Time Se ies Analysis o Bioma ke s o P og ession in
Neu odegene a i e Diseases
Íñigo Sanz Ilundain
Deg ee in Compu e Science
Facul y o Compu e Science and Enginee ing
Complu ense Uni e si y o Mad id
Deg ee Thesis in Compu e Science
May 30 2022
Tu o /s and/o colabo a o /s:
Lau a He nández Lo enzo
José Luis Ayala Rod igo
Resumen en cas ellano
Las en e medades neu odegene a i as son en e medades complejas y empo almen e de-
pendien es. En e ellas, la más común es la en e medad de Alzheime , en la que los pacien es
a a iesan una se ie de es ados sin omá icos an es de llega al diagnós ico de demencia
causada po el Alzheime . Debido a sus ca ac e ís icas, es necesa io es udia los bioma -
cado es asociados a es a en e medad desde el pun o de is a de las se ies empo ales. En
es e abajo, explo amos exhaus i amen e los bioma cado es encon ados en la coho e de
Alzheime ’s Disease Neu oimaging Ini ia i e (ADNI), aplicando una colección de algo i -
mos de clus e ing, an o empo ales como no empo ales. Se han aplicado es os modelos a
a ios conjun os de da os: conside ando un solo bioma cado , combinándolos po pa es y
u ilizando las egiones MRI. Los esul ados ob enidos con es os conjun os de da os ue on
e aluados desde un pun o de is a compu acional, al igual que uno clínico, es e úl imo co -
espondiendo a los esul ados espe ados. Es os esul ados mues an que, desde un pun o
de is a compu acional, los modelos no empo ales suelen ob ene mejo es esul ados que
los modelos empo ales. Adicionalmen e, los conjun os de da os combinando bioma cado es
con ca ac e ís icas simila es inc emen an el alo del esul ado. Mien as an o, desde un
pun o de is a clínico, el esul ado in luye mucho del algo i mo y del conjun o de da os u i-
lizado: los modelos no empo ales suelen ob ene mejo es esul ados en conjun os de da os
que con engan bioma cado es como AV45 o ABETA, pe o ob ienen peo es cuando se usan
o os bioma cado es como TAU o PTAU, un lími e que se puede supe a usando modelos
empo ales. Es e abajo pone de mani ies o un eno me po encial en el clus e ing de se-
ies empo ales en el conocimien o de las en e medades dependien es del iempo, como las
neu odegene a i as.
Palab as cla e
En e medad de Alzheime , bioma cado es, de o mación dinámica del iempo, clus e ing
Abs ac
Neu odegene a i e diseases a e complex and highly ime-dependen diseases. Among
hem, he mos common is Alzheime ’s Disease (AD), in which he pa ien goes h ough
a se ies o symp oma ic s ages be o e ecei ing he diagnosis o demen ia caused by AD.
Due o i s empo al cha ac e is ics, i is necessa y o s udy he bioma ke s associa ed wi h
he AD om a ime se ies poin o iew. In his wo k, we ha e exhaus i ely explo ed
he bioma ke s ound on he Alzheime ’s Disease Neu oimaging Ini ia i e (ADNI) coho
applying a wide a ay o clus e ing algo i hms bo h empo al and non- empo al. These
models we e applied o se e al bioma ke da ase s: implying one bioma ke only, combining
hem in pai s as well as making use o he MRI egions. The esul s ob ained wi h hese
da ase ypes we e e alua ed using a compu a ional and a clinical s andpoin , whe e he
la e co esponded e y clea ly wi h i s expec ed ou comes. Resul s show ha om a
compu a ional pe spec i e, non- empo al models gene ally ob ain g ea e ou comes han
empo al models. Mo eo e , da ase s combining bioma ke s wi h simila p ope ies also
inc ease he esul ing sco e. Con a ily, om a clinical s andpoin , he ou come depends
g ea ly on he algo i hm and he da ase used: non- empo al models ob ain be e esul s
in da ase s con aining AV45 o ABETA bu s uggle when used wi h TAU o PTAU, a
limi a ion ha can be su passed by making use o empo al models. The p esen wo k aises
eno mous po en ial ound in ime se ies clus e ing o disco e knowledge in ime-dependen
diseases such as he neu odegene a i e ones.
Keywo ds
Alzheime ’s Disease, bioma ke s, dynamic ime wa ping, clus e ing
Con en s
Índice i
Ag adecimien os ii
Dedica o ia iii
1 In oduc ion 1
2 Ma e ials and Me hods 6
2.1 Da abasedesc ip ion ............................... 6
2.2 Da a il e ing ................................... 10
2.3 Da ap ep ocessing ................................ 13
2.3.1 Missing alues............................... 13
2.3.2 Da a ans o ma ions . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Unsupe ised classi ica ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4.1 Agglome a i e Hie a chical Clus e ing . . . . . . . . . . . . . . . . . 16
2.4.2 K-Means.................................. 19
2.4.3 Densi y-Based Spa ial Clus e ing o Applica ion (DBSCAN) . . . . . 20
2.4.4 Sel O ganizing Maps (SOM) . . . . . . . . . . . . . . . . . . . . . . 21
2.4.5 Dynamic Time Wa ping wi h Hie a chical Clus e ing . . . . . . . . . 23
2.4.6 Dynamic Time Wa ping wi h DBSCAN . . . . . . . . . . . . . . . . . 26
2.5 E alua ionMe ics ................................ 27
3 Resul s 29
3.1 Non-Tempo almodels .............................. 29
3.1.1 Non-Tempo al models wi h sepa a ed bioma ke s . . . . . . . . . . . 30
3.1.2 Non-Tempo al models wi h pai s o bioma ke s . . . . . . . . . . . . 33
3.1.3 Non-Tempo al models wi h MRI egions . . . . . . . . . . . . . . . . 34
3.2 Tempo almodels ................................. 35
3.2.1 Tempo al models wi h sepa a ed bioma ke s . . . . . . . . . . . . . . 36
3.2.2 Tempo al models wi h pai s o bioma ke s . . . . . . . . . . . . . . . 39
3.2.3 Tempo al models wi h MRI egions . . . . . . . . . . . . . . . . . . . 40
4 Discussion 42
5 Conclusion 53
Bibliog aphy 56
i
Ag adecimien os
Quie o ag adece le a oda mi amilia el apoyo incondicional que me han dado. A mis
pad es, a mi ía Piluca y a mi ío Ca los po apoya me en los momen os más complicados.
Muchas g acias a Be a, a Víc o , y al g upo de ea o de la Complu ense, T iaca, po
habe me acompañado an de ce ca du an e odos es os años.
Es oy especialmen e ag adecido a mis u o es Lau a y José, no solo po habe me enseñado
an o sob e las en e medades neu odegene a i as y guiado inmensamen e a lo la go del año,
sino ambién po su in aluable apoyo du an e la elabo ación de es e abajo.
No hab ía sido posible ealiza es e abajo sin oso os.
ii

Dedica o ia
A mi abuela, a mis pad es y a mis he manos.
iii
Chap e 1
In oduc ion
Neu odegene a i e diseases a e complex diseases ha ake place in he pa ien ’s b ain,
causing he p og essi e loss o neu ons and i s s uc u e, a biological p ocess known as
neu odegene a ion. A wide a ie y o neu odegene a i e diseases exis , and he in e cep ions
and ea men s di e g ea ly om one disease o ano he . These diseases cause a g ea
sani a y cos , as he a ec ed pa ien s need o be in cons an moni o iza ion bo h p io and
a e neu odegene a ion begins in o de o slow down he cell loss a e. Neu odegene a i e
diseases also ha e an economic impac , since he ea men s employed a e complex and hus
expensi e. Las ly and mo e impo an ly, he social impac o hese diseases. Because o
he cogni i e impai men , pa ien s wi h neu odegene a ion canno li e hei li e in a no mal
way, depend on ca e ake s o pe o m hei daily li e ac i i ies and can ul ima ely end up
de eloping demen ia, some hing ha impac s in hei psychology, educing hei chances
o slow cogni i e decline, and also hei social en i onmen . The e o e i is essen ial o
unde s and how neu odegene a ion akes place and de elop accu a e echniques o diagnose
and p e en i . Un o una ely, mos neu odegene a i e diseases a e ex emely complex and
an icipa ing and cu ing hei biological mechanisms is gene ally unknown. Examples o
hese neu odegene a i e diseases a e Pa kinson’s o Hun ing on’s diseases, al hough he
mos common one is Alzheime ’s Disease, whe e one in 10 Ame icans a e a ec ed by i .1
Alzheime ’s Disease (AD) is a b ain disease ha mainly a ec s cogni i e unc ions,
beginning wi h mild memo y loss, wo sening o he ex en o being unable o espond o
1
he en i onmen . As s a ed, hese symp oms a e caused by neu odegene a ion meaning a
loss o neu ons and i s in e -connec ions, esul ing in b ain a ophy. This pa icula disease
is cha ac e ized by h ee main clinical s ages: p eclinical AD, mild cogni i e impai men
(MCI), and inally demen ia due o AD2. Depending on he cu en s age, di e se changes
ake place on he b ain, wi h no o a ying deg ees o cogni i e symp oms. Figu e 1.1 shows
hese s ages as well as he cogni i e symp oms o each one o hem.
