Au oma ic analysis o high dimensional
ca ego ical a iables in medical da abases
o he p edic ion o hospi al bac e emia
Po
Jaime del Rey Ga cía
G ado en Ingenie ía In o má ica
Facul ad de In o má ica
Di ec o es : Ósca Ga nica Alcáza y José Manuel Ruiz
Gia dín
Análisis au omá ico de a iables ca egó icas de
al a dimensionalidad en bases de da os médicas
pa a la p edicción de bac e iemias hospi ala ias
Mad id, 2020–2021
Au ho iza ion o dissemina ion and
use
The au ho s o his wo k au ho ize he Complu ense Uni e si y o Mad id o use bo h he
code and he epo p oduced, solely o didac ic pu poses and men ioning he au ho s
o he same.
Jaime del Rey Ga cía
iii
Acknowledgemen s
Fi s o all, hank Ósca and José Manuel o p o iding he da ase , sha ing he idea
and con ibu ing o he s udy. A special hanks o Ósca again o his dedica ion and
unde s anding h oughou he p ocess, he has made me eel ha he was wo king side by
side wi h me and con ibu ed as a u o a a le el beyond academic. To all he people
who ha e encou aged me o keep on going: o my a he , my mo he and my b o he o
hei pe se e ance; and o my iends who ha e no hesi a ed o suppo me.

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Despacho 110 - Facul ad de In o má ica
ii
Con en s
Page
1 In oduc ion 1
1.1 Bac e emia .................................. 1
1.2 Con ex .................................... 3
1.3 Objec i es................................... 3
2 Wo k o ganiza ion 5
2.1 Wo kplan ................................... 5
2.1.1 De elopmen en i onmen . . . . . . . . . . . . . . . . . . . . . . 6
2.1.2 Ve sioncon ol ............................ 6
3 The Da ase 7
3.1 S udyo heda a............................... 7
3.1.1 Di y ca ego ical a iables . . . . . . . . . . . . . . . . . . . . . . 12
3.1.2 Encoding S ing Ca ego ical Va iables . . . . . . . . . . . . . . . 14
3.2 Cleaning heda a............................... 15
3.3 P ocessing heda a.............................. 18
3.3.1 S ing simila i y . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.3.2 K-NN ................................. 22
4 Ca ego ies 25
4.1 Ca ego y ecogni ion............................. 25
4.1.1 Choosing h eshold alue . . . . . . . . . . . . . . . . . . . . . . 25
4.1.2 Noise emo al............................. 26
4.1.3 Iden i ying a ian s o s ings . . . . . . . . . . . . . . . . . . . . 27
4.1.4 De ining he classes . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4.1.5 E alua ing he esul s . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 I e a ing hep ocess ............................. 34
4.3 Subs i u ing ca ego ies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.3.1 Da ase inse ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.4 Da ase p epa a ion ............................. 36
5 Bias and a iance 39
5.1 A oiding Bias and Va iance . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.2 K-Fold C oss Valida ion . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
6 Random Fo es 43
6.1 Fi ing a Random Fo es . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
ix
G ado en Ingenie ía In o má ica Facul ad de In o má ica
Thus, he a ge o his p ojec is o ind he mos ele an a iables o he de ec ion
and diagnosis o bac e emia by means o ML models, including he nominal ca ego ical
a iables skipped in he p e ious s udy and imp o ing he esul s o he p edic ions in
he mos explainable models.
Jaime del Rey Ga cía 4

Chap e 2
Wo k o ganiza ion
2.1 Wo kplan
Be o e app oaching he p ojec , a weekly ollow-up was ag eed h ough which Ósca
could e alua e he p og ess made, gi ing con inui y o he wo k. In his i s con ac ,
he de elopmen en i onmen , he ool used o e sion con ol, as well as o he wo k
low, we e app o ed. Simila ly, he use o he Goole Mee s ool o communica ion and
mee ings, and he use o a Google Cha oom o messages be ween mee ings is se .
In he i s ins ance, Ósca explained ha i would be necessa y e iewing he wo k ca ied
ou he p e ious yea ; eading o esea ch on machine lea ning esul s wi h di e en coding
me hods applied o spa se ma ices and unde s anding he se was gi en equal ele ance
o da a wi h which o wo k and he e alua ion o he a iables ma ked as pending om
he p e ious s udy.
F om he e, he wo k plan was es ablished as ollows:
(i) C ea e Gi Hub di ec o y ee.
(ii) Ge access o he p e ious yea eposi o y.
(iii) Reed he a icles abou Missing Da a [8] om Yu en Ding and Je ey S. Simono ,
Encoding High Ca dinali y Va iables [9] and Simila i y encoding o lea ning wi h
di y ca ego ical a iables [10] om Pa icio Ce da.
(i ) Ins all Jupy e No ebook.
( ) Ins all Py hon 3.
( i) Ge amilia wi h he p e ious s udy and he sc ip used o wo k wi h he da a
ea u es.
( ii) E alua e he da ase a iables.
( iii) Check wi h he physician he ca ego ical a iables o s udy.
(ix) Find in he esul ing Da aF ame objec all dis inc alues o he s udy case a i-
ables.
(x) Modi y he sc ip acco ding o he needs o he cu en ea u es.
5
G ado en Ingenie ía In o má ica Facul ad de In o má ica
(xi) C ea e wo king en i onmen wo k low ile wi h pipen .
(xii) Cleaning accen s and s ange cha ac e s om he s udy ea u es.
(xiii) Ge all dis inc alues om he s udy a iable O ascomo .
(xi ) Dep h sea ch o ex analysis echniques and ools.
(x ) Apply s ing simila i y me hod o he esul ing bag o wo ds.
(x i) Iden i y each o he di e en en i ies om he bag o wo ds and eplace hem in he
Da aF ame o model e alua ion.
(x ii) Check bag o wo ds wi h 2 and 3 cha ac e minimum size abb e ia ions.
(x iii) C ea e subs i u ion lis o abb e ia ion eplacemen .
(xix) Run he sc ip ha ing applied he abb e ia ion subs i u ion.
(xx) Comple e he wo k low wi h he ca ego ies ob ained om unning he sc ip .
(xxi) Apply bina y codi ica ion o all ca ego ies wi hin he Da aF ame o he s udy
ea u e.
(xxii) Reo ganize and clean he sc ip .
(xxiii) Remo e all p edic o a iables om he Da aF ame be o e unning Random Fo es
model.
(xxi ) Apply Random Fo es o he Da aF ame wi h bina y codi ica ion.
(xx ) Run k- old c oss alida ion wi h 80/20 pa ame e s o aining and alida ion se s.
(xx i) Apply Random Fo es o he Da aF ame wi h bina y codi ica ion.
(xx ii) Re ie e g aph wi h he weigh ed ele ance o he ea u es.
(xx iii) Re ie e ROC g aph om he Random Fo es execu ion.
(xxix) W i e he p ojec epo .
2.1.1 De elopmen en i onmen
The de elopmen en i onmen ha has been used o his p ojec is Jupy e No ebook,
wi h he use o Py hon as p og amming language. Ósca emphasized he equi emen
o main ain a ile wi h he la es s able e sion o he so wa e and he lib a ies used
necessa y o he execu ion o he code. The use o pipen , a p oduc ion ool ha
c ea es i ual en i onmen s and main ains he build used du ing de elopmen , co e s
his need.
