demonstraceNoOutput.nb

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Demonstrace funkce a pou\[ZHacek]it\[IAcute] SVM klasifik\[AAcute]toru\
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Nejprve na\[CHacek]teme v\[SHacek]echny pot\[RHacek]ebn\[EAcute] knihovny.\
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A inicializujeme funkce, kter\[EAcute] jsou d\[AAcute]le \
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Pou\[ZHacek]it\[IAcute] SVM na jednoduch\[YAcute]ch datech\
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Vygenerujeme jednoduch\[AAcute] data, kter\[AAcute] budeme pomoc\[IAcute] SVM \
klasifikovat.\
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Cell["\<\
Data si m\[URing]\[ZHacek]eme prohl\[EAcute]dnout v grafu.\
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Vid\[IAcute]me, \[ZHacek]e data jsou velmi jednoduch\[AAcute], obsahuj\
\[IAcute] dv\[EHacek] t\[RHacek]\[IAcute]dy- \[CHacek]ervenou a zelenou. Na \
prvn\[IAcute] pohled je jasn\[EAcute], \[ZHacek]e data jsou line\[AAcute]rn\
\[EHacek] separabiln\[IAcute]. Nyn\[IAcute] na datech natr\[EAcute]nujeme SVM \
klasifik\[AAcute]tor a zobraz\[IAcute]me si jeho v\[YAcute]stup.\
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V grafu vid\[IAcute]me dv\[EHacek] op\[EHacek]rn\[EAcute] roviny (p\[RHacek]\
\[IAcute]mky) zobrazen\[EAcute] \[CHacek]\[AAcute]rkovan\[EHacek], Rovina, \
pomoc\[IAcute] kter\[EAcute] je prov\[AAcute]d\[EHacek]na klasifikace je \
zobrazena tlustou plnou \[CHacek]\[AAcute]rou - v\[SHacek]e nad rovinou pat\
\[RHacek]\[IAcute] do zelen\[EAcute] t\[RHacek]\[AAcute]dy, v\[SHacek]e pod n\
\[IAcute] pat\[RHacek]\[IAcute] do \[CHacek]erven\[EAcute] \
t\[RHacek]\[IAcute]dy. Modrou barvou jsou zv\[YAcute]razn\[EHacek]ny op\
\[EHacek]rn\[EAcute] vektory.\
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Cell["\<\
D\[AAcute]le si vygenerujeme trochu \
slo\[ZHacek]it\[EHacek]j\[SHacek]\[IAcute] data.\
\>", "Text",
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Cell["\<\
Jak je patrn\[EAcute] z grafu, tyto data ji\[ZHacek] nen\[IAcute] \
mo\[ZHacek]n\[EAcute] line\[AAcute]rn\[EHacek] separovat. V tom p\[RHacek]\
\[IAcute]pad\[EHacek] m\[URing]\[ZHacek]eme pokra\[CHacek]ovat dv\[EHacek]mi \
zp\[URing]soby. Prvn\[IAcute] a nej\[CHacek]ast\[EHacek]j\[SHacek]\[IAcute] \
zp\[URing]sob je p\[RHacek]esunout se pomoc\[IAcute] j\[AAcute]drov\[EAcute] \
funkce do vy\[SHacek]\[SHacek]\[IAcute] dimenze, ve kter\[EAcute] u\[ZHacek] \
budou data line\[AAcute]rn\[EHacek] separabiln\[IAcute]. Tomuto \
zp\[URing]sobu se budeme podrobn\[EHacek] v\[EHacek]novat pozd\[EHacek]ji. \
Druh\[AAcute] mo\[ZHacek]nost je trvat na line\[AAcute]rn\[IAcute] separaci a \
p\[RHacek]ipustit mo\[ZHacek]nou chybu.\
\>", "Text",
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Cell["\<\
Zobraz\[IAcute]me si v\[YAcute]stup line\[AAcute]rn\[IAcute] separace s \
povolenou chybou.\
\>", "Text",
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Cell["\<\
U SVM je mo\[ZHacek]n\[EAcute] nastavit si chybovou funkci, kter\[AAcute] ur\
\[CHacek]\[IAcute] jak moc je pro n\[AAcute]s chyba v\[YAcute]znamn\[AAcute]. \
Klasifik\[AAcute]tor se pot\[EAcute] sna\[ZHacek]\[IAcute] tuto chybu \
minimalizovat. Na n\[AAcute]sleduj\[IAcute]c\[IAcute]m grafu je mo\[ZHacek]n\
\[EAcute] odzkou\[SHacek]et, jak se bude vyv\[YAcute]jet klasifikace s m\
\[EHacek]n\[IAcute]c\[IAcute]m se v\[YAcute]znamem chyby.\
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Cell["\<\
J\[AAcute]drov\[EAcute] funkce jsou z\[AAcute]kladmn\[IAcute]m triken, pomoc\
\[IAcute] kter\[EAcute]ho se SVM p\[RHacek]esouv\[AAcute] do vy\[SHacek]\
\[SHacek]\[IAcute]ch dimenz\[IAcute]. (Opakovan\[YAcute]m) Aplikov\[AAcute]n\
\[IAcute]m t\[EHacek]chto funkc\[IAcute] na data se provede jejich \