Mild and unno iced
symp oms
No symp oms
Se e i y o symp oms
depends on deg ee o
Demen ia
PRECLINICAL AD MILD COGNITIVE
IMPAIRMENT
DEMENTIA DUE
TO AD
Figu e 1.1:Th ee main s ages and symp oms in Alzheime ’s disease con inuum. No e ha
he p eclinical s age is he ideal s age o an icipa e Demen ia be o e he biological mechanisms
ake place.
These s ages and hei pa icula i ies can be s udied wi h he use o ce ain bioma ke s
p esen among he a ec ed indi iduals as well as o he assessmen s. Bioma ke s a e sub-
s ances ha indica e a biological s a us which a e used o de ec diseases be o e hey ake
place as well as e alua e hei p og ession once hey ha e. Said biological s a us can be
s a ic measu es such as he geno ype o a pe son, o a a ying measu e, o ins ance molec-
ula es s. The biological ea u es o AD a e desc ibed by he accumula ion o wo p o eins
in hei pa hogenic o ms: be a-amyloid and Tau, o ming plaques and neu o ib illa y an-
gles, espec i ely. The e o e, one example o a e y common bioma ke is he p og ession
o inc eased be a-amyloid le els in Posi on Emission Tomog aphy (PET) scans. Howe e ,
simila ly o he o he neu odegene a i e diseases, AD’s main challenge is o o esee when
hese mechanisms will ake place and hei e olu ion in ime. All hese mechanisms al eady
igge in he p eclinical s age, long be o e any symp oms s a aking place. Consequen ly,
i is essen ial o s udy hese mechanisms and an icipa e hei p og ession o e ime and
implica ion a he clinical le el, o ins ance he diagnosis ansi ions and hei po en ial
2
ela ion wi h o he impo an bioma ke s such as in indi iduals’ gene ics.
While hese diseases a e ex emely complex, he medicine ield has also made ad ances
such as eseaching new possible ami ica ions o medicine. I is he case o “P4 medicine”3,
an app oach o make medicine mo e p edic i e, p e en i e, pe sonalized and pa icipa o y,
wi h he majo objec i e o imp o ing wellness and an icipa ing he appea ance o a disease’s
symp oms. This has bene i ed he ea men o neu odegene a i e diseases, especially he
pe sonalized app oach.
Due o he complexi y o AD, placing each pa ien in one o h ee speci ic s ages in he
Alzheime ’s Disease con inuum is limi ing a bes , as a conside able amoun o in o ma ion is
los and he di e ences be ween pa ien s a a gi en s age a e signi ican . The e o e, ins ead
o isualizing s ages, a mo e pe sonalized pe spec i e is he use o a g adien , whe e pa ien s
wi h simila bioma ke s a e placed close o each o he . Because o he complexi y in pa ien
diagnosis and he amoun o people a ec ed by Alzheime ’s Disease, a e y e icien ool o
compa e pa ien s oge he is he use o Machine Lea ning echniques. Machine Lea ning
is a discipline o A i icial In elligence ha allows sys ems o make obse a ions and lea n
om pa e ns in da a wi hou any kind o human in e en ion o assis ance. I s many
applica ions ange om da a p ocessing so wa e in ields such as inance and da a secu i y
o obo ics capable o pe o ming ope a ions on pa ien s wi h he use o senso s.
Machine Lea ning has many uses due o he h ee ypes o classi ica ions i is capable
o , hese being unsupe ised, supe ised and ein o cemen lea ning. Unsupe ised lea n-
ing o clus e ing is a echnique ha is based on g ouping oge he samples wi h simila
cha ac e is ics. The e o e i is a use ul ool in clinical applica ions because i pe mi s o
ind new ela ed g oups o pa ien s wi h he disease, which ul ima ely o e s new knowledge
abou how he disease occu s wi hou biasing he esul owa ds p e ious knowledge abou
i . When ea ing wi h AD, clus e ing is he mos in e es ing echnique as i lea ns om
he inpu da a wi hou he use o labels, which in ou applica ion ield would ep esen
he pa ien s’ diagnoses. Mo eo e , his echnique is also bene icial as i a oids aking in o
3
pa ien s had a MCI diagnosis and 791 (33.62%) su e ed om Demen ia, wi h he same 35
(1.49%) p e ious pa ien s ha did no ha e a se diagnosis. As we can see, he numbe o
pa ien s wi h Demen ia has inc eased since he baseline, he e o e his da abase is sui able
o s udy he p og ession o AD among hese pa ien s.
2.2 Da a il e ing
We di ided he en i e da ase in o smalle subse s, each being bioma ke speci ic o mee
wi h all he il e ing c i e ia, since a pa ien ha migh ha e all hei da apoin s a ailable
o a gi en bioma ke , may also con ain only a ew o he es o he bioma ke s. Hence,
each pa ien ’s ime se ies in he da ase has o go h ough a il e ing p ocess in o de o
make su e i is accu a e and does no show ambigui ies. Figu e 2.3 shows he il e ing s eps
ca ied ou in his wo k.
...
...
...
...
P1
P2
Pn
n pa ien s P ha e
a ime se ies each ...
We disca d pa ien s wi h
less han 3 poin s in ime
We disca d pa ien s wi h no
a iabili y in hei ime se ies
We disca d pa ien s wi h
un easable diagnosis ansi ions
P1
P2
Pm
INPUT DATASET
m pa ien s P, wi h
m ≤ n
Each ime se ies
has leng h 5
...
We i each pa ien in o a
speci ic ime se ies based on
a gi en bioma ke
Figu e 2.3:Desc ip ion o each s age in he il e ing p ocess.
Rega ding his bioma ke di ision, and he dis ibu ion o da apoin s shown in he p e-
ious Sec ion, we plo ed in Figu e 2.4 he numbe o da apoin s a ailable o each o he
bioma ke s used in his wo k as p edic o a iables. As i can be seen in Figu e 2.4, o each
bioma ke , he numbe o a ailable poin s has a di e en equency o measu emen o e
ime.
The e o e, we selec ed o each bioma ke da ase he pa ien s ha had a leas h ee
measu emen s o e ime o ha gi en bioma ke . The h eshold alue o h ee isi s was
10

Da a poin s dis ibu ion o e ime o each bioma ke
(a): AV45 da a poin s dis ibu ion o e ime
(b): TAU da a poin s dis ibu ion o e ime
(c): PTAU da a poin s dis ibu ion o e ime
(d): ABETA da a poin s dis ibu ion o e ime
(e): FDG da a poin s dis ibu ion o e ime
( ): MRI da a poin s dis ibu ion o e ime
Figu e 2.4:Dis ibu ion o he amoun o da a poin s in unc ion o he VISCODE o
each bioma ke . No e ha only pa ien s wi h a leas 3 poin s o e ime ha e been aken
in o accoun , since hose wi h less poin s a e no conside ed when de ining he imese ies.
decided due o wo main easons. In he i s place, selec ing a smalle numbe o needed
measu emen s (1 o 2) would make ou da a mo e inaccu a e. Mo eo e , selec ing a bigge
numbe as he h eshold (e.g. a leas 4 poin s) would ha e le us wi h ba ely any pa ien s
when combining bioma ke da ase s.
Secondly, we emo ed pa ien s wi h no a iabili y in hei bioma ke measu emen s,
which kep hei p og ession cons an .
11
Thi dly, we disca ded pa ien s depending on hei diagnosis ansi ions. The diagnosis
ansi ion is de ined by hei diagnosis a baseline and las medical isi s. We emo ed
subjec s ha s ayed wi h a no mal cogni i e p o ile du ing all isi s (CN o CN). We also
emo ed pa ien s ha p esen ed un easible diagnosis ansi ions, di e en om hose shown
in Figu e 2.2, such as going om Demen ia o MCI, om Demen ia o CN, o ansi ioning
be ween diagnoses mo e han wice du ing hei whole imeline.
Finally, we selec ed a ele an ime se ies o each bioma ke ; e.g, measu emen s aken
e e y six mon hs. This ime se ies was de ined aking in o accoun how equen ly he
pa ien s’ measu emen s a e upda ed o each bioma ke (Figu e 2.4) and as desc ibed in
ADNI’s p o ocol in hei webpage8. Da apoin s ou side his ime se ies we e no conside ed
since hey would only be a ailable in a small p opo ion o he o al amoun o pa ien s, and
i is c ucial ha all pa ien ime se ies among a gi en bioma ke ha e he same imeline.
As a esul o he il e ing s ep, Table 2.2 shows he numbe o da apoin s be o e and a e
he il e ing p ocess desc ibed abo e as well as he co esponding ime se ies (in mon hs)
o each bioma ke .
Table 2.2:Numbe o da a poin s be o e and a e he il e ing p ocess and co esponding
imese ies o each bioma ke
Bioma ke Be o e il . A e il . Timese ies
TAU 2370 1180 (bl, 12, 24, 36, 48)
PTAU 2369 1175 (bl, 12, 24, 36, 48)
ABETA 2370 1175 (bl, 12, 24, 36, 48)
AV45 2678 1645 (bl, 24, 48, 72, 96)
FDG 3605 1760 (bl, 6, 12, 18, 24)
Ven icles (MRI) 8955 6805 (bl, 12, 24, 36, 48)
Hippocampus (MRI) 8317 6335 (bl, 12, 24, 36, 48)
Mid emp (MRI) 7907 5975 (bl, 12, 24, 36, 48)
En o hinal (MRI) 7907 5975 (bl, 12, 24, 36, 48)
Fusi o m (MRI) 7907 5975 (bl, 12, 24, 36, 48)
WholeB ain (MRI) 9210 6930 (bl, 12, 24, 36, 48)
12
2.3 Da a p ep ocessing
We hen pe o med mul iple p ep ocessing s eps o e all da ase s meaning missing alues
p ocessing and se e al da a ans o ma ions.