2.1.2 Ve sion con ol
Fo e sion con ol, gi hub was used which, in addi ion o s o ing he code e sions, allows
c ea ing a ollow-up by a ge ca ds acco ding o he s a us o hei comple ion, allowing
con ol o e all p ojec asks apa om de elopmen asks.
Wi hin he p ojec , a olde s uc u e was es ablished o dis inguish be ween documen-
a ion, code, pa ien da a and esul s ob ained.
Jaime del Rey Ga cía 6
Chap e 3
The Da ase
3.1 S udy o he da a
This chap e will de elop all he in o ma ion abou he da ase , he ea men i has
ecei ed o i s co ec manipula ion, as well as i s in e p e a ion and subsequen p epa-
a ion o i s usage wi h Machine Lea ning ools.
The da ase is an anonymized da ase p o ided by José Manuel Ruiz, physician a he
Hospi al Uni e si a io de Fuenlab ada, a 350-bed hospi al wi h he ollowing se ices:
gene al su ge y, u ology, o hopaedic su ge y, gynaecology and obs e ics, paedia ics,
in ensi e ca e uni s (ICUs), haema ology-oncology, in e nal medicine and ca diology. The
da abase was ga he ed om 2005 o 2015, and i consis s o 4357 anonymous pa ien
eco ds, a.k.a. ins ances, con aining 117 ea u es pe pa ien , 49.3% emale wi h age 65.1
± 19.7, and 56.1% male wi h age 62.7 ± 20.2. Each ins ance con ains demog aphic and
medical da a (medical his o y, clinical analysis, como bidi ies, e c.) and he esul o he
blood cul u e, he ea u e o be p edic ed, which can ake one o wo alues: bac e aemia
and no bac e aemia. The da abase con ains 2123 bac e aemia (51.3%), which includes
ae obic, s ic anae obic and acul a i e anae obic bac e ia, and 2234 no bac e aemia
(48.7%), including 1844 con amina ions.The inal classi ica ion o ue bac e aemia was
done in p ospec i e ime by an in ec ious disease physician, using all he p e ious da a,
including mic obiological, clinical and analy ical da a.
The a ge a iables in his p ojec a e hose o nominal ype om he lis o a iables,
which esul in he ollowing: desmo uci,uci,o igin,o ascomo . A e a i s e alua ion,
he o igin a iable was disca ded due o i s na u e. This a iable ep esen s he o igin
o he bac e emia, which is a ea u e om he inal diagnosis. Fea u es ha can only be
ob ained a e he d awning o he blood cul u e should no be included because in he
eal p ocess he physicians would no be able o coun on ha alues. This would also
con amina e he esul s o he Machine Lea ning models.
Tables 3.1 and 3.2 display he ea u es in he da ase and he selec ed a iables o he
s udy.
7
G ado en Ingenie ía In o má ica Facul ad de In o má ica
Table 3.1: Fea u es om he da ase
Fea u es om he da ase
pe iodo Yea o he s udy case O dinal
mes Mon h o he s udy case O dinal
dia Day o he s udy case Scala
edad Age o he pa ien Scala
edada Age pe g oup O dinal
edada75 Age goe o 75 Scala
edada85 Age goe o 85 Scala
Diasde De ec ion ime in days Scala
P i pos Fi s cul u e o g ow Scala
mic o ga Mic oo ganism Scala
iden i Species o he bac e emia Nominal
Mic o gag upo G oup o he mic oo ganism Scala
anhonpol Anae obes O dinal
Anae obio P esence o anae obes agains all o he bac e ia O dinal
Hongos P esence o ungs agains all o he bac e ia O dinal
S a coag S aphyloccocus coag Scala
Polimic Polimic obian O dinal
mic obpoli Ge ms o mic obial bac e ia O dinal
g am G am s ain O dinal
medio T ue posi i e g ow h medium O dinal
asae G ow h a leas in ae obes Scala
asanae G ow h a leas in anae obic lask Scala
asex Bo les o ex ac ed blood cul u es Scala
con amin Pollu an g ow h O dinal
mediocon G ow h medium o he pollu an mic oo ganism O dinal
An ibiog ama Mic oo ganism an ibiog am Nominal
An i esis Ca ego ized an ibiog am Scala
glucosa Blood glucose Scala
U ea Blood u ea in mg/l Scala
c ea in C ea inine Scala
pc ca e Ca ego ical PCR Scala
pc PCR alue Scala
leuc Leukocy es Scala
hgb Hemoglobin Scala
pm n PMN pe cen age Scala
Jaime del Rey Ga cía 8
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
Fea u es om he da ase
hbca eg Ca ego ical Hb Scala
plaqu Pla ele s Scala
leucoci Leukocy osis O dinal
ombope Th ombopenia O dinal
Coagulación Al e ed coagula ion O dinal
so U ine sys em analysis Scala
sedo ina U ine sedimen Scala
diashosp Days in hospi al un il bloodcul u e ex ac ion Scala
lnghosp1m Hospi al admissions o e he las mon h Scala
lnghosp12m Hospi al admissions o o e 48h in he las yea Scala
comen a Commen s Nominal
COMORBIL Como bidi y Scala
Diabe es Diabe es Scala
Ca diopa ía Hea disease Scala
En esp Ch onic espi a o y disease Scala
Neoplasia Ac i e neoplasia Scala
Ins enal Renal insufficiency Scala
Hepa opa ia Li e disease Scala
Ud p Pa en e al d ug addic ion Scala
Alcoholismo Alcoholism Scala
O ascomo O he como bidi ies Nominal
en basWeins Weins ein’s unde lying disease O dinal
es e oid S e oids O dinal
d ogadic D ug addic ion O dinal
an ibio An ibio ics O dinal
inmunosu Immunosupp essan s O dinal
neu ope Neu openia O dinal
m_geni u Geni ou ina y manipula ions O dinal
m_ espi Respi a o y manipula ions O dinal
m_diges Diges i e manipula ions O dinal
ci ugia P e ious su ge y O dinal
diagnos Diagnosis o bac e emia O dinal
ca e e Days o las ca he e placemen Scala
ca e e 1 Type o ca he e O dinal
Especialidad Special y whe e he bac e emia is p oduced Scala
se icio Se ice whe e he bac e emia is p oduced Scala
9

G ado en Ingenie ía In o má ica Facul ad de In o má ica
Fea u es om he da ase
O dinal
u gencias Blood cul u es aken in he eme gency oom Scala
adquisic Adquisi ion O dinal
du ac Days o e e ebo e blood cul u e Scala
as Sys olic blood p essu e Scala
ad Dias olic blood p essu e Scala
c Hea a e Scala
p im emp Fi s ER empe a u e wi h which blood cul u es a e
d awn
Scala
empo al Tempe a u e based on o al and axilla y empe a u es Scala
ieb e Fe e when blood cul u es a e d awn O dinal
ieb ePi O al empe a u e classi ica ion in Pi scale Scala
hipo ens Hypo ension O dinal
Vasop e Use o asop esso agen s a he ime o bac e emia Scala
in ubacion Need o in uba ion a he ime o bac e emia Scala
RCP Ca diac esusci a ion a he ime o bac e emia Scala
Ale a Consciousness a he ime o bac e emia Scala
PITT Pi scale in numbe o ICU pa ien s Scala
me as as Me as asis O dinal
me as a1 Whe e he me as asis is p odued, i any O dinal
e olucio E olu ion O dinal
mue e Dea h O dinal
o igen O igin o bac e emia Nominal
dx inal Final diagnosis Scala
o igensos Suspec ed o igin o bac e emia a he ime he blood
cul u es a e d awn
Scala
o igen O igin o bac e emia in he inal diagnosis Scala
o igen a Vascula o igin Scala
a bempi Empi ical an ibio ic ea men Scala
_empi i Empi ical ea men adequa e o inadequa e O dinal
oesp Speci ic adequa e ea men Scala
_especi Speci ic ea men adequa e o inadequa e O dinal
dias o Days o ea men un il s a o inadequa e ea men Scala
_qui u Indica ion o no o su gical ea men O dinal
uci Bloodcul u es d awn in ICU Nominal
ucidiashem Days in ICU o blood cul u e d awn Scala
mo uci Reason o ICU admission Scala
Jaime del Rey Ga cía 10
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
Fea u es om he da ase
desmo uci Reaso o ICU admission as ex Nominal
cons ieb Consul o e e Scala
sin omas Fe e symp oms Scala
s local Loca o synd ome Scala
des Des ina ion Scala
uel a_a Re u n o ER Scala
a amie An ibio ic ea men Scala
Table 3.2: Selec ed ea u es in he s udy.