transformae do vy\[SHacek]\[SHacek]\[IAcute]ch dimenz\[IAcute], kde je ji\
\[ZHacek] mo\[ZHacek]n\[EAcute] data line\[AAcute]rn\[EHacek] separovat \
nadrovinou.\
\>", "Text",
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Cell["\<\
Nej\[CHacek]ast\[EHacek]ji se jako j\[AAcute]drov\[EAcute] funkce \
pou\[ZHacek]\[IAcute]vaj\[IAcute] n\[AAcute]sleduj\[IAcute]c\[IAcute] dv\
\[EHacek].\
\>", "Text",
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\[AAcute]sleduj\[IAcute]c\[IAcute]m p\[RHacek]edpisem ",
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 ". P\[RHacek]i jej\[IAcute]m pou\[ZHacek]it\[IAcute] je t\[RHacek]eba vhodn\
\[EHacek] nastavit stupe",
 "\[NHacek] polynomu - parametr d. "
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Cell["\<\
Jak polynomi\[AAcute]ln\[IAcute] kernel vypad\[AAcute] v z\[AAcute]vislosti \
na jeho stupni je mo\[ZHacek]n\[EAcute] si prohl\[EAcute]dnout na \
n\[AAcute]sleduj\[IAcute]c\[IAcute]m grafu.\
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Cell["\<\
Nyn\[IAcute] nech\[AAcute]me SVM, aby si transformovalo data do vy\[SHacek]\
\[SHacek]\[IAcute] dimenze pomoc\[IAcute] polynomi\[AAcute]ln\[IAcute]ho \
kernelu a n\[AAcute]sledn\[EHacek] provedlo klasifikaci. Ke klasifikaci pou\
\[ZHacek]ijeme stejn\[AAcute] data jako v p\[RHacek]\[IAcute]pad\[EHacek] \
klasifikace s chybovou funkc\[IAcute] v\[YAcute]\[SHacek]e.  Graf \
umo\[ZHacek]nuje interaktivn\[EHacek] nastavovat stupen polynomu.\
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Cell["\<\
Z graf\[URing] je patrn\[EAcute], \[ZHacek]e p\[RHacek]i pou\[ZHacek]it\
\[IAcute] n\[IAcute]zk\[EAcute]ho stupn\[EHacek] polynomu se SVM model nedou\
\[CHacek]uje, naopak p\[RHacek]i pou\[ZHacek]it\[IAcute] vysok\[EAcute]ho \
stupn\[EHacek] je model p\[RHacek]eu\[CHacek]en\[YAcute]. Vhodn\[AAcute] \
hodnota stupn\[EHacek] polynomu se hled\[AAcute] experiment\[AAcute]ln\
\[EHacek], nej\[CHacek]ast\[EHacek]ji k\[RHacek]\[IAcute]\[ZHacek]ovou \
validac\[IAcute].\
\>", "Text",
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\[AAcute]drov\[AAcute] funkce. Jej\[IAcute] p\[RHacek]edpis je \
n\[AAcute]sleduj\[IAcute]c\[IAcute] ",
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nastavit parametr t."
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Z\[AAcute]vislost RBF kernelu na parametru t si m\[URing]\[ZHacek]ete prohl\
\[EAcute]dnout na n\[AAcute]sleduj\[IAcute]c\[IAcute]m grafu.\
\>", "Text",
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Cell["\<\
Nyn\[IAcute] nau\[CHacek]\[IAcute]me SVM za pou\[ZHacek]it\[IAcute] \
transformace dat pomoc\[IAcute] RBF kernelu. Data pou\[ZHacek]ijeme stejn\
\[AAcute] jako v p\[RHacek]\[IAcute]pad\[EHacek] \
polynomi\[AAcute]ln\[IAcute]ho kernelu.\
\>", "Text",
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Cell["\<\
Graf umo\[ZHacek]nuje interaktivn\[EHacek] m\[EHacek]nit patametr t.\
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Cell["\<\
Jak je z graf\[URing] v\[YAcute]\[SHacek]e vid\[EHacek]t, pro ni\[ZHacek]\
\[SHacek]\[IAcute] hodnoty parametru t se SVM nedou\[CHacek]uje, a pro vysok\
\[EAcute] hodnoty se siln\[EHacek] p\[RHacek]eu\[CHacek]uje. Optim\[AAcute]ln\
\[IAcute] hodnota parametru se ur\[CHacek]uje experiment\[AAcute]ln\[EHacek], \
nap\[RHacek]\[IAcute]klad k\[RHacek]\[IAcute]\[ZHacek]ovou validac\[IAcute].\
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Cell["\<\
Ilustrace p\[RHacek]echodu do vy\[SHacek]\[SHacek]\[IAcute] dimenze\
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Cell["\<\
V t\[EAcute]to kapitole si podrobn\[EHacek]ji rozebereme transformaci dat do \
vy\[SHacek]\[SHacek]\[IAcute] dimenze.\
\>", "Text",
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Cell["\<\
Nejprve si vygenerujeme data, na kter\[YAcute]ch budeme transformaci \