2.3.1 Missing alues
As desc ibed in Sec ion 2.2, by i ing each bioma ke in o a gi en ime se ies speci ied by
ADNI8and desc ibed by he da ase we conside ably educed he numbe o poin s wi hou
measu emen s, known as missing alues. Howe e , e en wi h he ecommended ime se ies
o each bioma ke , some measu emen s o e ime we e s ill missing. We inpu hese missing
alues depending on he ime poin hey we e ound.
Fo missing alues a he baseline ime poin ( = 0) o a gi en bioma ke , we inpu he
mean o all a ailable pa ien s’ alues in baseline o ha bioma ke . This way, he a iance
o he da ase is kep cons an , which will be use ul when we begin using unsupe ised
classi ica ion.
Missing alues ound a non-baseline and las ime poin s we e illed using he me hods
known as ’ o wa d illing’ and ’linea illing’9, espec i ely. Figu e 2.5 summa izes bo h o
hese me hods.
Missing alues appea ing a non-baseline and non-las ime poin s we e illed using
’linea - illing’9. This me hod uses linea in e pola ion in o de o keep he p og ession
linea , which wo ks as ollows. Le ybe he missing alue and xi s posi ion in he ime
se ies. Mo eo e , le y0,x0be he same pa ame e s o a known poin be o e x; and y1,
x1 he same pa ame e s o a known poin a e x. As long as he e a e wo known poin s
in he ime se ies, all o he poin s in be ween can be compu ed ia in e pola ion wi h he
o mula:
y=y0+ (x−x0)∗(y1−y0)
(x1−x0)
This me hod can be used o any ime se ies in ou da ase since he baseline is always
p esen (i i is no , i is illed in as explained abo e) and he e a e a leas wo o he known
13
0 1 2 3 4 5 Time
y
6
Time
0
1
2
3
4
5
6
Value o
ea u e y
y0
y1
N/A
N/A
y4
N/A
N/A
Poin p esen in da ase
Missing poin illed using linea - illing
Missing poin illed using o wa d- illing
i poin a baseline is
missing, ill wi h he
mean o all o he
pa ien s' y alue i
a ailable
Figu e 2.5:Explana ion o he me hods ’ o wa d illing’ and ’linea illing’ used o ill in
missing alues.
alues in he ime se ies.
Las ly, missing alues appea ing a he end o he ime se ies (las isi ) we e illed using
’ o wa d- illing’9, in o de o keep he emainde o he ime se ies cons an . Le yibe he
las known alue in ou ime se ies o leng h nand xii s posi ion in he se ies, wi h i < n.
Le also [yi+1, . . . , yn−1, yn]be missing poin s a e yi. Wi h ’ o wa d- illing’, yk=yiwhe e
k∈[i+ 1, n].
14
2.3.2 Da a ans o ma ions
We pe o med se e al da a ans o ma ions ega ding he clinical adjus emen s needed o
some measu es and he ype o da ase s we wan ed o build.
Fo he da ase s in ol ing he MRI a iables, he b ain egions’ olumes in a pa ien
a e all dependen on hei in ac anial olume (ICV). This means ha while wo pa ien s
may ha e an iden ical olume on a ce ain b ain egion, hey in ac depend on hei ICV.
The e o e, we no malized a each poin in he imeline, he pa ien s’ b ain egion olumes
by hei own ICV.
Because we wan ed o ake in o accoun he empo ali y o he da a while keeping hem
in abula o ma , we ca ied ou he ollowing ans o ma ion o AV45, ABETA, TAU,
PTAU, FDG and MRI bioma ke s. We calcula ed hei polynomial coe icien s o pe o m
a ea u e ex ac ion. Fo his, we i each ime se ies in o he equa ion ax2+bx +c, wi h a,
band cpolynomial coe icien s.
Rega ding da ase s combining di e en bioma ke s, since each bioma ke has i s own
ange, we no malized he alues o each bioma ke in o de o keep hem in he in e al [0,1],
he e o e bioma ke s wi h highe alues will no add g ea e weigh du ing he clus e ing
decisions han bioma ke s wi h a smalle ange o alues. Las ly, when he unsupe ised
classi ica ion algo i hm applied needed i , we s anda dized he da a so ha i had a mean
o 0 and a s anda d de ia ion o 1.
2.4 Unsupe ised classi ica ion
The aim o his s udy is o g oup hese pa ien s oge he by means o unsupe ised clas-
si ica ion o clus e ing. As such we used he ollowing algo i hms wi h abula - o ma ed
da ase s: (i) Agglome a i e Hie a chical Clus e ing, (ii) K-Means, (iii) Densi y-Based Spa-
ial Clus e ing o Applica ion wi h Noise (DBSCAN) and (i ) Sel -O ganizing Maps (SOM).
Rega ding ime se ies da ase s, we used Dynamic Time Wa ping combined wi h ( ) Hie -
a chical o ( i) DBSCAN clus e ing me hods.
15

Rega ding all Sec ion 2.3, we buil six di e en ypes o da ase s which will be e alua ed
in Chap e 3using he desc ibed unsupe ised classi ica ion algo i hms. The da ase s names
and he unsupe ised classi ica ion me hods applied o each o hem a e shown in Table 2.3.
Table 2.3:Da ase s and unsupe ised algo i hms applied in his wo k.
Bioma ke ype Bioma ke s employed Algo i hm
Tabula
One bioma ke AV45, ABETA, TAU, PTAU, FDG, MRI
KMeans
Hie a chical
SOM
Tabula
Pai o bioma ke s
AV45-ABETA, AV45-TAU, AV45-PTAU, AV45-FDG,
ABETA-TAU, ABETA-PTAU, ABETA-FDG,
TAU-PTAU, TAU-FDG, PTAU-FDG
KMeans
Hie a chical
SOM
Tabula
Se e al bioma ke s
MRI egions: Ven icles, Hippocampus,
En o hinal, Fusi o m, Mid emp, WholeB ain
KMeans
Hie a chical
SOM
Polynomial ans o ma ion
One bioma ke AV45, ABETA, TAU, PTAU, FDG, MRI
KMeans
Hie a chical
SOM
Polynomial ans o ma ion
Pai o bioma ke s
AV45-ABETA, AV45-TAU, AV45-PTAU, AV45-FDG,
ABETA-TAU, ABETA-PTAU, ABETA-FDG,
TAU-PTAU, TAU-FDG, PTAU-FDG
KMeans
Hie a chical
SOM
Polynomial ans o ma ion
Se e al bioma ke s
MRI egions: Ven icles, Hippocampus,
En o hinal, Fusi o m, Mid emp, WholeB ain
KMeans
Hie a chical
SOM
Timese ies
One bioma ke AV45, ABETA, TAU, PTAU, FDG, MRI DTW + Hie a chical
DTW + DBSCAN
Timese ies
Pai o bioma ke s
AV45-ABETA, AV45-TAU, AV45-PTAU, AV45-FDG,
ABETA-TAU, ABETA-PTAU, ABETA-FDG,
TAU-PTAU, TAU-FDG, PTAU-FDG
DTW + Hie a chical
DTW + DBSCAN
Timese ies
Se e al bioma ke s
MRI egions: Ven icles, Hippocampus,
En o hinal, Fusi o m, Mid emp, WholeB ain
DTW + Hie a chical
DTW + DBSCAN
The nex subsec ions desc ibe all o he men ioned clus e ing algo i hms.
2.4.1 Agglome a i e Hie a chical Clus e ing
Hie a chical clus e ing is a clus e ing echnique ha , depending on i s ype, me ges da a
poin s in o one clus e o di ides a clus e in o mul iple clus e s. Bo h ypes can be ep e-
sen ed as a dend og am o know which clus e s we e me ged oge he o spli up. Hie a -
chical clus e ing can use an agglome a i e o bo om-up app oach, whe e each da a poin is
i s own clus e and acco ding o hei dis ance wi h o he clus e s hey a e me ged oge he
o le alone. Meanwhile, he e is he di isi e o op-down app oach, whe e all da a poin s
16
a e conside ed one unique clus e and based on hei dis ance wi h each o he hey a e spli
up in o smalle clus e s. While bo h ypes o hie a chical clus e ing yield he same esul s,
we chose he agglome a i e ype o e he di isi e one since a bo om-up app oach seemed
easie o analyze o e a op-down one. This explana ion can be u he isualized in Figu e
2.6.
BA
CD
E
F
S ep 1: Da a sample o 6
poin s labeled A-F
BA
CD
E
F
S ep 2: We compu e pai wise dis ances o each pai o poin s
based on a dis ance me ic and a linkage c i e ia.
In his example we use Euclidean dis ance and single linkage.
B
A
CD
E
F
S ep 3: We pick he pai o poin s wi h he
minimal dis ance and g oup hem oge he .