Selec ed ea u es
desmo uci Reason o admission o ICU
uci Blood cul u es om ICU
o igin O igin o he bac e emia
O ascomo O he como bidi ies
A s udy o he a iables is ca ied ou indi idually o iden i y he cha ac e is ics o each
a iable. S a ing wi h he a iable o ascomo ha con ains he como bidi ies wi h
which each pa ien was admi ed.
Como bidi ies a e addi ional diso de s ha pa ien s p esen in addi ion o he disease o
which hey a e admi ed. This a iable is cha ac e is ic because i can help o iden i y
unde wha condi ions a pa ien is mo e likely o ha e bac e emia.
This a iable con ains como bidi ies as nouns sepa a ed by punc ua ion ma ks o o he
ex cha ac e s. Como bidi ies a e no w i en in a homogeneous way, ha is, some a e
w i en wi h diminu i es, o he s con ac ions o di e en leng hs o cha ac e s on he
same wo d. The s uc u e o he a iable is i sel a se ies om he pandas lib a y whe e
each index in he lis ep esen s he pa ien e e ed and he con en wi hin he lis is a
s ing de ailing he como bidi ies.
11
G ado en Ingenie ía In o má ica Facul ad de In o má ica
[1]: _nominales['O ascomo ']
[1]:
0de e io o cogni i o
1
2CARDIOPATIA.EPILEPSIA
3 al ulopa ia
4bcno, dm, h a, ci
...
5389
5390 Obesidad
5391
5392
5393
Name: O ascomo , Leng h: 5394, d ype: objec
Figu e 3.1: Sample o he ea u e O ascomo .
The ypo o he a iable is no homogeneous ei he , coun ing wi h uppe and lowe
case indisc imina ely. The sepa a o s, which indica e he end and he beginning o each
como bidi y in succession, a e also he e ogeneous in a ange om punc ua ion ma ks such
as ’,’ o ’.’ o o he ypes o elemen s such as ’+’ o ’e’.
Ano he a ibu e ha can be obse ed is he appea ance o spaces as p e ixes and suffixes,
in addi ion o he indexes o he se ies ha ha e no con en . The e a e also s ings
h oughou he se ies ha con ain accen s, apos ophes and o he elemen s ha pose
difficul ies o he ep esen a ion o he ex acco ding o wha o ma s may be used.
3.1.1 Di y ca ego ical a iables
In he con ex o Machine Lea ning wi h na u al language a iables, di y ca ego ies
a e he de ini ion o non-cu a ed da a wi h high ca dinali y bu edundancy: se e al
ca ego ies e lec he same en i y.
One o he main challenges wi h di y ca ego ical a iables is o iden i y all he elemen s
ha a e ela ed and e e o he same en i y o class. Wi hou da a cleaning, di e en
s ing ep esen a ions o he same ca ego y will lead o comple ely di e en esul s o sub-
ca ego ies, no only because he di e en elemen s e e o he same ca ego y hemsel es
bu also because o e o s such as ypos ha cause mo phological a ia ions.
F om a da a-in eg a ion s andpoin , hese ca ego ies may be seen as a da a cleaning
p oblem abou en i y esolu ion. Tasks such as deduplica ion, ha ies o me ge di e en
a ian s o he same en i y, seek o ecognize di e en a ian s o he same en i y, which
may be he bes case o apply as a p ep ocessing s ep. Howe e , da a cleaning usually
equi es human in e en ion and majo cos s in da a analysis.
In his da ase almos all he examples a e di y and ca ego ical o he a iables o
s udy. I wo examples o he a iable O ascomo a e aken, i can be unde s ood ha
wi hin his s udy he e is a di y ca ego ical a iable p oblem. To ca e o di e en ways
Jaime del Rey Ga cía 12
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
in o ma ion migh appea , se e al en i ies a e shown in Figu es 3.2 and 3.3 o each o
he possible subclasses.
[1]: anemi
anemia,
anemia c onica,
anemica c onica e ,
anemia e openica,
anemia hemoli ica,
anemia megaloblas ic,
anemia mic oci ica,
anemia n-n,
anemia nn,
anemia no moci ica no moc onica,
anemia po de ici b12,
anemia c onicos
Figu e 3.2: Sample o he elemen s in he ea u e O ascomo e e ing o anemia as di y
ca ego ies.
[1]: alzheime
alzheime a anzado,
alzheime e olucionado,
alzheime e olucionado (ins i ucionalizada,
alzheime e minal,
alzheime .,
alzheime .asma,
alzheime .dm,
alzheime .en e medad ascula ce eb al,
alzheime .i us de epe icion.,
ca.p os a a.alzheime a anzado.pa kinson,
demencia alzheime ,
dm.alzheime . p.i us de ep.,
d alzheime a anzado,
en e medad de alzheime ,
epoc.neumonia.alzheime .,
e c es adio 3. alzheime .,
hemo agia ceeb al; e de alzheime ,
h a; alzheime
Figu e 3.3: Sample o he elemen s in he ea u e O ascomo e e ing o alzheime as
di y ca ego ies.
In bo h examples, all he a iables con ain he wo d ha we migh conside as he en i y
13
G ado en Ingenie ía In o má ica Facul ad de In o má ica
Figu e 3.5: Example o a hea map o e di y ca ego ies o di e en wo ks.
The ea u e ma ix in Figu e 3.5 is compu ed using, a i s , he bag o wo ds wi h
commas as sepa a o s. The p esence o a la ge numbe o ca ego ies calls o ep esen ing
he ela ionships be ween hem so he hea map is used o ha end.
The esul s a e p omising a e he e alua ion o he i s example shown in Figu e 3.6,
in which he map shows a high ela ionship alue be ween all he chains ha sha e
he wo d adenoca cinoma in a he e ogeneous way, such as adnoca cinoma,adenoma o
adenocea. Adenoca cinoma is a e m ha e e s o cance . Al hough he di e en ypes
o cance a ec he body in di e en ways, he esul se s a clea guideline o es ablish
adenoca cinoma as a class.
Jaime del Rey Ga cía 20

Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
Figu e 3.6: Example 1 o a hea map o e 25 andom di y ca ego ies om he da ase .
