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Credit Card Fraud (C4.5)
70
Average Aggregate Cost ($)
tN_`[^[^p|dNh¢ýcÐY\_`ddNcytM_ m a#tp-jknÏnbh¢dNcygÍaNh¢Y|j‘tí
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gp|dun©z`Y m nbcedutÏ]kp|dMauh¢p mim } õê]+Y\tutMh `m } cj„aNh¢duc m } ú ]kp“}ñvêY\d8auz`c
m Y\tutaNzkdNY\_`{|zìz`h¢{|zkcd.h¢j„aNcedNcytPa.d#p³aucete€7z`hi{\z`cd([^c[  cd#tNz`hi]
vêccyt€bp|jknÛducenb_‘gcen  cej`cð`a#tí Bcjkgc|€bhiaGhot  Y|aNzaNz`c  p-jkªt (
p-j‘nâgp|dunzkY m nbcd#&t (+h¢j\aucducetMaauYducenb_‘gc.h m¢m ce{|hiaNh¢[^p-aNcr_ktNc(Y|v
gducen`h¥aÛgp|dunkt€]‘p-dNaNhog_ m p-d m }ì§zkcj ] m p\tPauh¢gÏhot^]`duc¤³p m cj„a^hij
aNYbn`p“} ( th¢jkgducep\tMh¢j`{ m }8c m cegÍaudNY\j`hogtMYbgh¢caP}\íXZzkp|tNc ~ p|j`zkp-aMé
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tNª|c§GcenÏõ " ú aNz`c ƒ|† ï † nbhotPaudNh  _bauhiY\jrhot7§zkp-a§Zc
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aNd#p-¡ j‘_`tNp\cGgÍauaNYh¢Y|aujz`cp-j‘nbn,h +Y-cedNaNcezkj\cadnbv×p\Y gÍmimaNp-Y\d7dutep-€[^aNzkY\c._`j„ga3Y„Y|tPav‘ceY|p\v3g#v×z(p|h gm h¢dNj`cy{^nbh¥aNa
Ygp|n`ducn é
aNcygÍa^nbh «cducj„avêd#p-_‘nb_ m cj„a.audup|jktNp\gÍauhiY\jkthotj`Y|aaNz`cÏtNp|[^c|í
cejkgc§Gcnbcð‘j`c|ï
Overhead = 25
Overhead = 50
Overhead = 75
Overhead = 100
Overhead = 125
Overhead = 150
60
50
40
30
20
l ¢h {|_kdNc ‡ ïxwxd#p-h¢j`h¢j`{BnbhotMaNduh  _`aNh¢Y|j¤btíxaNz`cGgducenbhia3gep-d#nvêdup|_kn
gY\tMa[^Yn`c m
10
20
30
40
50
60
70
Distribution of minority class (%)
80
90
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hij`{tNcautauY ü € %„†|† audup|jktup|gÍauhiY\jkte€‘§z`hog#zèp-duc(tup-[^] m cenCd#p-j`é
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aNz`cY³¤\cduz`cep\nhot m p-du{|cede€`aNz`c  p-j`ª
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aNY m cd#p³auc[^Y|duc[^h¢tutMcyt.õ pÛz`h¢{|z`ced l7¦ d#p³auc ú €‘§z`hog#zCgp|j  c
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aNzkp-ae€«p³atNY|[^c]+Y|h¢j„ae€‘aNz`c(Y³¤|cduz`cyp|nÏgp-j  c m p-du{|ccej`Y|_k{|z
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w:z`cBaNcytPa:tMcaŸõ vêduY|[ J… ³…\ü\ú zkp\t %„† € †|‚ Ÿaudup|jktup|gÍauhiY\jktp|jkn
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p“¤“p|h m p km c\€-Y|jraNzkcBp“¤|cedup|{|c|€ ’ ‚|ü í …\ü hot m Y\tMa´]‘ced