B
A
CD
E
F
S ep 4: We con inue he p ocess un il only
one clus e emains.
S ep 5: ob ain he necessa y numbe o
clus e s om he dend og am. (e.g 2)
A B C D E F
2 clus e s
AGGLOMERATIVE
DIVISIVE
Figu e 2.6:Explana ion o he agglome a i e hie a chical clus e ing me hod.
As men ioned p e iously, he agglome a i e hie a chical clus e ing i s conside s all da a
poin s as hei own clus e s and g oups hem oge he based on wo pa ame e s: he dis ance
17
me ic and he linkage c i e ia. The dis ance me ic is used o de e mine he sepa a ion
be ween each clus e using one o he a ailable me ics such as he Euclidean dis ance10,
which measu es he linea dis ance be ween wo poin s, o he Manha an dis ance10, which
is he sum o he absolu e di e ence be ween he measu es in all dimensions o wo poin s,
among many o he s. The linkage c i e ia is he basis by which each pai o clus e s is
g ouped oge he based on hei dis ance. These c i e ia can be single-linkage -whe e we
g oup oge he pai s o clus e s ha a e closes o each o he -, comple e-linkage -whe e
we g oup oge he pai s o clus e s ha a e he u hes om each o he -, cen oid-linkage
-whe e pai s o clus e s a e g ouped oge he based on he closes cen oid dis ance- o
a e age-linkage -whe e we g oup oge he pai s o clus e s ha ha e he sho es mean
dis ance be ween pai s o elemen s om each o he clus e s-, among o he s. The explained
linkages a e isually de ailed in Figu e 2.7.
BA
CD
Single linkage:
e u ns minimal dis ance
be ween clus e s
BA
CD
Comple e linkage:
e u ns maximal dis ance
be ween clus e s
BA
CD
A e age linkage:
e u ns mean o all pai
dis ances be ween clus e s
Cen oid linkage:
e u ns dis ance o cen oids
be ween clus e s
BA
CD
Figu e 2.7:Explana ion o some o he di e en ypes o linkage ha can be used in hie -
a chical clus e ing.
Since he e a e mul iple me ics and linkages ha can be used o clus e ou da a, we
18
pe o med a g id-sea ch conside ing each combina ion me ic-linkage. In sec ion 3, we kep
o each bioma ke he combina ion ha e u ned he bes ou comes based on he e alua ion
me ics and analyzed he esul s.
2.4.2 K-Means
K-Means11 is a clus e ing algo i hm ha clus e s da a in o Kclus e s while keeping each
clus e ’s a iance as minimal as possible. The me hodology o his algo i hm can be isual-
ized in Figu e 2.8.
Da ase o 13 samples which
we wan o clus e in o 3 g oups.
S ep 1: We ini ialize each cen oid and
assign i o a andom sample
x
x
x
S ep 2: Each sample is assigned
o a clus e depending on wha i s
nea es cen oid is
x
x
x
S ep 3: Cen oid posi ions a e
upda ed acco ding o he new
samples p esen in hei clus e
x
x
x
epea S ep 2 un il cen oids
no longe change
K clus e s a e now de ined
x
x
x
Figu e 2.8:Explana ion o he K-Means clus e ing me hod.
I unc ions by sepa a ing Nsamples om a da ase in o Kdisjoin clus e s. Each clus e
is de ined by a cen oid, which is he mean uko all he samples con ained among a clus e .
A i s , Kcen oids a e placed ei he in Kdi e en samples o ini ialized andomly in he
19
ailed because he h eshold was se oo high-, o he minimal dis ance be ween ajec o ies
is bigge han he h eshold. Since we g oup ajec o ies oge he , and a ajec o y can
ei he be a ime se ies o a p o o ype clus e made o wo o mo e imese ies, we mus de ine
a speci ic o mula o compu e he DTW dis ance in hese speci ic cases.
Le A and B be ajec o ies o one o mo e imese ies:
DT W(A, B) = op(DT W (∀A, ∀B))
As hie a chical clus e ing has mul iple linkage c i e ia ha need o be conside ed, he
ope a o op in he o mula abo e depends on he chosen c i e ia. This ope a o can be
eplaced as ollows. When we pe o m comple e-linkage, we wan o ge he maximal possible
dis ance be ween a pai o poin s o he wo imese ies, he e o e we can use max ins ead.
When pe o ming single-linkage, we seek he minimal dis ance be ween a pai o poin s o he
imese ies, hus we eplace op wi h min. We also pe o med a e age-linkage, by calcula ing
he mean o all he compu ed dis ances, by using mean. Finally, we used median-linkage,
inding he median o all he compu ed dis ances using median ins ead.
Each linkage c i e ia has been used wi h each kind o da ase bo h in uni- and mul-
idimensional ones. Rega ding mul idimensional da ase s, o ou algo i hm o unc ion
co ec ly we modi ied he dimensionali y o he inpu and used a di e en me hod o DTW
compu a ion.14
2.4.6 Dynamic Time Wa ping wi h DBSCAN
We also combined DTW wi h he DBSCAN algo i hm since i excels in da ase s wi h egions
o high densi y and DTW seemed o be a p omising lead. We i s compu ed o each pai
o ajec o ies hei DTW dis ance and c ea ed a ma ix o N×Nwi h i,jco esponding
o he dis ance be ween he ajec o y o pa ien iand he ajec o y o pa ien j. We hen
used his dis ance ma ix as inpu da a ins ead o he pa ien s’ imese ies. In o de o ob ain
he bes esul s, we pe o med a g id sea ch o ind he hype pa ame e s ha wo ked bes
26

wi h he algo i hm, aking in o conside a ion ce ain il e ing c i e ia, such as a maximum
o 20% o pa ien s being conside ed as ou lie s, as well as each clus e ha ing a minimum o
10% o o al pa ien s.
2.5 E alua ion Me ics
To e alua e how well each o ou algo i hms clus e he da a, we ha e used wo me ics: he
Silhoue e Sco e (SI), e y o en used in clus e ing applica ions, as well as he P og ession
Accu acy (PA), a cus om me ic ha indica es he di e ences among each clus e om a
clinical s andpoin .
The Silhoue e Sco e15 is a use ul me ic when conside ing how dense and well de ined
he esul ing clus e s a e. I anges om -1 o 1, and he highe he sco e, he mo e de ined
he clus e s will u n ou o be. I he sco e is in he nega i e ange, i usually conside s he
clus e ing o be inco ec , while a sco e close o 0 signi ies ha he clus e s a e o e lapping
each o he .
Since his sco e only de e mines how well he clus e ing algo i hm is pe o med om a
compu a ional iewpoin , i is also necessa y o e alua e he clus e ing pe o mance om a
clinical poin o iew.
The P og ession Accu acy is a me ic ha aims o compu e he quali y o he diagnoses
sepa a ion be ween clus e s. We conside a pa ien ha p og esses u he in he Alzheime ’s
Disease con inuum as one ha s a ed wi h a ce ain diagnosis and has p og essed owa ds
a mo e ad anced s age by hei inal diagnosis. These pa ien s will be conside ed as ac i e.
Con a ily, a pa ien ha has a s a ic diagnosis ansi ion be ween he baseline and hei
las isi is conside ed o ha e a slowe p og ession owa ds Demen ia. These o he pa ien s
will be conside ed as s a ic. The e o e his me ic compu es he p opo ion be ween ac i e
and s a ic pa ien s, a o ing clus e ing esul s ha show conside able di e ence in diagnosis
p og ession be ween clus e s.
We wan o ind he PA alue o N clus e s. Le S be he combina ions o all pai s o
27
clus e s wi hou epe i ions, such as:
S= (i, j)|i∈[0, N], j ∈[0, N], i < j
To calcula e his me ic, we i s need o compu e he p og ession a io (PR) be ween
all pai s o clus e s in S.
Le Ciand Cjbe wo clus e s, wi h Aiand Sibeing he amoun o ac i e and s a ic
pa ien s o Ci espec i ely, and Ajand Sj he amoun o ac i e and s a ic pa ien s o Cj.
Then, he PR be ween clus e s Ciand Cjcan be conside ed as:
PR(Ci, Cj) = max(Ai+Aj, Si+Sj)
Ai+Aj+Si+Sj
Thus, in o de o ind he PA be ween N clus e s:
PA(C1, . . . , Cn) = P R(Ci, Cj)wi h (i, j)∈S
We will use hese me ics o conside o each clus e ing bo h he compu a ional and he
clinical s andpoin s and compa e each clus e ing algo i hm wi h ano he .
When compa ing how each da ase wo ked wi h each ype o algo i hm, we will desc ibe
he bes clus e ing esul in e ms o he P og ession Accu acy. This desc ip ion is done om
he poin o iew o diagnosis change and demog aphic a iables as p e iously desc ibed.
Addi ionally, when wo king wi h empo al models, we compu ed o each biomake he
eg ession line y=Ax+Bo each clus e so ha we could measu e mo e p ecisely how each
clus e p og essed o e ime, depending on he alue o A. Finally, we analyzed each clus e
using he demog aphical da a a ou disposal. We pe o med a - es o each a iable so
ha , by ob aining i s p- alue, we could conclude whe he he e was a signi ican di e ence
be ween clus e s ega ding hese demog aphic a iables. A esul is conside ed signi ican i
i s p- alue be ween clus e s is less han 0.05.