Howe e , a e e alua ing he second example depic ed in igu e 3.7, a p oblem appea s
ha will accompany much o he es o he p ojec : he map does no show a simila -
i y alue no e en close o 0.4 be ween chains such as ac ca dioembolico and ac con
hemipa esia, bo h being a ype o s oke. One ela ionship ha is s iking is he low sim-
ila i y alue o acciden e ce eb o ascula and ac . Bo h chains e e o he exac same
concep , being able o o m he same class bu acco ding o he ma ix hey show almos
no simila i y.
21
G ado en Ingenie ía In o má ica Facul ad de In o má ica
Figu e 3.7: Example 2 o a hea map o e 25 andom di y ca ego ies om he da ase .
3.3.2 K-NN
The K-NN algo i hm is a supe ised classi ica ion me hod ha allows da a subse s o be
g ouped by dis ance be ween he elemen s o each subse . This algo i hm classi ies each
new en y in a class, acco ding o he kneighbo s closes o a ce ain g oup. To do his,
i calcula es he dis ance o he new en y o each da a al eady exis ing in he model and
o de s hose dis ances om lowes o highes o choose he g oup o which i belongs.
This means ha he algo i hm will use he simila i y be ween wo s ings o measu e he
dis ances. The g oup chosen will be he one ha ep esen s he sho es dis ance, o ha
g oup wi h he g ea es ep esen a ion in a g ea e longi udinal spec um.
The numbe o neighbo s o a gi en example allows adjus ing he noise o a classi ica ion,
including in each class he poin s o he hype plane ha a e alike he mos . Howe e ,
signi ican ly educing he numbe o neighbo s causes an e ec ha may no be desi ed:
c ea ing classes o elemen s ha a e no necessa ily di e en .
Jaime del Rey Ga cía 22
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Figu e 3.8: Example o he classes g ouped ela i e o he numbe o neighbo s
[12]
K-NN is qui e sensi i e o:
a). The a iable k, so ha wi h di e en alues o kwe can also ob ain e y di e en
esul s.
b). The simila i y me ic used, since his will s ongly in luence he closeness ela ion-
ships ha will be es ablished in he algo i hm cons uc ion p ocess. The dis ance
me ic can con ain weigh s ha will help us calib a e he classi ica ion algo i hm,
making i , in e ec , a cus om me ic.
Thus, he algo i hm is highly bene i ed by he na u e o he da ase wi h which i is going
o wo k. The ma ix al eady p o ides a weigh ed me ic be ween each pai o elemen s
o he same.
Fi ing a K-NN model
The nex s ep is o i he model o he da ase and check i he e is an es ima e ha he
algo i hm can make based on he alues ob ained in he simila i y me ic. The inpu o
he alue kis chosen o be 4. The objec i e is o ha e a glance o whe he he algo i hm is
able o g oup s ings ha he hea map did no ma ch bu ha ac ually e e o he same
concep , ha is why he e is no in es men o esou ces in inding he op imal numbe o
neighbo s.
om sklea n.neighbo s impo Nea es Neighbo s
nn_c =Nea es Neighbo s(n_neighbo s=4). i ( ans o med_ alues_c)
_, indices_ =nn_c.kneighbo s( ans o med_ alues_c[ andom_poin s])
indices =np.unique(indices_.squeeze())
Figu e 3.9 shows o 20 selec ed i ems in he bag o wo ds g ouped. I is obse ed ha
chains such as a osis de columna,a i is euma oide o posible a e i is de la em-
23
G ado en Ingenie ía In o má ica Facul ad de In o má ica
po al a e loca ed nea by. This esul is p omising since he a h i is class is he mos
ep esen a i e elemen in bo h cases and hey ha e been classi ied as simila .
On he o he hand, i is obse ed in he same g aph ha elemen s such as polia osis o
polinosis appea as simila elemen s and, al hough i is ue ha hey sha e he p e ix
poli, hey ha e widely di e en meanings: he i s class, polya h osis is he de ini ion
o in lamma ion o se e al join s a he same ime while polinois is an alle gic disease
ha a ec s he eyes, nose and lungs p oduced as a eac ion o he immune sys em o
pollen.
Figu e 3.9: K-NN o e he bag o wo ds using k=4 neighbo s
Conclusion o he me hod
The in ui ion behind his e alua ion is ha o s ings wi h a low numbe o cha ac e s,
he s ing simila i y algo i hm p esen s mo e noise, as he n-g ams ha e g ea e weigh
o e he o al s ing.
Jaime del Rey Ga cía 24
Chap e 4
Ca ego ies
4.1 Ca ego y ecogni ion
Despi e he conclusion shown in he p e ious sec ion, he elemen s o he bag o wo ds
a e e alua ed, eaching he conclusion ha possibly a la ge numbe o examples ha e
simila i y alues high enough o be able o wo k wi h hem and ob ain a easonable
numbe o ca ego ies ha include he highes numbe o como bidi ies exposed in he
a iable.
In o de o ace he p oblem om a Machine Lea ning poin o iew, he nex s ep is o
be able o iden i y all he ca ego ies using he ma ix o alues and o be able o me ge all
he simila s ings in o he one ha iden i ies he class by adap ing he da ase ob ained
up o now o adjus i o he needs o he s udy.
This p ocess o adap ing he da ase o he p oblem is manually coded as he e is no ool
o pe o ms hese asks so cus omized as i is needed; he e o e a se ies o unc ions a e
de ined and de eloped ha will be shown o each speci ic s ep. Each o he unc ions
wen h ough se e al es s on he da ase , so he p ocess in ol ed a g ea in es men in
ime, his sec ion being he bulk o he p ojec
Based on he da a ob ained so a , he app oach ha is ca ied ou is he ollowing:
a). Se a ele ance h eshold o he simila i y alue.
b). Ge id o as much noise as possible.
c). Iden i y o each oken all hose ha sha e a ele an simila i y.
d). Se a class o each se o s ings.
e). Replace each elemen in he o iginal a iable wi h i s supe class.
4.1.1 Choosing h eshold alue
The idea o es ablishing a h eshold alue o he simila i y o he s ings is o be able
o elimina e he la ges numbe o candida es ha do no p esen a ela ionship close o
he iden i ica ion as an en i y wi h each o he s ings o he bag o wo ds.
25

G ado en Ingenie ía In o má ica Facul ad de In o má ica
This, o begin wi h, makes i possible o elimina e noise om he da ase by making he
ca ego ies ob ained ep esen as eliable a e lec ion as possible o how a p o essional in
he ield would in e p e and g oup he da ase .
The alue aken by his pa ame e is signi ican ly ele an o he es o he p ocess,
wi h he unc ions and esul s ob ained being sensi i e o he inc ease o dec ease o he
h eshold.
Based on he i s esul ob ained om e alua ing he ea u e ma ix om igu e 3.6, a
h eshold alue g ea e han 0.5 sugges s ha he esul ing s ings will necessa ily be
e y simila o each o he , ensu ing a ela i ely small numbe o ca ego ies and ai h ul
o he g oups ha make up each o he subse s o s ings.
On he o he hand, looking a he esul s o he second hea map on igu e 3.7, he choice
o such a high h eshold alue would ule ou , in his speci ic example, all he s ings ha
e e o di e en ypes o ac .
A e assessing i wi h Ósca , he decision ha seems he mos app op ia e is o es ablish
di e en alues o he h eshold and es he execu ion o he en i e p ocess o each
o hem. Las ly, he esul s would be e alua ed and he mos con enien one would be
chosen.
