ence 128 bea s Tu ning poin s, RMSSDD, Shannon
en opy, ROC. 94.4 95.1 – –
Lake e al.
2011 [15]RR di e ence 12 bea s Coe icien o sample en opy
(CoSEn), ROC. 91 94 – –
Kennedy e al.
2016 [32]RR di e ence 30 bea s Random o es , k-nea es neighbo . 97.6 98.3 92.1 –
Ande sen e al.
2017 [39]
RR in e al
ECG ea u es
300 bea s
30 s
Sample en opy, Shannon en opy,
CoSEn, SVM.
96.81
94.27
96.20
98.84 –96.45
96.68
Kuma e al.
2018 [76]ECG ea u es 1000
samples Wa ele ans o m, Random o es . 95.8 97.8 – 96.8
Nu yani e al.
2015 [40]RR di e ence SVM wi h adial basis unc ion. 95.81 98.44 – 97.50
Colloca e al.
2013 [41]
RR di e ence
Median HR 30 En opy, SVM wi h adial basis
unc ion 99.20 - 59.33 86.60
Faus e al.
2018 [46]- 100
Deep Recu en Neu al Ne wo k
(RNN) wi h Long Sho -Te m
Memo y (LSTM).
98.51 98.32 – 98.67
Ande sen e al.
2019 [45]- 31
Deep lea ning combining wi h he
con olu ional- and Recu en -Neu al
Ne wo ks.
98.98 96.95 95.76 97.80
W obel e al.
2018 [53]
HR i egula i y
ea u es 21 Linea classi ie 95.42 96.12 94.97 95.62
P oposed
me hod 2019
HR i egula i y
ea u es 21 LSVM 98.94 98.39 98.86 98.66
Senso s 2020,20, 765 18 o 24
The sequence o RR in e al is assumed o be con olled by a s a iona y i s -o de Ma ko p ocess
cha ac e ized by a ansi ion p obabili y ma ix as i was p oposed o he i s ime by Moody and
Ma k [
4
] o au oma ed de ec ion o he AF episodes. As Ma ko sco e e lec s he ela i e likelihood
o RR in e als sequence in AF episode e sus no-AF one, i can be compa ed o he ixed h eshold
applied o classi y he sequences [
16
]. In ha wo k he du a ion s a is ics wi h combining all eco ds
in o one p o ided he alues o Se, Sp, and PPV: 94%, 98% and 97%. Fu he mo e, a possibili y
o imp o emen o he AF episode de ec ion by addi ional in o ma ion on ECG mo phology was
in es iga ed. When he RR in e al Ma ko sco e was comple ed wi h he wo P-wa e measu emen s:
he loca ion (P-R in e al a ia ion) and he mo phology (simila i y be ween wo consecu i e P-wa es)
he Sp and PPV inc eased o 99%, while he Se emained unchanged. As he au ho concluded
educ ion o he alse posi i e cases is a esul o de ec ing alid P-wa es on he ECG eco ding wi h
i egula hy hm o he han AF. Ne e heless, he sensi i i y which de ines he abili y o de ec ue AF
occu ences was signi ican ly lowe han he alue achie ed by ou me hod.
In [
37
] he changes in RR du a ion du ing he sequence ha e been ep esen ed as he bina y
wo ds, whe e alue o 1 co esponds o inc ease o in e al du a ion, and 0 means no change o
a dec ease. Then, he es ing segmen is classi ied by compa ing i s in o ma ion-based dissimila i y
index wi h hose ob ained o he empla es o AF episode and no mal sinus hy hm. Pa ame e s
o he classi ica ion model: he numbe o bi s, window leng h and he shi o he dissimila i y
compa ison bounda y we e op imized o p o ide he bes pe o mance exp essed by sensi i i y o
97.04%, speci ici y o 97.96% and classi ica ion accu acy o 97.78%. Ano he app oach based on
mapping he RR sequence in o symbolic one was p oposed in [
36
]. The de ec ion p oceeds in h ee
s ages: he ini ial, whe e a RR in e al sequence is p e-p ocessed wi h nonlinea and in ege il e s,
he second, whe e he in o ma ion o he RR in e al changes is con e ed in o symbolic sequence, and
inal, whe e he Shannon en opy is calcula ed o disc imina e whe he o no he sequence ela es o
AF episode. Op imal disc imina ion h eshold o Shannon En opy was ob ained by ROC analysis.
The RR sequences o 127 bea s we e p ocessed. The ollowing alue o Se, Sp, PPV and CA we e:
96.89% 98.25% 97.62% 97.67%, while o he online e sion o he algo i hm: 97.37%, 98.44%, 97.89%
and 97.99% [75].