28
Chap e 3
Resul s
As in oduced in Sec ion 2.4, we applied a wide a ay o clus e ing algo i hms o y on
ou da a. Because said a ay is leng hy, we ha e sepa a ed he ollowing desc ip ion o he
esul s in o wo main sec ions. Fi s ly, in Sec ion 3.1, we desc ibe algo i hms ha do no
ake in o accoun he empo ali y o he da ase , meaning models ha ake as inpu no mal
abula da ase s whe e he ea u es ep esen di e en imes amps o when he bioma ke
was measu ed. Secondly and con a ily, Sec ion 3.2 desc ibes esul s wi h algo i hms ha
do ake in o accoun he empo ali y o he da ase .
Fo each ype o model, we desc ibe di e ences in he e alua ion me ics be ween he
a ious clus e ing algo i hms. Nex , we epo bo h he bioma ke da ase and clus e ing
algo i hm ha ob ained he bes p og ession accu acy sco e desc ibed in Sec ion 2.5. Las ly,
we desc ibe he clus e s ob ained in he bes esul s using he sociodemog aphic a iables
we men ioned in Sec ion 2.1. All he pe cen ages shown in his sec ion a e calcula ed o e
he o al numbe o pa ien s in each clus e .
3.1 Non-Tempo al models
We applied se e al canonical clus e ing algo i hms such as KMeans, Hie a chical Clus e -
ing and Sel O ganizing Maps, gi ing hem as inpu wo di e en da ase s: (i) only one
ea u e co esponding o he i s bioma ke s’ measu emen (i.e. baseline isi ) a ailable in
he imese ies, and (ii) all ea u es a ailable in a pa ien ’s imese ies, meaning each ea u e
29
ep esen s a pa ien s’ isi o he doc o . The i s kind o models could se e us as a e e -
ence, showing wha we could expec om he e y i s isi and measu emen aken o each
bioma ke bo h in e ms o clus e ing and he diagnosis p og ession. Mo eo e , we e alua ed
hese wo kinds o inpu da ase s using in o ma ion om (i) only one bioma ke (e.g. AV45),
(ii) a pai o bioma ke s (e.g. AV45+ABETA) o (iii) se e al bioma ke s (MRI). The e o e
esul ing in six di e en kinds o da ase s e alua ed wi h he abo emen ioned clus e ing
algo i hms. Fo he sake o unde s andabili y we ha e di ided hese esul s in ca ego ies
in ol ing non- emp al and empo al models. Figu e 3.1 displays he p opo ion o diagnosis
ansi ions be ween clus e s in he non- empo al models ha will be desc ibed. Meanwhile,
Figu e 3.2 shows he dis ibu ion o he sociodemog aphic a iables o said models.
Figu e 3.1:Ba plo s showing he diagnosis ansi ions o each clus e in he h ee bes clus-
e ing esul s o non- empo al models: (a) bes non- empo al model o sepa a ed bioma ke s
(SOM wi h AV45, all ea u es), (b) bes non- empo al model o pai ed bioma ke s (SOM
wi h AV45+FDG, all ea u es) , (c) bes non- empo al model o he MRI da ase . (SOM,
all ea u es)
3.1.1 Non-Tempo al models wi h sepa a ed bioma ke s
We applied KMeans, Hie a chical and SOM clus e ing o da ase s con aining only in o ma-
ion o one bioma ke using (i) only he baseline isi measu emen , and (ii) all he isi s’
measu emen s. Figu e 3.3 shows he esul s ob ained in e ms o SI sco e and accu acy.
As i can be seen in Figu e 3.3a, mos o he clus e ing models ob ained a SI sco e g ea e
30
Gende APOE e4 s a us MMSE sco e a las isi AGE a baseline isi Educa ion yea s
Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1
Gende APOE e4 s a us MMSE sco e a las isi AGE a baseline isi Educa ion yea s
Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1
(b) SOM (all) and AV45 + FDG
* * * *
* *
(a) SOM (all) and AV45
Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1
Gende APOE e4 s a us MMSE sco e a las isi AGE a baseline isi Educa ion yea s
(c): SOM (all) and MRI
* * * *
Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1 Clus e 0 Clus e 1
Figu e 3.2:Dis ibu ion o i e di e en sociodemog aphical ea u es by clus e s: gende ,
APOE e4 geno ype, MMSE sco e a he las isi , age a baseline isi , and educa ion yea s
in non- empo al models. Plo s ha a e labeled wi h an as e isk on op indica e ha he
sociodemog aphic a iable conside ed is signi ican ly di e en (p- alue <0.05) be ween clus-
e s.
han 0.5, excep o he majo i y o FDG da ase s and algo i hms combina ions. In h ee ou
o i e e alua ed bioma ke s (AV45, ABETA and FDG), K-Means was he algo i hm ha
ob ained he bes esul s in e ms o SI sco e, bo h using only he baseline isi (KMeans
31

AV45 TAU PTAU ABETA FDG
Da ase
0
0.2
0.4
0.6
0.8
1
Silhoue e Index
(a)
AV45 TAU PTAU ABETA FDG
Da ase
0
0.2
0.4
0.6
0.8
1
P og ession Accu acy
(b)
KMeans baseline
KMeans all isi s
Hie a chical baseline
Hie a chical all isi s
SOM baseline
SOM all isi s
Figu e 3.3:E alua ion me ics ob ained o each non- empo al model. Figu e (a) shows
he Silhoue e Index Sco e and Figu e (b) shows he P og ession Accu acy achie ed wi h
unidimensional da ase s.
baseline, see Figu e 3.3a) and all isi s (KMeans all isi s, see Figu e 3.3a). The e o e, K-
Means makes mo e de ined clus e s in e ms o dis ance ega ding non- empo al models. In
ac , he highes SI sco e is ob ained wi h K-Means using he baseline ABETA measu emen
(SI sco e o 0.7143). Rega ding he p og ession accu acy de ined in Sec ion 2.5, as seen in
Figu e 3.3b, only da ase s using AV45 and ABETA ob ained an accu acy g ea e han
0.60. O e all, AV45 da ase s ob ained he bes p og ession accu acy alues compa ed o
he o he bioma ke s. In ac , he combina ion ha ob ained he bes accu acy esul s in
AV45 da ase s was he SOM model using all he a ailable ea u es (0.7083).
SOM model using all he a ailable AV45 ea u es ga e wo clus e s, con aining 115
and 77 pa ien s, espec i ely. In he smalle clus e , 80.52% (62/77) o he subjec s we e
diagnosed bo h a he baseline and las isi wi h MCI, while only 19.48 % (15/77) ad anced
owa ds he Alzheime ’s Disease con inuum be ween hei ini ial and las isi . Unlike he
smalle g oup, only 37.39% (43/115) in he bigge clus e s ayed on he e y same diagnosis,
meanwhile a o al o 62.61% (72/115) p og essed owa ds a wo se diagnosis. Thus, we can
clea ly see wo e y di e en g oups, one o hem con aining mainly pa ien s ha s ayed on
he same s age o AD, and ano he g oup wi h pa ien s ha con inued o a mo e ad anced
s age. These esul s also co ela e wi h he demog aphic a iables: we ob ained a signi ican
32
di e ence ega ding he numbe o pa ien s o hei mean alues in each clus e o ou ou o
he i e sociodemog aphic a iables used. Figu e 3.2 shows he dis ibu ion o hese a iables
in each clus e . The a iables ha ob ained a signi ican p- alue, meaning a signi ican
di e ence be ween clus e s we e (p- alues be ween pa en heses): APOE4 (9.30e−08), he
MMSE sco e (7.35e−09), he pa ien s’ age a baseline (AGE, 1.7e−02) and inally he
yea s o educa ion o he pa ien s (PTEDUCAT, 2.5e−02).
3.1.2 Non-Tempo al models wi h pai s o bioma ke s
The same algo i hms we e applied in he e y same da ase s (baseline isi s and all isi s
measu emen s) combined by pai s, in o de o gain a be e unde s anding whe he a ce ain
combina ion o bioma ke s a o s highe e alua ion esul s.
In Figu e 3.4a, he Silhoue e Index sco es ob ained wi h combina ions o bioma ke s
ange om sco es s a ing om 0.193 o 0.5743, wi h he majo i y abo e 0.4. The bes
sco e is ob ained when combining he TAU and PTAU da ase s, wi h a maximum alue o
0.5743 when used wi h KMeans. As o he P og ession Accu acy sco e, in Figu e 3.4b, i
seems ha hose pai s o bioma ke s ha we e combined wi h AV45 ob ained a ema kable
esul when used wi h Sel O ganizing Maps, compa ed o he o he wo algo i hms, wi h
a maximum o 0.741 in AV45 + FDG when using all a ailable ea u es. Wi h mos o he
o he pai s, i also seems like Sel O ganizing Maps ob ains a be e esul han he o he
algo i hms.
When applying SOM in he da ase combining AV45 and FDG, we ob ained wo clus e s,
each one con aining 27 pa ien s, as such we will name hem C0 and C1. C0 only con ains
a o al o 22.2 % (6/27) pa ien s ha do no ansi ion owa ds a mo e ad anced s age.