Se o h eshold alues:
0.2 0.3 0.4 0.5 0.65 (4.1)
4.1.2 Noise emo al
The denoising p ocess begins by using he ma ix i sel wi h he simila i y alues as he
s uc u e o wo k on.
Since he goal is ha all hose s ings ha do no espec he h eshold a e disca ded, he
p ocess ca ied ou is simila o applying a bina y encoding o he ma ix o , analogously,
applying a one-ho encoding o each simila i y ec o in which he elemen s ha mee
he condi ion a e kep .
Le 𝑥be he ec o ep esen ing he i s ow o he ma ix, wi h 𝑥𝑖,𝑖 ∈ [0..𝑚] being 𝑚
he o al size o he bag o wo ds. We should emembe ha in each ow o he ma ix
he oken o he bag o wo ds ha ep esen s he index o he ow is compa ed wi h each
o he o he s ings. We know ha , being he i s oken, he elemen 𝑥0has he alue
o 1 because i is compa ed wi h i sel .
Taking in o accoun ha he simila i y alues oscilla e in a ange o [0..1] we apply,
ha ing 𝑢as he h eshold alue and de ining a unc ion 𝐹on he ec o such ha
𝐹(𝑥𝑖)=0,∀𝑥<𝑢.
This is he unc ion shown below. Knowing ha i is going o wo k wi h he elemen s
ha mee he condi ion, he unc ion e u ns a lis wi h he indexes o i s ow ha ha e
no been a 0.
Jaime del Rey Ga cía 26
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
de co e_ alo es(lis a_ca ego ias,ma iz_simili ud,co e):
ma ix =np.emp y([len(ma iz_simili ud),len(ma iz_simili ud)])
”””
A gumen os cla e:
lis a_ca ego ias -- obje o ipo nda ay, con iene
los alo es de la bolsa de palab as
ma iz_simili ud -- obje o ipo nda ay, con iene pa a
cada alo su alo de simili ud con el es o (0..1)
co e -- alo decimal (0..1) pa a il a las palab as
Pone a ce o odos los alo es en la ma iz po debajo del co e
De uel e: lis a => pa a cada ca ego ía las posiciones de las ca ego ías
cuya simili ud es ele an e (según co e)
”””
o i, alue in enume a e(ma iz_simili ud):
ma ix[i] =lis (map((lambda x: 0i x<co e else x),ma iz_simili ud[i]))
ma iz_indices =[]
o i, alue in enume a e(ma ix):
ma iz_indices.append(lis (np.nonze o(ma ix[i])[0]))
lis a_co e =[]
o i, alue in enume a e(ma iz_indices):
lis a_co e.append([i,0,[j o jin ma iz_indices[i]]])
e u n lis a_co e
I u ns ou ha , as each elemen o he a ay has been compa ed wi h he es o he
elemen s in he same o de , he alues o he posi ions o each o he s ings sha e he
same e e ence, ha is, i he elemen 𝑦has in he ec o o simila okens he index 37,
his same index will ep esen he same s ing ega dless o whe he i appea s in he
ec o 𝑥o 𝑧, whe e 𝑥,𝑦,𝑧 a e en i ies o he wo d bag and, hus, ha e a ow assigned in
he ma ix. This is an ad an age because i a oids ha ing o sa e an objec o each o
he s ings in he wo d bag, sa ing esou ces in ime and memo y.
4.1.3 Iden i ying a ian s o s ings
The nex s ep is o iden i y all he s ings ha sha e simila i y and es ablish a class o
g oup hem all.
Ha ing applied he unc ion 𝐹o e he en i e ea u e ma ix, i emains in a s a e ha
can be in e p e ed as an adjacency ma ix, gi ing he possibili y o seeing he p oblem
om a g aph poin o iew.
I we es ablish ha a g aph is a pai o se s 𝐺 = (𝑉,𝐴) whe e 𝑉is he se o e ices
and 𝐴is he se o edges as pai s o he o m (𝑢,𝑣) such ha 𝑢,𝑣 ∈ 𝑉, we de ine, hen,
∀𝑢,𝑣 ∈𝑉 exis s a uple o he o m (𝑢,𝑣)∈𝐴 i and only i 𝑢[𝑣]>0 o 𝑣[𝑢]>0.
27
G ado en Ingenie ía In o má ica Facul ad de In o má ica
The ollowing illus a ion allows us o see how he ma ix would be in e p e ed, i we
conside ha e e y elemen g ea e han 0 can be shown as 1.
Figu e 4.1: Example o g aph wi h adjacency ma ix
[13]
Taking he e ices and edges, we know ha each edge (𝑢,𝑣) ul ills he condi ion ha
bo h 𝑢and 𝑣ha e a simila i y alue g ea e han o equal o he h eshold and, he e o e,
hey can be iden i ied unde he same ca ego y.
The unc ion co e_ alo es e u ned a lis o indices in which he alues we e no 0 a e
applying he 𝐹 unc ion on a s ing. Conside ing his lis 𝐴′as an adjacency lis , he
p ocess o ollow is o go h ough 𝑣,∀𝑣∈𝐴′and ma k he node as isi ed and changing
he alue o he node o ha o he node om which he sea ch s a s, ha is, upda ing
he index alue ha heads he adjacency lis by he index alue ha s a ed om.
In he example below, an example adjacency lis is conside ed:
0→0 1 4 6 (4.2)
I we ollow he algo i hm s a ed abo e, hen we should isi all he nodes un il he nex
esul is achie ed.
0→1 7 24 146 89 (4.3)
0→4 3 (4.4)
0→6 11 43 94 159 271 (4.5)
Fo each o he nodes in he i s adjacency lis , hey ha e been isi ed and changed
he head o 0, which is he head o he s a ing node. I can s ill be associa ed o which
elemen he adjacency lis belonged as he i s elemen o each oken is always he oken
i sel .
Ini ially, an in dep h algo i hm was un o e each o he nodes o he g aph, bu s ing
simila i y is no a ansi i e p ope y and i was disca ded.
The e o e, i a node has al eady been isi ed, i s adjacency lis is no a e sed since i
would ela e elemen s in a ansi i e way and would lead o an inco ec g ouping by
Jaime del Rey Ga cía 28
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
classes. The ollowing unc ion shows he p ocess, which e u ns he upda ed adjacency
lis s wi h he changed lis head alues. I is no ewo hy o no e ha his p ocess is only
execu ed o hose nodes ha ha e mo e han one node in hei adjacency lis , since all
will ha e a leas one node: hemsel es.
de aplica_ca ego ias(posiciones_equi alencia):
”””
De uel e las ca ego ías únicas esul an es de aplica
a la bolsa de palab as los alo es de simili ud con umb al
”””
o i, lis a_simila es in enume a e(posiciones_equi alencia):
posiciones_equi alencia[i][1]= 1
i len(lis a_simila es[2]) > 1:
o pos in lis a_simila es[2]:
i (posiciones_equi alencia[pos][1]== 0):
posiciones_equi alencia[pos][0]=posiciones_equi alencia[i][0]
posiciones_equi alencia[pos][1]= 1
#p in ( alo es_cp[pos] + ' ' + s (posiciones_equi alencia[pos][1]))
e u n np.a ay(posiciones_equi alencia,d ype='objec ')
4.1.4 De ining he classes
Once he connec ions be ween all he okens ha e been es ablished, he ca ego ies ha
will g oup he es o he s ings a e de ined, hus dealing wi h he p oblem o di y
ca ego ies.