The en opy concep , e e ing o he diso de o unce ain y o a p ocess, was used in many
me hods o au oma ed de ec ion o AF episodes, usually being included in he ea u e se , bu also as
he only measu e o RR i egula i y. Th ee s a is ics desc ibing andomness, a iabili y and complexi y
o he RR in e al ime se ies we e p oposed in [
38
]. The u ning poin s a io, oo mean squa e o
successi e RR di e ences and Shannon en opy we e employed o cha ac e ize he a ial ib illa ion.
Using he h esholds and da a segmen o 128 bea s de e mined by ROC he sensi i i y o 94.4%
and speci ici y o 95.1% we e achie ed o he signals om he MIT-BIH A ial Fib illa ion Da abase.
The op imized sample en opy measu e, called coe icien o sample en opy (CoSEn), being able o
de ec e y sho AF episodes (e en 12 bea s) was p oposed by Lake and Moo man [
15
]. This ea u e
es ima ed he p obabili y ha sho empla es will ma ch wi h o he segmen s wi hin he analyzed
RR in e al ime se ies. Tha p ocess was con olled by wo pa ame e s: he empla e leng h and he
ole ance ma ching, whose op imal alues we e es ablished by ROC analysis. The au ho s ound he
cu o CoSEn alue, which di e en ia e be ween AF and no mal sinus hy hms, o p o ide a sensi i i y
o 91% and a speci ici y o 94%. In [
32
] he CoSEn was combined wi h h ee o he ea u es: he
coe icien o a iance, oo mean squa e o he successi e di e ences, and median absolu e de ia ion.
The de ec ion pe o mance o each i egula i y measu e was assessed indi idually by ROC analysis,
and CoSEn pe o med bes . The abo e pa ame e s we e also used as he inpu ea u es se o
wo classi ie s: andom o es (RF) and k-nea es neighbo . Bo h classi ica ion models signi ican ly
imp o ed he Sp and PPV alues o e CoSEn, bu wi h subs an ial d op in Se. The bes speci ici y o
98.3% and PPV o 92.1% we e p o ided by RF model, while he sensi i i y achie ed he bes alue
97.6% when using CoSEn as he only disc imina i e ea u e. Those esul s we e epo ed o he
combined da abase, wi h MIT-BIH AF among o he s. When only MIT-BIH AF da abase was employed,
Senso s 2020,20, 765 19 o 24
he au ho s no iced signi ican educ ion o de ec ion pe o mance o CoSEn and median absolu e
de ia ion, exp essed by smalle a ea unde he ROC cu e.
Th ee en opy ea u es: sample en opy, coe icien o sample en opy, Shannon en opy, oge he
wi h wo linea measu es: oo mean squa e and no malized oo mean squa e o successi e di e ences
cons i u ed he se o RR i egula i y measu es being es ed in [
39
]. Apa om ha HR app oach,
he au ho s in es iga ed he ECG-d i en app oach wi h wo ea u es: peak- o-a e age powe a io
and log-ene gy en opy, ex ac ed om 2-le el s a iona y wa ele ans o m coe icien s. The suppo
ec o machine was used o classi ica ion in bo h app oaches. Th ee di e en segmen leng hs we e
e alua ed: 60, 100, 300 bea s o HR and 10, 15, 30 s o ECG da a. Like in [
35
], any segmen con aining
a leas o 50% AF bea s was labeled as ue AF when p ocessing ECG. Fo HR app oach his le el was
educed o 30%. The longes windows p o ided he bes esul s o bo h HR (Se 96.81%, Sp 96.20%, CA
96.45%) and ECG (94.27%, 98.84%, 96.98%, espec i ely) app oaches.
The pe o mance o AF de ec ion using he ea u es ex ac ed exclusi ely om ECG signals was
assessed by Kuma [
76
]. As he da a was aken om MIT-BIH da abase, he ob ained esul s may
be ela ed o hose p o ided by he HR-based me hods desc ibed he e. The p oposed classi ica ion
me hod employed wo ea u es: he log-ene gy en opy and pe mu a ion en opy compu ed om he
sub-band signals ob ained using lexible analy ic wa ele ans o m. Using andom o es classi ie ,
he au ho s epo ed sensi i i y o 95.8%, speci ici y o 97.8% and accu acy o 96.8%.
Two ea u es: he a e age o RR di e ences in a de ined du a ion, and he s anda d de ia ion o
di e ences in a de ined du a ion, we e examined as he inpu s o he classi ie based on SVM wi h
adial basis unc ion in [
40
]. The p oposed me hod showed ollowing pe o mance on he MIT-BIH AF
da abase: Se =95.81%, Sp =98.44% and CA =97.50%. The same SVM classi ie was employed in [
41
].