Meanwhile he o he 77.8 % (21/27) did su e om mo e neu odegene a ion. Con a ily, C1
has a o al o 70.4 % (19/27) o pa ien s ha s ay in he same diagnosis, and he emaining
29.6 % (8/27) ha do p og ess owa ds a mo e ad anced s age. As o he demog aphic
a iables, bo h he APOE4 gene (1.9e−03) and he MMSE sco e (1.4e−02) a e signi ican .
33
AV45+TAU
AV45+PTAU
AV45+ABETA
AV45+FDG
TAU+PTAU
TAU+ABETA
TAU+FDG
PTAU+ABETA
PTAU+FDG
ABETA+FDG
Da ase
0
0.2
0.4
0.6
0.8
1
Silhoue e Index
(a)
AV45+TAU
AV45+PTAU
AV45+ABETA
AV45+FDG
TAU+PTAU
TAU+ABETA
TAU+FDG
PTAU+ABETA
PTAU+FDG
ABETA+FDG
Da ase
0
0.2
0.4
0.6
0.8
1
P og ession Accu acy
(b)
KMeans baseline
KMeans all isi s
Hie a chical baseline
Hie a chical all isi s
SOM baseline
SOM all isi s
Figu e 3.4:E alua ion me ics ob ained o each non- empo al model. Figu e (a) shows
he Silhoue e Index sco e and Figu e (b) shows he P og ession Accu acy achie ed wi h
mul idimensional da ase s.
3.1.3 Non-Tempo al models wi h MRI egions
Finally, we applied he a o emen ioned clus e ing algo i hms o a da ase con aining all
o he ce eb al egions desc ibed in Sec ion 2.1, wi h he same a ia ions ha he o he
da ase s had, hese being (i) only baseline measu emen s, and (ii) all isi s’ measu emen s.
Figu e 3.5 shows he esul s ob ained ega ding SI sco es and P og ession Accu acies.
As seen in Figu e 3.5a, all clus e ing models ob ained a Silhoue e Index sco e simila
o 0.3, wi h a maximum o 0.322 when using K-Means and all a ailable ea u es in he ime
se ies. Rega ding he algo i hm a ian s, i seems ha he algo i hms ha use all o he
a ailable ea u es in he da ase ob ain a be e sco e han hose ha do no . Rega ding
he accu acies ob ained, we can ga he om Figu e 3.5b ha all models ob ain an accu acy
below 0.6, wi h Sel O ganizing Maps and he a ian ha uses all ea u es ob aining a
maximum accu acy o 0.593. As wi h he Silhoue e Index sco es, he algo i hms ha use
all o he a ailable ea u es ob ain a be e accu acy han hose ha only use he baseline
isi measu emen .
When combining he a ian o SOM ha uses all he a ailable ea u es wi h he MRI
34
MRI
Da ase
0
0.2
0.4
0.6
0.8
1
Silhoue e Index
(a)
MRI
Da ase
0
0.2
0.4
0.6
0.8
1
P og ession Accu acy
(b)
KMeans baseline
KMeans all isi s
Hie a chical baseline
Hie a chical all isi s
SOM baseline
SOM all isi s
Figu e 3.5:E alua ion me ics ob ained o each non- empo al model. Figu e (a) shows
he Silhoue e Index Sco e and Figu e (b) shows he P og ession Accu acy achie ed wi h he
MRI da ase .
egions, we ob ain wo clus e s, a smalle one con aining 374 pa ien s and a bigge one wi h
462 pa ien s. In he smalle clus e , a o al o 61.8 % (255/374) had a s a ic diagnosis ansi-
ion, while he emaining 38.2 % (119/374) mo ed o a mo e ad anced s age. Meanwhile, in
he bigge clus e , 49.8 % (230/462) o pa ien s s ayed in he same diagnosis while he o he
50.2 % (232/462) did no . Rega ding he sociodemog aphic a iables, ou a iables we e
conside ed signi ican , hese being he APOE4 (2.61e−06), he MMSE sco e (2.50e−49),
he pa ien s’ age (AGE, 4.46e−15) and he pa ien s’ yea s o educa ion (PTEDUCAT,
4.9e−02)
3.2 Tempo al models
A e applying canonical clus e ing algo i hms o he da ase s, we applied o he clus e ing
echniques ha conside empo ali y (a) wi hin he da ase s, o (b) wi hin he algo i hm.
I s main pu pose is o compa e he di e ence w. . he non- empo al models e alua ed
p e iously (Sec ion 3.1) o assess whe he including any kind o empo al s uc u e o he
da a could gi e be e esul s.
Fi s ly, as desc ibed in Sec ion 2.4, o each o he i e bioma ke s, we applied a poly-
35
Chap e 4
Discussion
We ha e pe o med an ex ensi e esea ch o combina ions be ween mul iple clus e ing algo-
i hms and bioma ke s da ase s o he disco e y o new clus e s ela ed o he p og ession
o AD. Rega ding he clus e ing algo i hms, we e alua ed se e al algo i hms anging om
hose ha do no ake in o accoun he empo ali y o he da a (Sec ion 3.1) o o he algo-
i hms ha do use ime se ies (Sec ion 3.2) o g ouping pa ien s. Mo eo e , he a ay o
da ase s used s a ed wi h hose ha do no ha e any empo al componen s o o he s ha
do in eg a e hem and also combina ed di e en bioma ke s alone and in pai s, as well as
he MRI egions. The e o e, we will analyze in his sec ion whe he he e is a co ela ion
be ween in eg a ing empo ali y o he model and ob aining a be e esul in each o he
bioma ke s, using he e alua ion me ics p oposed. In he ollowing pa ag aphs we employ
he e m "model" as he applica ion o a ce ain clus e ing algo i hm wi h a speci ic da ase ,
e.g. K-Means wi h AV45 da ase .
In gene al, SI sco es seemed o a y be ween models, as some sco es each up o 0.7 and
o he s ba ely make i o 0.2. Because o he une en SI sco es be ween models, he ollowing
discussion is o ganized o gi e an in e p e a ion om di e en pe spec i es, di e en ia ing
he esul s ob ained be ween da ase s and he algo i hms used.
Rega ding non- empo al models ha used indi idual bioma ke s da ase s, om a da ase
pe spec i e, he e is a di e ence o esul s be ween linea algo i hms such as K-Means and
Hie a chical clus e ing, and non-linea algo i hms like SOM. AV45 and ABETA da ase s
42

wo ked be e wi h linea algo i hms, ob aining SI sco es highe han 0.6, con a ily o non-
linea algo i hms. Howe e , FDG da ase wo ked be e wi h SOM, ob aining a SI sco e as
good as he ones p e iously desc ibed wi h linea algo i hms. F om an algo i hmic poin
o iew, bo h K-Means and Hie a chical clus e ing algo i hms ob ained be e esul s han
SOM. These esul s make sense because he o me algo i hms use an app oach comple ely
based on dis ances be ween samples, he p inciple in which SI sco e is based. Specially, he
K-Means algo i hm as i is highly dis ance-based, since i is an algo i hm ha minimizes
clus e a iance and he e o e a o s a good SI sco e. Meanwhile, SOM in eg a es he
unde lying s uc u e o he da a and a o s a highe dis ance be ween neu ons, bu hese
neu ons do no necessa ily imi a e he a iance o he da a, specially because we ha e
pe o med a ea u e ex ac ion and some in o ma ion abou he o iginal da a will be los .
Mo eo e , when using AV45 and ABETA da ase s, we ob ained a be e SI sco e when
gi ing as inpu only he baseline isi measu e. On he con a y, we ob ained be e SI
esul s when using all ea u es in he TAU o PTAU da ase s.
As o pai s o bioma ke s, om a da ase pe spec i e, he SI sco es ob ained a e gen-
e ally wo se han hose acqui ed when using sepa a ed bioma ke s. This is p obably due
o he inc eased dimensionali y when adding ano he bioma ke in o he da ase : wi h he
da ase s ha only ocus on he i s ea u e, he dimensionali y o each sample becomes 2
since we add he i s ea u e o he o he bioma ke , meanwhile o hose ha use all 5
componen s, he dimensionali y inc eases o 10. This dimensionali y inc eases he dis ance
be ween samples, and he clus e s ob ained a e less dense, he e o e ob ained a lowe SI
sco e. The da ase ha ob ained he bes sco e was he TAU+PTAU pai as mos o he
algo i hms ha use his da ase ob ained a sco e close o 0.6. A da ase ha also pe -
o med well is he pai combining he AV45+ABETA bioma ke s, which seemingly ob ains
he second bes sco e ou o he o he da ase s. The eason o ob aining dense clus e s
wi h he pai s TAU+PTAU, as well as AV45+ABETA make sense acco dingly o he p o-
cesses ha hese bioma ke s ep esen . Bo h TAU and PTAU measu e he amoun o Tau
43
p o ein in hei no mal and phospo ila ed o m, espec i ely. Mo eo e , bo h AV45 and
ABETA measu e he amoun o accumula ed be a-amyloid in he b ain o in he CSF, e-
spec i ely. The e o e, he e will be a highe co ela ion be ween bioma ke measu emen s in
hese pai s, han be ween hose ha a e less simila . Fo example, he pai AV45 and FDG
pe o ms he wo s be ween all he da ase s, as all o he algo i hms ha use i ob ained
a sco e lowe han 0.40. Al hough bo h AV45 and FDG a e measu es ob ained h ough
PET scans and measu e neu odegene a ion, AV45 measu es he quan i y o be a-amyloid
while FDG measu es he amoun o glucose consumed in he b ain, hus hey co espond o
e y di e en neu odegene a ion biological p ocesses. The e o e, i seems ha he SI sco e is
highly a ec ed by he na u e o he pai ed bioma ke s. Algo i hmically-wise, as i happened
and was explained be o e wi h he sepa a ed bioma ke s’ da ase s, linea algo i hms usually
ob ained a highe sco e han non-linea algo i hms in each o he da ase s. Mo eo e , o
each algo i hm, he a ian ha only uses he i s ea u e ob ains a sligh ly highe SI sco e
han he a ian ha uses all o he a ailable ea u es. This is explained o he eason ha
a ian s ha only use he i s ea u e ha e lowe dimensionali y in hei da ase s han he
o he a ian , he e o e clus e s ha e lowe in a-clus e dis ance.