aNd#p-j‘tNp\gÍaNh¢Y|jxí
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hij`{ ™˜™–&!šp—^dNce]`ducetNcj„autaNzkcÛ]‘cedugcj„aup|{|crY-vtNp“¤h¢j`{\tvêduY|[
aNz`c^p“¤|cedup|{|c m Y\tutBY|`v ’ ‚\ü í …|ü œ›"–&!š,—rtNz`Y³§tBaNz`craNY|aup m n`Y m é
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vêduY|[ ’ |† aNYh’ ‡y†|† €-aNzkc m cep|dNj`h¢j`{rp m {|Y|duhiaNz`[>t§GcŸ_ktMcyn>{|cejbé
cd#p m¢m }p|g#zkhice¤|cenÐp-a m cyp|tMa ƒ-†J
h¢jtNp“¤h¢j`{\t«Y\dxp³a m cyp|tMa ’ ‚\†|† ÿ^í
+ hiaNzCp-jY³¤\cduz`cep\nÛY-v’ ¬" Y|d m cetut€kp-a m cyp|tMazkp m vpr[rh m¢m h¢Y|j
nbY mim p-d#tÐhijìtup“¤hij`{„tÐgp-j  cÛp³aNaup-h¢j`cyn²í ~ Y\dNc^h¢[r]+Y|dNaup|j„a m }|€
[>p bh¢[._`[ tup“¤hijk{\tZ§ZcedNcp|g#zkhice¤|cen ¬ Y\_baY-v … auhi[^cyt:§z`cj
aNzkc.vêd#p-_knâ]‘cedugcj„aup|{|c_‘tMcynCh¢jCaNd#p-h¢j`h¢j`{hot -J† €«§z`hog#zâhot
j`Y|aaNz`c Njkp³au_`dup m ƒ-J† hijÏauz`cY|duhi{\hij‘p m n`p³a#p^tMcaeí
qsj tN_`[^[>p-du}|€  p\tMcyn Y|jY|_`d^ce[r]khiduh¢gep m ducetN_ m a#trhijaNz`hot
tMaN_knb}\€§ZcY  tNcdu¤|c:auzkp³aG¤“p|dN}h¢j`{auz`cBaudup|hijkhij`{(g m p|tut´nbhotPaudNhié
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h¢[^p-aNc(aNd#p-jktup|gaNh¢Y|jkt(õêY\d ü\† Y-vZp mim auz`c.audup|jktup|gÍauhiY\jkt ú €«p|t
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nbhotNg_ktutMcyt´p-j8p-]`]`duY\p\g#zraNzkp-aZ_bauh m hiýecetGp m¢m auz`cnkp³aup(p-jknÛhi[ré
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aNduh  _baNh¢Y|jì[^h¢{|z„a.j`Y|a.}hic m nìaNz`cÛ[^Y„tPa.&c +cygÍauhi¤\cg m p|tutMhiðkcedut
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HŸh¢¤|cjñpìtNª|c§GcennbhotPaudNh  _bauhiY\j5€:§Zc§GY|_ m n m h¢ª|cÏaNYì{\cj`cedMé
p³aucGaNz`cnbcytMh¢dNcyn(n`h¢tMaNduh  _baNh¢Y|jr§h¥auz`Y|_`a7duc[^Y³¤h¢j`{Ÿp|j}n`p³a#p`í
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nbhotPaudNh  _bauhiY\j5€x{\cj`cedup-aNcrg m p|tutMhiðkcd#tvêdNY\[áaNzkcÛtM_  tMcaute€xp-jkn
h¢j\auc{\dup-aNcraNz`ce[  } m cyp-duj`h¢j`{ìõê[^ca#p³é m cyp-duj`hijk{ ú vêdNY\[Dauz`ch¢d
g m p|tutNh¥ð‘gep³auhiY\j  czkp“¤h¢Y|dyí
qsjY|_`dvêd#p-_‘n8nbY\[>p-h¢j5€baNzkcjkp³au_bé
d#p m tMª\c§GcenCnbhotMaNduh  _`aNh¢Y|jâhot ƒ-† ï † p-jknaNz`c>nbcytMh¢dNcynCnbhotPaudNhié