The inpu se comp ised mo e RR in e al ea u es: median hea a e, minimum RR in e al, mean RR
in e al, a ious en opy measu es, and di e ence i egula i y measu e. The MIT-BIH AF da abase
was used in ha s udy, bu only du ing he aining s age, when e y good esul s ha e been achie ed
(sensi i i y =99.07%, PPV =98.27%, accu acy =98.84). When es ing on a se ies o 200 signals om he
MIT-BIH A hy hmia da abase, he bes accu acy was 86.60% o he window o 30 bea s, sensi i i y
eached 99.20%, bu PPV was only 59.33%.
The newes app oach o au oma ed AF de ec ion p oposed in [
46
] and [
45
] has been based on deep
lea ning algo i hm, which aims o de elop he classi ica ion model by using all a ailable in o ma ion
om he inpu . In case o AF de ec ion om he ECG signals i means no need o ex ac ion o he
ea u e nei he om aw ECG no om RR in e al ime se ies. In hose wo ks he RR da a om
MIT-BIH AF we e pa i ioned using sliding window o 100 bea s [
46
] o 31 bea s bu shi ed wi h
10 bea s [
45
], and hen ed o Recu en Neu al Ne wo k wi h Long Sho -Te m Memo y. In bo h
wo ks e y good esul s we e epo ed: Se =98.51%, Sp =98.32%, CA =98.67% in [
46
], and 98.98%,
96.95%, 97.80% wi h PPV o 95.76% in [
45
], when median il e ing was used as pos p ocessing o
imp o e he de ec ion pe o mance. I should be no ed, howe e ha de elopmen o he deep lea ning
algo i hm has been enabled by ecen ad ances in pa allel compu ing on G aphics P ocessing Uni s.
The compu a ional complexi y o deep lea ning model is much highe han adi ional ea u e-based
classi ie . This limi s i s applica ion in wea able de ices o long e m moni o ing wi h online AF
de ec ion, like w is band moni o in a o m o w is b acele .
5. Conclusions
Despi e se ious medical consequences, a ial ib illa ion is s ill an unde es ima ed clinical and
diagnos ic p oblem. Recogni ion o his o m o a hy hmia equi es a long- e m moni o ing o he
hea hy hm, since e y o en pa ien s a e asymp oma ic. Mo eo e , he AF episodes can occu
acciden ally and may las om minu es o hou s. The objec i i y and e iciency o he isual analysis
o long- e m eco dings can be imp o ed by au oma ed AF de ec ion.
The pape p oposed a LSVM-based app oach wi h an o iginal aining s age which ou pe o ms
o he au oma ed AF de ec ion me hods based on he in o ma ion on bea - o-bea i egula i y p oposed
Senso s 2020,20, 765 20 o 24
in he li e a u e. Ou me hod ensu es a e y high e iciency in de ec ion o ue AF episodes exp essed
by sensi i i y o 98.94%, and a he same ime low numbe o alse episodes, as he posi i e p edic i e
alue eached 98.36%. These esul s we e achie ed wi h pos -p ocessing agg ega ion s age, showing
a need o inal e i ica ion o he classi ied bea s. I also u ned ou ha ex ending he inpu ea u e
ec o o include pa ame e s desc ibing he hea i egula i y and being ypically used in he e al hea
a e analysis, had posi i e e ec on classi ica ion e iciency. Designing he LSVM-based classi ie o
deal wi h such la ge amoun o da a like om MIT-BIH AF Da abase led us o aluable conclusion.
No he size o he aining se is o c ucial impo ance, bu he occu ence o he inpu ec o s
con aining he quan i a i e pa ame e s o HR a iabili y desc ip ion which allow sepa a ing he AF
and non-AF hea bea s wi h he wides sepa a ion ma gin (suppo ec o s), hus gua an eeing he
bes classi ica ion quali y.
Au ho Con ibu ions:
Concep ualiza ion, R.C, K.H. and J.W.; Da a cu a ion, A.M., R.M and R.K.; Me hodology,
R.M., T.K., R.K. and J.J.; So wa e, R.C., J.W. and A.M.; Supe ision, K.H. and R.C.; Valida ion, J.W., T.K., M.J. and
J.M.L.; W i ing-o iginal d a , K.H. and R.C.; W i ing- e iew & edi ing, K.H., M.J., J.J. and J.M.L. All au ho s ha e
ead and ag eed o he published e sion o he manusc ip .
Funding: This esea ch ecei ed no ex e nal unding.
Acknowledgmen s:
This scien i ic esea ch wo k was suppo ed by he Na ional Science Cen e and
he Na ional Cen e o Resea ch and De elopmen in Poland unde he g an s 2017/27/B/ST6/01989 and
STRATEGMED2/269343/18/NCBR/2016, as well as om he Minis y o Science and Highe Educa ion unding o
s a u o y ac i i ies (BK-2019, BK-2020).
Con lic s o In e es : The au ho s decla e no con lic o in e es .
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