As o MRI, om an algo i hmic pe spec i e, all models ob ained a e y poo SI sco e
when compa ed o he p io models. Howe e , since we ha e in oduced 6 new dimensions o
ou algo i hm o wo k wi h, and whe e he Ven icles egion has a di e en di ec ion han
he o he egions in e ms o inc eased neu odegene a ion, i is logical ha he dis ance
be ween samples will inc ease conside ably, di icul ing he possibili y o ob aining high
sco es. Ne e heless, models ha use all o he a ailable ea u es ob ain highe sco es han
he models ha do no , as e idenced by Figu e 3.5. The e o e, a plausible hypo hesis could
be ha in mul idimensional da ase s, a ian s ha use all ea u es ob ain highe sco es as
opposed o unidimensional da ase s, whe e a ian s using only he baseline isi ea u e
ob ain be e sco es. Mo eo e , in bo h a ian s, he K-Means algo i hm ob ains highe
sco es han SOM, which suppo s he idea ha linea models ob ain be e sco es han
44
non-linea ones.
In conclusion, o non- empo al models, we ha e seen ha in he majo i y o cases,
an algo i hm ha is based on linea eg ession ob ains a highe SI sco e han non-linea
algo i hms. Mo eo e , unidimensional da ase s seem o ob ain be e sco es when only
using he baseline isi whe eas mul idimensional da ase s ob ain highe sco es when using
all he a ailable ea u es, as e idenced by he MRI egions which ob ained g ea e sco es
wi h he a ian s ha make use o all ea u es, unlike he sepa a ed bioma ke s. Finally,
we ha e seen how pai s o simila bioma ke s gene ally ob ained highe sco es. We wan ed
o con i m u he hese esul s wi h empo al models.
Among empo al models, we di e en ia e be ween hose (a) including he empo ali y
wi hin he da ase h ough a polynomial eg ession ans o ma ion; and (b) hose including
he empo ali y wi hin he algo i hm he e o e he da ase is buil as a ime se ies and he
algo i hm (DTW) wo ks wi h ha kind o da a. Rega ding polynomial eg ession models,
when using indi idual bioma ke s, i is clea ha hese models ob ained a wo se sco e ( he
majo i y alling unde a SI sco e o 0.40) han he non- empo al models (SI sco e highe
han 0.60). The main eason o his could be ela ed wi h he polynomial ans o ma ion
pe o med. This ans o ma ion wo ks as a ea u e ex ac ion echnique: we change he ea-
u es in which he da a is ep esen ed. Howe e polynomial eg ession could no accu a ely
ep esen he o iginal ime se ies p og ession, he e o e in o ma ion is los . This can be
obse ed when applying he polynomial a ian o SOM, whe e we i s ly pe o m a ea u e
ex ac ion om 5 o 3 ea u es, and a second ea u e ex ac ion om 3 o 2 ea u es. Rega d-
ing ha las s a emen , linea i y in models ob ains a highe sco e han non-linea models,
as e idenced by K-Means and Hie a chical clus e ing ob aining a highe SI sco e han SOM.
Mo eo e , a key di e ence be ween hese models and he non- empo al models is ha AV45
no longe ob ained he highes sco e, ins ead, TAU and PTAU, which p e iously ob ained
wo se sco es in non- empo al models, now gi e be e esul s. Fu he mo e, ega ding DTW
models om he da ase pe spec i e, we ob ained uni o m esul s o each da ase as hey
45
all ob ained a sco e o e 0.50, excep o FDG da ase . In o de o calcula e he SI sco e o
hese models, we ha e conside ed DTW dis ance ins ead o Euclidean dis ance since clus e s
will be made based on he o me ins ead o he la e . F om an algo i hmic poin o iew, i
seems ha he combina ion o DTW and DBSCAN s uggles wi h bioma ke s such as TAU,
whe e i does no ob ain a esul based on he il e ing c i e ia, o PTAU, whe e i ob ained
a e y low SI sco e. Howe e , DTW+DBSCAN models ob ained be e esul s when using
AV45 o ABETA da ase s.
Tempo al models we e also es ed using pai s o bioma ke s, as done wi h non- empo al
models. Rega ding he polynomial eg ession model, om a da ase poin o iew, all pai s
ha con ained ei he AV45 o ABETA ea u es pe o med wo se compa ed o o he da ase s
ha con ained ei he TAU o FDG. The e o e, when empo ali y is aken in o accoun , i
seems he AV45 da ase is no longe he da ase ha ob ains he bes sco e, as i p e iously
happened wi h non- empo al models. Mo eo e , om an algo i hmic poin o iew, once
again linea algo i hms (KMeans and Hie a chical clus e ing) ob ained conside ably be e
esul s han he non-linea ones (SOM). Finally, ega ding DTW models, we ob ained uni-
o m esul s be ween da ase s, gene ally SI sco es a ound 0.4 wi h a ew excep ions. In he
case o DTW, i makes sense o he SI sco e o be lowe compa ed o he DTW models wi h
bioma ke s alone, as we ha e added dimensionali y. Mo eo e we ob ained he same esul s
han one-bioma ke models: pai s wi h AV45 ob ained wo se sco es han hose wi h TAU o
PTAU, con a ily o he non- empo al models. Finally, combining DTW+DBSCAN gene -
ally e u ns be e esul s han DTW+Hie a chical clus e ing. This is due o he ac ha
DBSCAN by de ini ion is a clus e ing algo i hm ha c ea es clus e s ou o ini ial samples
and builds a ound hem, he e o e a o ing a be e SI sco e.
Rega ding he MRI models om an algo i hmic poin o iew, he e is a clea di e ence
be ween he sco es ob ained when using polynomial eg ession and hose ob ained using
DTW, as he o me sco e close o 0.1 whe eas he la e sco e abo e 0.2. Simila ly o
he non- empo al models, he sco es a e lowe when compa ed o sepa a ed bioma ke s o
46
when combined by pai s as he dimensionali y has inc eased g ea ly, dis ancing each sample
u he . Finally, as o he algo i hms using he polynomial a ian , once again linea models
ob ain be e sco es. Rega ding algo i hms ha use DTW, DBSCAN ob ains a be e SI
sco e because o i s na u e as explained abo e.
In conclusion, o empo al models, he SI sco es ob ained a e gene ally wo se han he
non- empo al models since we use ea u e selec ion like in DTW. Mo eo e , when conside ing
empo ali y, mo e complex bioma ke s such as TAU o PTAU ob ained be e sco es han
bioma ke s like AV45 o ABETA. Finally, da ase s wi h highe dimensionali y, such as MRI
da ase s, will gene ally ob ain lowe sco es.
Al hough he esul s ob ained wi h SI sco es yielded in e es ing discussions abou which
bioma ke s wo k be e and wha clus e ing algo i hms a e p e e ed om he poin o iew
o SI sco e, we also wan ed o see i he ob ained clus e s we e making sense wi h he known
diagnosis ansi ions and he sociodemog aphic in o ma ion o he subjec s. One o he
g ea es po en iali ies o clus e ing is he disco e ing o new knowledge, and he e o e i is
impo an o ake in o accoun clinical in o ma ion, o p ope ly label hese new pa ien s’
g oups ob ained.
The e o e, we de eloped a me ic based on accu acy sco e o measu e he eliabili y o
hese new g oups om a clinical poin o iew. We named his me ic "p og ession accu acy"
(see Sec ion 2.5). This me ic measu es he o e ep esen a ion o pa ien s ha p og ess
wo se in diagnosis ( owa ds MCI o Demen ia) agains pa ien s ha did no p og ess, s aying
in hei diagnosis. The e o e in he ollowing lines we desc ibed wha happened ega ding
he p e iously desc ibed models.
When using sepa a ed bioma ke da ase s, om a da ase pe spec i e, AV45 and ABETA
ob ained conside ably be e accu acies han he es o he bioma ke s ega dless o he
algo i hm used, as all o hei accu acy sco es a e o e 0.60, con a ily o he es o he
da ase s. Mo eo e , TAU and PTAU ob ain simila accu acies as well as he wo s ones
be ween all he da ase s. AV45 is a bioma ke ha is e y conside ed when gi ing a pa ien
47

diagnosis16, as i measu es amyloid bu den in he b ain, he e o e i di e en ia es bes
be ween pa ien s in he Alzheime ’s disease con inuum. Algo i hmically-wise, in gene al
Sel O ganizing Maps seem o ob ain highe accu acies han he o he algo i hms, specially
in AV45. Mo eo e , in AV45 ega ding he ea u es used, conside ing all i e ea u es seems
o ob ain a highe accu acy, specially in linea algo i hms as a co ela ion17 highe han 0.8
be ween ea u es can be obse ed. Howe e , Sel O ganizing Maps wi h only one ea u e
ob ains as high an accu acy as linea algo i hms wi h all ea u es, which sugges s ha non-
linea models a e capable o in e ing u he han linea algo i hms. Finally, as o he
o he da ase s, using all ea u es in a ime se ies does no necessa ily imp o e he accu acy.