Following he p ocess es ablished a he beginning o he sec ion, i is necessa y o de ine a
map ha allows iden i ying he ca ego y ha de ines o g oups i o each class. Wi h he
da a s uc u es o med so a , he simples op ion o de elop is o es ablish a dic iona y
whe e he key is he index o he elemen o be consul ed and he alue is he ca ego y
ha g oups i . This p ocess is he one ha is encoded in he ollowing unc ion, e u ning
said dic iona y.
29
G ado en Ingenie ía In o má ica Facul ad de In o má ica
The hi d op ion, on he o he hand, signi ican ly inc eases he numbe o columns in he
Da aF ame bu is much easie o unde s and o bo h models and people. Each ca ego y
will o m a new column in which each pa ien su e ing om his como bidi y will ha e
he ow a 1.
de aniade_ca ego ias_po _columnas(columna_ca ego ias,
bolsa_ca ego ias,da F ame):
o i, ba 1 in enume a e(bolsa_ca ego ias):
col =[0 o xin ange(len(da F ame))]
o j, oo1 in enume a e(columna_ca ego ias):
o oo2 in oo1:
i (ba 1 == oo2):
col[j] = 1
da F ame[bolsa_ca ego ias[i]] =col
e u n da F ame
4.4 Da ase p epa a ion
Finally, be o e ca ying ou he es s wi h he model, he choice o a iables emains. In
he s udy ca ied ou las yea , hey es ablished which a iables we e he mos ele an
o op imizing he esul s ob ained wi h he models. This includes he elimina ion o
unusable a iables, as well as hose ha can se e as p edic o s o he model and, as
such, mus be elimina ed.
Table 4.1: Remaining ea u es
Fea u es selec ed by he algo i hm
Clasi ica edad sexo Polimic anhonpol
Anae obio Hongos pe iodo mes dia
medio mic obpoli asae asanae asex
COMORBIL so an ibio diashosp Especialid
hgb Inghosp1m plaqu s local pm n
leuc Inghosp12m Neoplasia Hepa opa ia En esp
Diabe es Ca diopa ia Ins enal Ud p Alcoholismo
c ea in sedo ina en basWeins d ogadic inmunosu
es e oid ci ugia neu ope glucosa sin omas
m_diges m_ espi leucoci ombope m_geni u
m_ ascul
None heless he e is a modi ica ion o be ca ied ou . The ea u e COMORBIL is a
a iable ha indica es whe he he pa ien had any como bidi y a he ime o hospi al-
iza ion. This ea u e has al eady no use, each como bidi y will be checked o each o
Jaime del Rey Ga cía 36

Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
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he pa ien s as a bina y a iable, he e o e COMORBIL ⊂O ascomo . The ea u e is
no needed, he in o ma ion ha i b ings o he da ase is sp ead and speci ied o e he
di e en columns o each o he como bidi ies. Lea ing he a iable COMORBIL in he
da ase would only add edundan da a and one mo e dimension o he da ase ea u es,
so i is emo ed.
37
Chap e 5
Bias and a iance
Supe ised Machine Lea ning algo i hms equi e a la ge olume o da a ha will be
used du ing he aining and es ing o alida ion phases. The aining phase in Machine
Lea ning algo i hms is whe e he algo i hms ind ela ionships o co ela ions in he da a,
depending on he p oblem and model, among he da a o be ween he da a in oduced
and he ou pu expec ed. The es ing phase consis s on supplying a smalle se o da a
o check whe he he p edic ions a e accu a e o each o he cases. I is used o measu e
he accu acy o he model.
The p ocedu e desc ibed abo e is called induc i e lea ning. The induc ion capaci y o
a model de e mines he le el o p ecision ha an algo i hm has when ying o sol e a
p oblem simila o hose p o ided as an example. The goal o any Machine Lea ning
algo i hm is o deduc he aining da a well o any domain o he p oblem. The pu pose
o he echnique is o p edic u u e ac ions on ne e -be o e-seen da a.
The main causes o a model wi h un eliable accu acy a e called o e i ing o high a iance
and unde i ing o high bias. As he name says, o e i ing is p oduced when, du ing he
lea ning phase, he model adjus s he weighs oo igh o he aining se in oduced.
The easies way o ecognize his si ua ion is when a model has e y good accu acy le els
wi h he aining da a bu su p isingly poo accu acy a es wi h he es da a. This is
usually due o he use o small da ase s.
On he con a y, unde i ing does no achie e high accu acy a es nei he wi h he
aining no he es da ase s. This can be p oduced due o la ge se s o da a du ing
he aining phase and sho pe iods o aining. The algo i hms hen lack o ime o
adjus ing p ope ly he weighs and esul s in a gene ic model whe e no esul is ” oo good”
no ” oo bad”.
39
G ado en Ingenie ía In o má ica Facul ad de In o má ica
Figu e 5.1: Bias and Va iance
[14]
5.1 A oiding Bias and Va iance
O e i ing and unde i ing di ec ly a ec he accu acy and eliabili y o he models we
a e wo king wi h. I is impo an o a oid his si ua ions by es ing he da a we a e going
o wo k wi h [15].
• Ensu e ha we ha e a sufficien numbe o samples o bo h ain he model and
alida e i .
• Subdi ide ou da a se and keep a po ion o i o es he model. This will allow us
o e alua e he pe o mance o he algo i hm and will also allow us o easily de ec
he e ec s o o e i ing o unde i ing.
• Make su e ha he es se is la ge enough o yield s a is ically meaning ul esul s
and is ep esen a i e o he da a se as a whole. In o he wo ds, do no pick a es
se wi h di e en cha ac e is ics han he aining se .
• The excessi e numbe o a ibu es should be a oided, since i would gene a e a
la ge numbe o dimensions in ou model. This is because each a ibu e makes
up one dimension o he model’s sample space. The numbe o dimensions o he
sample space mus be p opo ional o he numbe o cases a ailable o ca y ou
he s udy, ha is, he g ea e he numbe o a ibu es, he g ea e he numbe
o case s udies, o ice e sa, in he case o ha ing ew case s udies ew a ibu es
should be used.
In his p ojec , we a e using he da ase le om he s udy ca ied he p e ious yea ,
which has he ad an ages o no malized da a, missing da a ea men and a ibu e il-
e ing.
Figu e 5.2 illus a es how each o he si ua ions desc ibed abo e in luence he decisions
o e a se o da a and how should a model beha e.
Jaime del Rey Ga cía 40
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
Figu e 5.2: Examples o o e i ing and unde i ing
[16]
5.2 K-Fold C oss Valida ion
C oss- alida ion is a esampling p ocedu e used o e alua e Machine Lea ning models on
a limi ed da a sample. I allows gene a ing di e en models om he same da ase . The
echnique di ides in o di e en subse s om he o iginal se and gene a es a model so
ha each subse o da a is used o bo h he aining pa and he alida ion pa . Mo e
speci ically, i andomly mixes he da a ame and subdi ides i in o equal g oups.
C oss- alida ion is p ima ily used in applied Machine Lea ning o es ima e he skill o a
Machine Lea ning model on unseen da a. Tha is, o use a limi ed sample in o de o
es ima e how he model is expec ed o pe o m in gene al when used o make p edic ions
on da a no used du ing he aining o he model.
I is a popula me hod because i is simple o unde s and and because i gene ally esul s
in a less biased o less op imis ic es ima e o he model skill han o he me hods, such as
a simple ain/ es spli .