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tMaup-j‘gcetZh¢j\auY % ]kp|dMauh¥auhiY\jkt:p-jkn % n`p-auprtM_  tMcaut:p-ducvêY\dN[^cen
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[^hijkY|duh¥aP}8hijktMaup|jkgcytBp|dNcduc] m hogp³aucenp|gdNY„tNt % nkp³auptM_  tMcaut
aNY({|cej`cd#p³aucaNzkcŸnbcytMh¢ducen |† ï -† nbhotPaudNh  _bauhiY\j5í l hi{\_`duc ƒ n`cé
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g m p|tut ú p-jkYn X"ï C  c´aNz`cGnbcetNhiducen.nbh¢tMaNduh  _baNh¢Y|jxí¾w:z`cZj„_k[  cd
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ih jñcep\g#z tN_  tNcay€:§z`h¢g#zñhotdgcfhe i Y|dkle Zm`^ í<õ + z`cjôhiaÛh¢t
j`Y-apr§z`Y m cj_`[  cede€b§Gcaup-ª\j cBauz`cgceh m hijk{Ïõ/n el Z `^@o ú p|jkn
dNce] m hogp-aNctNY|[^c8[^pPY|duh¥aP}Uh¢jktPa#p-jkgcet.aNYJcjktN_`ducp m¢m Y|vaNzkc
[^p PY|duh¥aP}h¢jktMaup|jkgcyt
p-ducGh¢jraNz`ctM_  tMcauteí ú w:zkp³ahot€\§Zc:zkp“¤\c
e Z ` tN_  tNca#t€cyp|g#zÛY|v5§z`h¢g#zzkp|a
t @FV8[^h¢j`Y|duhiaP}rh¢jktMaup|jkgcyt
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Credit Card Fraud (BAYES)
Credit Card Fraud (BAYES)
70
Overhead = 25
Overhead = 50
Overhead = 75
Overhead = 100
Overhead = 125
Overhead = 150
60
50
Average Aggregate Cost ($)
Average Aggregate Cost ($)
70
40
30
20
Overhead = 25
Overhead = 50
Overhead = 75
Overhead = 100
Overhead = 125
Overhead = 150
60
50
40
30
20
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¤“p m hon`p-aNh¢Y|j8tNca§hiaNz`Y\_banbc{\dup\nbh¢j`{auz`cgY„tPa:]‘cedMvêY\dN[>p|jkgc\í
w:zkp³aÐh¢te€«aNzkh¢tÐp-]k]`dNY„p|g#z]`duY³¤h¢n`cetŸp[^cep|jktBvêY|dÐc )Ûgh¢cj„a m }
10
20
30
40
50
60
70
Distribution of minority class (%)
80
 † ……]ˆ€ … „f€Œ „E€PƒR€Nƒm„ }†P € ˆ†F„E€PƒŠ…}U„
90
w:z_kt²v×p|dx§Gczkp“¤\cgY|j‘gcj„audup-aNcenŸY\jaNz`cZg m p|tutxnbhotPaudNh  _bauhiY\jkt
h¢j(audup|hijkhij`{aNzkc  p|tNcg m p|tutMhiðkcd#teí + cGz}]+Y-aNzkcetNhiýecZauzkp³a
auz`c
g m p|tutnbhotPaudNh  _bauhiY\jìhijUauz`cÛ¤³p m h¢nkp³aNh¢Y|jìtNcaõ p-jknèz`cejkgc^auz`c
[^ca#p³é m ce¤|c m audup|hijkhij`{>tNca ú p«cegautGaNzkcY³¤|cedup mim ]+cdNvêY|du[^p|jkgc
Y-v`[^caup³é m cep-duj`h¢j`{kí¾wxYhij¤|cytPauhi{„p³auc
aNzkp-a3z}]+Y-aNzkcetNh¢te€³hijaNz`hot
tNcaZY|v²c b]‘cedNh¢[^cj„aute€„§Zc/ð cyn^aNzkcaNd#p-h¢j`h¢j`{.nbhotMaNduh  _`aNh¢Y|jÛY|v