As o pai s o bioma ke s, om a da ase s andpoin , pai s ha conside he AV45
bioma ke always ob ain a highe accu acy han o he pai s, specially he combina ion o
he AV45 and FDG da ase s which ob ains he highes esul when used wi h Sel O ganizing
Maps. Mo eo e , he FDG da ase , which ob ains a e y good accu acy wi h AV45, does
no ob ain as good a esul when combined wi h o he da ase s, which indica es ha he
bioma ke s in he pai ha e a conside able in luence on he accu acy ob ained. F om an
algo i hmic pe spec i e, gene ally he algo i hm ha wo ks bes is Sel O ganizing Maps.
Mo eo e , linea algo i hms ob ain be e accu acies ei he when using he i s componen
o all o hem, depending on he pai o bioma ke s used.
Rega ding he MRI da ase , he accu acies ob ained a e low, as all o he models’ ac-
cu acies a e lowe han 0.6. Howe e , as a o emen ioned, non-linea models such as SOM
pe o med be e han linea models. I is impo an o no e ha , while hese models
ob ained poo esul s ega ding he accu acies, hey ha e an ex emely high po en ial o de-
sc ibe he clus e s o med, as SOM’s ob ained clus e s wi h MRI biomake s esul ed in ou
signi ican ly di e en sociodemog aphic a iables be ween hem (wi h e y low p- alues, in
he o de o e−49 o he MMSE sco e). This esul p o es ha he amoun o signi ican
a iables in a model does no depend o he p og ession accu acy ob ained, bu a he o
he bioma ke used: in his case he MRI egions. Fu he mo e, he AV45 bioma ke is an
48
a e age o all he ce eb al egions, and while he o me usually ob ains e y high accu acies,
he la e seems o desc ibe clus e s be e . The e o e using bioma ke s ha make up he
a e age o o he bioma ke s will e en ually omi in o ma ion abou i s pa ien s and poo ly
desc ibe he clus e s.
The e o e wi h non- empo al models we can su mise ha , i s and o emos , non-linea
models wo k be e han linea algo i hms, con a y o he compu a ional pe spec i e de-
sc ibed abo e. Mo eo e , he AV45 bioma ke seems o a o a be e accu acy han o he
da ase s. Finally, he combina ion o bioma ke s when used in mul idimensional da ase s
in luences he P og ession Accu acy as well as he signi ican a iables ob ained o ha
model.
F om a clinical pe spec i e in empo al models, when using sepa a ed bioma ke s, and
aking in o accoun polynomial eg ession, om a da ase pe spec i e we can ind be e
accu acies when using he AV45 da ase , as ound in non- empo al models. Howe e , he
es o he da ase s ob ain a e y simila accu acy, especi ically TAU and PTAU, which now
ob ain a e y high accu acy. Rega ding he algo i hms employed, SOM ob ained he bes
accu acies, specially when applied o AV45 da ase . Meanwhile, K-Means and Hie a chi-
cal clus e ing ob ain simila esul s, due o how simila ly hey bo h unc ion. Mo eo e ,
when conside ing he DTW models, om a da ase pe spec i e, models ha include AV45
no longe ob ain as good an accu acy as wi h non- empo al models. Mo eo e , TAU and
PTAU models imp o ed hei accu acies, eaching an accu acy highe han 0.60. The e o e,
i seemed ha empo ali y, specially algo i hms ha exploi empo ali y like DTW, a o
be e accu acy while also wo sening i in da ase s like AV45. F om an algo i hmic s and-
poin , bo h algo i hms implemen ing DTW ob ained simila esul s, al hough one o e comes
he o he depending on he da ase : Hie a chical clus e ing wi h DTW ob ains be e accu-
acies in AV45 and FDG da ase s, meanwhile he DBSCAN a ian ob ains be e esul s
in PTAU and ABETA da ase s, specially s uggling in inding a sui able esul in he TAU
da ase .
49
As o pai s o bioma ke s when using polynomial eg ession, ega ding he da ase s, he
bes accu acies a e ob ained om he pai s con aining he AV45 bioma ke , specially when
i is pai ed wi h FDG. Models using o he da ase s ha e inc eased oo, o example he pai
TAU+PTAU. This pai now yields an accu acy close o he o he models, educing he
dis ance be ween hem. An in e p e a ion simila o he one we ga e wi h non- empo al
models can be made: ce ain combina ions o bioma ke s a o a highe accu acy. Mo eo e ,
empo ali y seems o inc ease he accu acy in da ase s like TAU o PTAU. As o he
algo i hms, SOM models ob ained he highes accu acy in AV45 da ase s, specially in he
pai AV45+FDG. While FDG on i s own gene ally ob ains low accu acies, when pai ed
wi h o he bioma ke s, especi ically AV45, he esul ing accu acy is much highe . As o K-
Means and Hie a chical clus e ing, hey bo h ob ained simila accu acies, bu depending on
he da ase one o e comes he o he . Finally, DTW models combining bioma ke s in pai s,
om a da ase s andpoin , wo ked bes when using he pai AV45+PTAU. The majo i y o
he sco es ob ained wi h DTW models in he case o pai s o bioma ke s we e close o 0.60.
As o he algo i hms used, bo h DTW+Hie a chical clus e ing DTW+DBSCAN ob ained
simila sco es and o e came each o he depending on he bioma ke s.
Rega ding he MRI da ase , all models ob ain an accu acy close o 0.6. Howe e , when
compa ed o he non- empo al models, i seems ha hese models pe o m be e as a ew
go beyond 0.6. This migh be explained by he ac ha we a e no longe using only
AV45, which ep esen s he a e age o all egions, bu a he six complex bioma ke s ha
do no necessa ily ollow he same di ec ion and he e o e, adding empo ali y o he model
imp o es he accu acy. As o he algo i hms used, he polynomial a ian o K-Means seems
o do be e han i s o he polynomial coun e pa s, meanwhile Hie a chical clus e ing and
DTW do be e han DBSCAN combined wi h DTW. K-Means ob aining a be e accu acy
han Sel O ganizing Maps migh be due o he possibili y ha due o he high empo ali y,
he la e is no able o mo ph i s g id o neu ons o ep esen accu a ely he da a, he e o e
ob aining a poo esul . Finally, his model ob ained h ee signi ican a iables, and no
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only is i a bigge amoun han o he models when used wi h hei polynomial a ian s, bu
also he desc ip i e powe o he MRI da ase e u ns e y low p- alues (MMSE, e−60).
The e o e, empo al models seemed o wo k excep ionally well combining non-linea
models wi h he AV45 bioma ke . Mo eo e , inc easing he empo ali y in he model in-
c eases he accu acies ob ained in TAU and PTAU da ase s, al hough i does no a o he
AV45 bioma ke . Las ly, as o he MRI da ase , while he accu acies ob ained a e low, i is
mo e desc ip i e han o he bioma ke s. Finally, we ha e seen how SI sco es and p og ession
accu acies (PA) a e no in e ela ed, since he SI sco e is ul ima ely based on ou e - and
in a-clus e dis ance while he PA conside s diagnosis ansi ions. The Alzheime ’s Dis-
ease con inuum does no ollow a linea p og ession o a pa ien o be placed in one o he
h ee s ages he e o e he clus e s ob ained in a pe ec PA se ing will ine i ably o e lap
eacho he .
Las ly, we e alua ed he di e ences be ween clus e s ega ding he sociodemog aphic
a iables o he pa ien s on he models ha ob ained he bes p og ession accu acies. We
obse ed ha a signi ican di e ence in one o hese a iables be ween clus e s is no neces-
sa ily linked o he P og ession Accu acy ob ained. Fo ins ance, he empo al model ha
ob ained an accu acy o 0.778 when using SOM and he pai o bioma ke s AV45 and FDG
only had wo signi ican a iables: he APOE4 geno ype and MMSE sco e. Meanwhile,
in he non- empo al model ha ob ained an accu acy o 0.7083 using SOM and he AV45
da ase , he e we e a o al o ou signi ican a iables: APOE4 geno ype, MMSE sco e,
he pa ien s’ age a baseline isi , and he educa ion yea s o he pa ien . Addi ionally,
he pai AV45+PTAU ob ained a o al o h ee ou o i e signi ican a iables. The e o e
he signi ican di e ence be ween clus e s ega ding a sociodemog aphic a iable could be
linked o he bioma ke s in ques ion: AV45 -i being an a e age o he olume o six b ain
egions- is mo e desc ip i e o Demen ia, and when combined wi h o he bioma ke s, said
desc ip i e po en ial is los .
Mo eo e , om a clinical pe spec i e and o he sake o in e p e abili y, we can ga he
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