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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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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\
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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]\
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Cell["\<\
U SVM je mo\[ZHacek]n\[EAcute] nastavit si chybovou funkci, kter\[AAcute] ur\
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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.\
\>", "Text",
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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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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.\
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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.\
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Cell["\<\
Nejprve si vygenerujeme data, na kter\[YAcute]ch budeme transformaci \
demonstrovat.\
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Cell["\<\
Jak je patrn\[EAcute] z grafu, data jsou line\[AAcute]rn\[EHacek] \
neseparabiln\[IAcute]. Proto pou\[ZHacek]ijeme polynomi\[AAcute]ln\[IAcute] \
kernel k jejich trasformaci do t\[RHacek]\[IAcute] rozm\[EHacek]r\[URing].\
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Cell["\<\
Nejprve si p\[RHacek]iprav\[IAcute]me p\[RHacek]edpisy pro funkce \
pou\[ZHacek]\[IAcute]van\[EAcute] pro samotnou transformaci.\
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Cell["\<\
V grafu jsou vid\[EHacek]t transformovan\[AAcute] data, a tak\[EAcute] funkce \
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Sv\[EHacek]tlej\[SHacek]\[IAcute], barevn\[EHacek] or\[AAcute]movan\[EAcute] \
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Cell["\<\
Tlust\[AAcute] \[CHacek]ern\[AAcute] \[CHacek]\[AAcute]ra p\[RHacek]edstavuje \
v\[YAcute]slednou klasifikaci a slab\[SHacek]\[IAcute] \[CHacek]\[AAcute]ry \
zobrazuj\[IAcute] op\[EHacek]rn\[EAcute] roviny. Sv\[EHacek]tle mod\[RHacek]e \
jsou zv\[YAcute]razn\[EHacek]ny op\[EHacek]rn\[EAcute] vektory.\
\>", "Text",
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Cell["Pou\[ZHacek]it\[IAcute] SVM na re\[AAcute]ln\[YAcute]ch datech", \
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Cell["\<\
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.\
\>", "Text",
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Cell["\<\
Nejprve si data na\[CHacek]teme. Pozor, je pot\[RHacek]eba p\[RHacek]ipojen\
\[IAcute] k internetu.\
\>", "Text",
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D\[AAcute]le provedeme jednoduch\[EAcute] p\[RHacek]edzpracov\[AAcute]n\
\[IAcute] dat. Nejprve rozd\[EHacek]l\[IAcute]me data na vstupn\[IAcute] a v\
\[YAcute]stupn\[IAcute] mno\[ZHacek]inu. V\[YAcute]stupn\[IAcute] \
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\[CHacek]\[IAcute]seln\[EAcute].\
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Cell["\<\
N\[IAcute]\[ZHacek]e jsou parametry pou\[ZHacek]it\[EAcute] pro klasifikaci. \
Jejich zm\[EHacek]nou a n\[AAcute]sledn\[YAcute]m znovuvyhodnocen\[IAcute]m \
bu\[NHacek]ky, ve kter\[EAcute] se prov\[AAcute]d\[IAcute] klasifikace je mo\
\[ZHacek]n\[EAcute] prov\[AAcute]d\[EHacek]t jednoduch\[EAcute] experimenty.\
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Cell["\<\
SVM v z\[AAcute]kladn\[IAcute] podob\[EHacek] um\[IAcute] klasifikovat pouze \
do dvou t\[RHacek]\[IAcute]d. Proto\[ZHacek]e na\[SHacek]e data obsahuj\
\[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. \
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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\
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