The gene al p ocedu e is as ollows:
• Shu le he da ase andomly.
• Spli he da ase in o 𝑘g oups.
• Fo each unique g oup:
–Take he g oup as a hold ou o es da ase .
–Take he emaining g oups as a aining da ase .
–Fi a model on he aining se and e alua e i on he es se
–Re ain he e alua ion sco e and disca d he model
• Summa ize he skill o he model using he sample o model e alua ion sco es
41

G ado en Ingenie ía In o má ica Facul ad de In o má ica
Impo an ly, each obse a ion in he da a sample is assigned o an indi idual g oup and
s ays in ha g oup o he du a ion o he p ocedu e. This means ha each sample is
gi en he oppo uni y o be used in he hold ou se 1 ime and used o ain he model
k-1 imes.
K-Fold C oss alida ion is one o many p ocesses used o ha end, bu is wha will be
used in his s udy. Figu e 5.3 illus a es he p ocess.
Figu e 5.3: Examples o o e i ing and unde i ing
[17]
Jaime del Rey Ga cía 42
Chap e 6
Random Fo es
The Random Fo es algo i hm is a supe ised lea ning echnique ha includes di e en
me hods in he aining phase.
I is a model equen ly used o deal wi h o e i ing and unde i ing p oblems. This
algo i hm is used o sol ing eg ession and classi ica ion p oblems. I has a co ec
ope a ion e en wi hou adjus ing i s own pa ame e s and emains s able when new da a
is en e ed. On he o he hand, i equi es high p ocessing imes, i is difficul o in e p e
and small da a ames a e no p ocessed op imally.
A Random Fo es is an ensemble o decision ees combined wi h bagging. When using
bagging [18], wha is ac ually happening is ha di e en ees see di e en po ions o
he da a. The low co ela ion be ween models ( ees) is he key. The eason o his
e ec is ha he ees p o ec each o he om hei indi idual e o s (as long as hey
don’ cons an ly all e in he same di ec ion). No ee sees all he aining da a. This
causes each ee o be ained wi h di e en da a samples o he same p oblem. In his
way, when combining hei esul s, some e o s a e compensa ed o o he s and we ha e
a p edic ion ha gene alizes be e .
When we using bagging, we also combine a ious Machine Lea ning models. Unlike o he
me hods, he way o ge e o s o compensa e o each o he is ha each model is ained
wi h subse s o he aining se . These subse s a e o med by andomly choosing samples
(wi h epe i ion) om he aining se .
6.1 Fi ing a Random Fo es
To adjus he model based on his classi ie , i is necessa y o adjus he n_es ima o s
pa ame e . This pa ame e ep esen s he numbe o ees ha will make up he model
and on which each case s udy will be e alua ed. In addi ion, he andom_s a e pa ame e
is se o be able o eplica e he accu acy alues o he model wi h he same inpu
pa ame e s.
This pa ame e helps o con ol he andomness o he algo i hm when gene a ing he
decision ees. I is impo an while changing be ween da ase s, pa ame e s on he same
da ase o ee alua ing models.
43
G ado en Ingenie ía In o má ica Facul ad de In o má ica
Fi s , o a oid o e i ing and unde i ing, we will spli he da a using 80% o he da a
o he aining p ocess and he emaining 20% o he model alida ion. Taking in o
accoun he amoun o samples in he da ase and he amoun o a ibu es o each
sample, he 80-20 olding dis ibu ion lea es oom o a co ec i ing p ocess.
om sklea n.model_selec ion impo ain_ es _spli
X_T ain, X_Tes , Y_T ain, Y_Tes = ain_ es _spli (X, Y, es _size=0.2)
Once we ha e applied K-Fold C oss Valida ion, we can execu e he code ha will adjus
he numbe o es ima o s o minimize he e o . A ange be ween 20 and 90 es ima o s
is ixed. Now he model has o ain using he aining da a om he C oss Valida ion
me hod and hen calcula e he accu acy wi h he se s o da a used o he es phase.
a ayP ed =[]
o ind in ange(20,90):
p in (ind, end =' ')
RF =RandomFo es Classi ie (ind, andom_s a e=0)
RF. i (X_T ain, Y_T ain)
p edicciones =RF.p edic (X_Tes )
accu acy =accu acy_sco e(Y_Tes , p edicciones)
a ayP ed.append(accu acy)
i accu acy >maxi_accu acy:
maxi =ind
maxi_accu acy =accu acy
_max=RF
In Figu e 6.1 we can see ha o e all he e a e e y decen accu acy alues, bu he peak
is eached o 54 es ima o s ( he highes alue in he eco d is placed in posi ion 34, as
he sample goes om 20 o 90 he o al numbe o es ima o s is 34+20), a andom_s a e
alue o 0wi h an accu acy o o e 0.940. Fo his execu ion, K-Fold pa i ion wi h
80% o aining and 20% o es ing was used. The esul s a e shown o he aining
phase.
Jaime del Rey Ga cía 44
Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
Figu e 6.1: S udy o e he numbe o es ima o s
Once he e u ned alues a e known, we alida e he model and he e u ned accu acy
alue in o de o de ec o e i ing o unde i ing p oblems. To do his, he p edic ions
o a new da ase no used du ing he aining phase and he accu acy o he model on
his da ase a e calcula ed. We use now he alida ion se .
# un model wi h op imal pa ame e s
RF =RandomFo es Classi ie (54, andom_s a e=0)
RF = _max
RF. i (X_T ain, Y_T ain)
# es
p edicciones =RF.p edic (X_Tes )
epo =pd.Da aF ame()
epo e_ac ual =classi ica ion_ epo (Y_Tes , p edicciones, ou pu _dic =T ue)
epo ['1']= epo e_ac ual['1']. alues()
Model accu acy is:0.935
In his case, sligh ly lowe accu acy alues a e ob ained han hose p e iously collec ed,
which indica es ha he model does no p esen o e i ing o unde i ing p oblems.
6.2 E alua ion me ics
In o de o ully unde s and he deg ee o p ecision o he model in ques ion, he e a e
a ious in e p e abili y echniques o Machine Lea ning models in classi ica ion p oblems
as he e can be p oduced di e en ou comes. In his example, he p edic ed alue can
45
G ado en Ingenie ía In o má ica Facul ad de In o má ica
had al eady been d awn. The ea u es we e asae and asanae and we e also emo ed
om he da ase .
In Figu e 6.11 we can see he esul s o he aining p ocess o he Random Fo es . The
model accu acy alue was 0.871 a e es ing he model wi h he alida ion se .
Figu e 6.11: S udy o e he numbe o es ima o s wi h il e ed ea u es
This esul is a mo e cohe en aking in o accoun he esul s om he p e ious s udy
ha sco ed an accu acy o 0.86 and he lis o mos ele an a iables, now upda ed in
Figu e 6.12, whe e none o he new ea u es ep esen a signi ican decision alue and
he e o e ou model should beha e almos he same.