aNzkc  p|tNcg m p|tutMhiðkcd#tZaNY -† ï |† p|jknϤ“p|dNh¢cenaNzkcÐn`h¢tMaNduh  _baNh¢Y|j
Y-vxaNz`cФ³p m h¢nkp³aNh¢Y|jÏtMcaZvêduY|[ ‚\† ï ¬³† aNY ¬³† ï ‚|† õ×p\tZh¢j8aNz`cŸ]`ducé
10
20
30
40
50
60
70
Distribution of minority class (%)
80
90
w3p `m c ƒ Zï XZY„tPap-j‘n8tup“¤hij`{„tG_ktMh¢j`{>[^ca#p³é m cyp-duj`h¢j`{
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n`h¢tMaNduh  _baNh¢Y|jkte€
j`Y\jbé _kj`h¥vêY\dN[ gY\tMaG]+cdcedNduY|dy€p-jkn m p|dN{\cp-[^Y\_`j„autGY-v7n`p³a#p`í
¦ Y|a.Y|j m }Jh¢t.Y|_`d[^cauz`Ybnìc)Ûghicej\ay€¾hia.hot.p m tNYtNgep m p `m c^aNY
m p-du{|cdp|[rY\_`j„aut:Y|v3n`p-aup`í
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g m p|tutôhot j`Y|a©j`ce§ vêY\d©zkp|jkn m hijk{ tMª\c§Gcen4nbhotPaudNh  _bauhiY\jkt
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p-[^Y\_`j„autrY-vÐn`p³a#pJ&c )Ûgh¢cj„a m }|€:p-jkn]+cdu[rhiautrauz`c_ktup-{\c8Y|v
[._ m auhi] m c NY +é auz`céstMzkc m -v m cyp-duj`hijk{^p m {\Y|duh¥auz`[>tGaNY>h¢jkgducep\tMc
nbh¢¤|cedutNh¥aP}p-[^Y|j`{Uauz`c m cyp-duj`cenñg m p\tNtNh¥ð‘cd#tí l _`dMauz`cdu[^Y|duc|€
z`Y³§ auz`c>n`p³a#pp-duc(tup-[^] m cenâh¢t  p\tMcynCY\jaNz`c>gY\tMa[^Ybnbc m €
§z`hog#zÛ[^hi{\z„aZnbhogÍaup-aNcŸnbY³§jktup-[^] m hij`{.hijktMaup|jkgcytY|v+auz`cŸ[rhié
j`Y\dNhiaP}g m p|tutGhij‘tPaucep|nÏY|vxaNzkc[^p PY|duh¥aP}8g m p|tutí
îj`c m h¢[^h¥a#p³aNh¢Y|jrY-v+Y|_`d
p|]`]`duY\p|g#z.h¢t3auz`cj`ccyn.Y|v‘du_`j`j`h¢j`{
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aNduh  _baNh¢Y|j  p|tNcenâY|jâpÏnbcðkj`cenJgY„tPaÐ[^Yn`c m íw:z`h¢tŸ]`duYbgcytNt
gp|j  cGp-_bauY|[>p³aucen  _ba¾hia¾hotx_kjkp“¤|Y\h¢n`p `m ctMh¢jkgcaNz`cGnbcetNhiducen
nbhotPaudNh  _bauhiY\jhotGz`hi{\z m }Ûnbc]+cjkn`cj„aY|jÛauz`cgY„tPaG[rYbnbc m p-jkn
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£BtNhij`{vêY|_`d m cep-duj`h¢j`{8p m {\Y|duh¥auz`[>t€+Y|_kdp-]k]`dNY„p|g#z{\cj`cedMé
p³aucet ‡yƒ 8g m p\tNtNhiðkcd#tvêduY|[ùp |† ï -† g m p|tutŸn`h¢tMaNduh  _baNh¢Y|jèp-jkn
ch¢{|z„a[^Y|j„auzktY|v:n`p-aupkí + cÛ[^hi{\z„a.j`Y-ajkccenUauYCª|cec]ìp m¢m
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{|cej`cd#p³aucenì§zkcj auz`cn`p³a#pâtNca^h¢t([^Y|duc8tNª|c§Gcen Y|d^p|n`nbhié
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