demonstrovat.\
\>", "Text",
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Jak je patrn\[EAcute] z grafu, data jsou line\[AAcute]rn\[EHacek] \
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Nejprve si p\[RHacek]iprav\[IAcute]me p\[RHacek]edpisy pro funkce \
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V grafu jsou vid\[EHacek]t transformovan\[AAcute] data, a tak\[EAcute] funkce \
polynomi\[AAcute]ln\[IAcute]ho kernelu, pomoc\[IAcute] kter\[EAcute]ho byla \
transformace provedena. Za pov\[SHacek]imnut\[IAcute] stoj\[IAcute] hodnoty \
osy z. Vid\[IAcute]me tedy, \[ZHacek]e data jsou po transformaci ji\[ZHacek] \
line\[AAcute]rn\[EHacek] separabiln\[IAcute] pomoc\[IAcute] roviny.\
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Najeme op\[EHacek]rn\[EAcute] vektory pro roviny, kter\[EAcute] separuj\
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Sv\[EHacek]tlej\[SHacek]\[IAcute], barevn\[EHacek] or\[AAcute]movan\[EAcute] \
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\[IAcute]d, \[CapitalCHacek]ern\[EHacek] or\[AAcute]movan\[AAcute], nejv\
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V\[YAcute]slednou klasifikaci si m\[URing]\[ZHacek]eme p\[RHacek]ibl\[IAcute]\
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Tlust\[AAcute] \[CHacek]ern\[AAcute] \[CHacek]\[AAcute]ra p\[RHacek]edstavuje \
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V posledn\[IAcute] \[CHacek]\[AAcute]sti si uk\[AAcute]\[ZHacek]eme pou\
\[ZHacek]\[IAcute]t\[IAcute] SVM na re\[AAcute]ln\[YAcute]ch datech z datab\
\[AAcute]ze UCI. K tomuto \[UAcute]\[CHacek]elu pou\[ZHacek]ijeme \
zn\[AAcute]m\[AAcute] Iris data.\
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Nejprve si data na\[CHacek]teme. Pozor, je pot\[RHacek]eba p\[RHacek]ipojen\
\[IAcute] k internetu.\
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D\[AAcute]le provedeme jednoduch\[EAcute] p\[RHacek]edzpracov\[AAcute]n\
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N\[IAcute]\[ZHacek]e jsou parametry pou\[ZHacek]it\[EAcute] pro klasifikaci. \
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SVM v z\[AAcute]kladn\[IAcute] podob\[EHacek] um\[IAcute] klasifikovat pouze \
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\[IAcute] t\[RHacek]i t\[RHacek]\[IAcute]dy, mus\[IAcute]me pou\[ZHacek]\
\[IAcute]t men\[SHacek]\[IAcute] okliku.
Nejsna\[ZHacek]\[SHacek]i je zobecn\[EHacek]n\[IAcute] dat na dv\[EHacek] t\
\[RHacek]\[IAcute]dy n\[AAcute]sleduj\[IAcute]c\[IAcute]m zp\[URing]sobem. \
Vybereme jednu t\[RHacek]\[IAcute]du, tu nech\[AAcute]me beze zm\[EHacek]ny a \
zbyl\[EAcute] dv\[EHacek] t\[RHacek]\[IAcute]dy slou\[CHacek]\[IAcute]me do \
jedn\[EAcute] (1 vs. others). Takto budedme postupovat pro v\[SHacek]echny t\
\[RHacek]\[IAcute]dy. V na\[SHacek]em p\[RHacek]\[IAcute]pad\[EHacek] z\
\[IAcute]sk\[AAcute]me 3 datasety. Na ka\[ZHacek]d\[EAcute]m datasetu natr\
\[EAcute]nujeme jeden SVM model.\
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V\[YAcute]stupem jsou t\[RHacek]i grafy. Prvn\[IAcute] graf ud\[AAcute]v\
\[AAcute] klasifikaci do prvn\[IAcute] t\[RHacek]\[IAcute]dy, druh\[YAcute] \
graf do druh\[EAcute] t\[RHacek]\[IAcute]dy a t\[RHacek]et\[IAcute] graf do t\
\[RHacek]et\[IAcute] t\[RHacek]\[IAcute]dy. V\[YAcute]slednou klasifikaci ur\
\[CHacek]\[IAcute]me tak, \[ZHacek]e jako v\[YAcute]stupn\[IAcute] t\[RHacek]\
\[IAcute]du bereme tu t\[RHacek]\[IAcute]du, jej\[IAcute]\[ZHacek] model \
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Pro porovn\[AAcute]m\[IAcute] si zobraz\[IAcute]me je\[SHacek]t\[EHacek] spr\
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\[CapitalUAcute]sp\[EHacek]\[SHacek]nost klasifikace si \
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