Jaime del Rey Ga cía 52

Au oma ic analysis o high dimensional ca ego ical a iables in medical da abases o
he p edic ion o hospi al bac e emia UCM
Figu e 6.12: Mos ele an ea u es in he second execu ion
53
Chap e 7
Conclusions
Wo king wi h such a he e ogeneous da ase has been a eal challenge o he en i e da ase
p epa a ion p ocess. The i s conclusion is ha he whole s udy and, in gene al, any
p ocess ha is epea ed simila o his, would g ea ly bene i om a mo e speci ic desc ip-
ion o he ex s ings. Al hough i is a wo k ha emains o he w i ing o doc o s, we
ha e seen how he subs i u ion o , o example, s oke o ce eb o ascula acciden , allows
he g ouping and iden i ica ion o ca ego ies in a much mo e eliable and exac way. As
explained in he sec ion on s ing simila i y, misspellings we e ele an when compa ing
sho -leng h okens, so ano he ad an age o his si ua ion would be he dec ease in he
ele ance o misspellings in ob aining o he simila i y be ween wo s ings.
Using he ile p o ided by Ósca has allowed he con e gence o all he cleaning and da a
p epa a ion wo k in o a use ul esul . This ile, e en so, does no collec all he a ian s
o abb e ia ions o spelling mis akes ha he se o a iables con ains. This leads o
he conclusion ha he ool alone did no p o ide sufficien suppo o ca y ou he
s udy.
In sho , is no iceable ha na u al language p ocessing is a ask ha s ill has oom o
imp o emen , howe e he use o his ool has made i possible o educe a se o mo e
han 1000 ca ego ies o app oxima ely one en h.
Looking a he inal da ase , he amoun o a ibu es ini ially added by using a bina y
encoding o include he ca ego ies in he da ase seemed excessi e, inc easing he o al
numbe o a ibu es o 247, since i is a pe ec example o a case ha may su e high
bias and gene alize he weigh s associa ed wi h he pa ame e s in he lea ning p ocess.
Howe e , since he e we e mo e han 4,300 examples, no only has i no p oduced his
e ec , bu i has also con ibu ed o an imp o emen in he success a e compa ed o he
s udy ca ied ou las yea .
Rega ding he model used, he conclusion d awn om he p e ious s udy showed a be e
success a e wi h he applica ion o Random Fo es on he da ase . The ad an age o
using his model o e o he Machine Lea ning models is ha i is one o he models wi h
mo e explana o y powe , as i is di ec ly o med by decision ees. The model esul ing
om his algo i hm ained on he p e iously men ioned da ase has an accu acy o
app oxima ely 94%.
One o he easons ha he i ness o he i s model can be conside ed success ul is he
55
G ado en Ingenie ía In o má ica Facul ad de In o má ica
esul o displaying he ROC cu e (6.7) and he con usion ma ix (6.3). The conclusion
o he co ec classi ica ion by he model is suppo ed by he me ics ha allow us o
app ecia e he clea di e en ia ion be ween bo h dis ibu ions.
We can no igno e ha , a e all, he p ocess o cleaning he da a, compu ing he simila i y
be ween all he okens and inally ob aining he di e en ca ego ies om he ea u e
O ascomo , none o hem we e in he op 50 o he mos weighed ca ego ies. The
conclusion is ha , ega ding he esul o he second model, wi h he da a p o ided and
he Machine Lea ning ype o model used, i is a he difficul o make a co ec ea ly
diagnosis o bac e emia.
Jaime del Rey Ga cía 56
Chap e 8
Fu u e imp o emen s
This p ojec began wi h he idea o wo king on all he nominal a iables o he da ase
p o ided by Hospi al Uni e si a io de Fuenlab ada. Howe e , he o ganiza ion and wo k
ha has led o he ea men o a single a iable has aken up mos o his s udy.
Fo his eason, one o he possible b anches in which his s udy can lead is he one in
which he es o he a iables a e ea ed and Machine Lea ning me hods a e applied o
he complemen ed se . Taking in o accoun he da ase esul ing om his s udy, i is
possible ha he inclusion o he o he a iables may o e load he numbe o a ibu es
o he se p o ided when coding hem o co ec ea men by Machine Lea ning models,
ye i seems he mos u gen s ep o ake ega ding he esul s o he las model.
O he possible a ian s a e he applica ion o o he Machine Lea ning models such as
Neu al Ne wo ks o Suppo Vec o Machines (SVM). These models ha e he g ea dis-
ad an age o lacking explicabili y. The e o e, i would equi e an in-dep h s udy o he
a iables and he weigh s associa ed wi h hem. Howe e , hey a e models ha can de ec
complex ela ionships be ween a ibu es ha help imp o e p edic ion efficiency. This is
specially ele an in he con ex o his p ojec , whe e i would also be in e es ing o ind
possible ela ionships be ween he ca ego ies ob ained and he o iginal a iables om he
da ase .
In addi ion, he s udy ca ied ou las yea and his one ha complemen s i , p o ide
conclusions and help o ecognize bac e emia as a bina y class, bu in eali y he e a e a
di e si y o ypes o bac e emia and no all sha e symp oms o ea men . The e o e, he
conclusions d awn du ing hese wo yea s could be applied o he s udy o he de ec ion o
bac e emia as a mul iclass classi ica ion p oblem. This pa icula s udy may be he mos
labo ious, since i may equi e di e en da ase s o each ype o bac e aemia, howe e ,
i he esul s we e success ul, i would be a g ea boos in he p edic ion o bac e emia
diagnoses.
57

Lis o Figu es
1.1 Blood cul u e examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
3.1 Sample o he ea u e O ascomo . ..................... 12
3.2 Sample o he elemen s in he ea u e O ascomo e e ing o anemia as
di yca ego ies................................. 13
3.3 Sample o he elemen s in he ea u e O ascomo e e ing o alzheime as
di yca ego ies................................. 13
3.4 Sample o he elemen s in he bag o wo ds. . . . . . . . . . . . . . . . . 18
3.5 Example o a hea map o e di y ca ego ies o di e en wo ks. . . . . . . 20
3.6 Example 1 o a hea map o e 25 andom di y ca ego ies om he da ase . 21
3.7 Example 2 o a hea map o e 25 andom di y ca ego ies om he da ase . 22
3.8 Example o he classes g ouped ela i e o he numbe o neighbo s . . . 23
3.9 K-NN o e he bag o wo ds using k=4 neighbo s . . . . . . . . . . . . . 24
4.1 Example o g aph wi h adjacency ma ix . . . . . . . . . . . . . . . . . . 28
5.1 BiasandVa iance............................... 40
5.2 Examples o o e i ing and unde i ing . . . . . . . . . . . . . . . . . . 41
5.3 Examples o o e i ing and unde i ing . . . . . . . . . . . . . . . . . . 42
6.1 S udy o e he numbe o es ima o s . . . . . . . . . . . . . . . . . . . . 45
6.2 Hypo hesis es ing .............................. 46
6.3 Con usionma ix............................... 48
6.4 IdealAUCscena io.............................. 49
6.5 Wo s ROCscena io ............................. 49
6.6 IdealROCscena io.............................. 49
6.7 ROC cu e om Random Fo es . . . . . . . . . . . . . . . . . . . . . . 50
6.8 Es ima ed weigh pe ea u e . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.9 Mos weighed ea u es . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
6.10 SHAP alue (impac on model ou pu ) . . . . . . . . . . . . . . . . . . . 51
6.11 S udy o e he numbe o es ima o s wi h il e ed ea u es . . . . . . . . 52
6.12 Mos ele an ea u es in he second execu ion . . . . . . . . . . . . . . . 53
59
Lis o Tables
3.1 Fea u es om he da ase . . . . . . . . . . . . . . . . . . . . . . . . . . 8
3.2 Selec ed ea u es in he s udy. . . . . . . . . . . . . . . . . . . . . . . . . 11
4.1 Remaining ea u es.............................. 36
61