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カーネル関数とは

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January 14, 2019

 カーネル関数とは

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kichinosukey

January 14, 2019
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  1. ಺ੵͷΧʔωϧදݱ ↟ȃ Y ͺϖϮϦ⑲τ΀಺᧤͹͔Ν  ᙚ΁fᚌᐠၞ͡΀Y Y hhhΤ᧱ ᨜ͽᕅΈͺᤎ᷀΀ṟ͹࿄ᑾͫΝͥͺ͞͹͟Ν ↟ΰ⑲ϒϰؔ਺΁ᴰ௃Ϟδύϰ΀಺᧤fଈͳᤎ᷀͹ᨷᤅͧΞΝ

    ↟ͥΞ΁fϖϮϦ⑲τ⑲XΤᤎ᷀΀ṟͽᷟᨷ͹͟ΝͥͺΤ᣾ዳͫΝ f(x) = ∑ i αi k(xi , x) ⋯ (5) f(x) = ∑ i αi ϕ(xi )Tϕ(x) ⋯ (6) w = ∑ i αi ϕ(xi )
  2. ਖ਼ఆ஋ੑ ↟͔Νؔ਺L Y Ys ͞ᩆᨷᲩ͹͔Νͺ΁f᥅᣾΀O෪΀ᨨY@ hhh Y@O ͝ΛຌᒿͧΞΝᤎ᷀΀ḝᅾďεϮϥḝᅾĐ͔͞Ν ↟ͥΞͽͶ͖͸ęᮈṟᙚ͞ᓝͽᑤᐔ͹͔Νͺ͟fᤎ᷀΀ᙚ͞᥅᣾΀O ᮈϞδύϰǯ

    ǯ@ hhh ǯ@O ?5ͽͶ͖͸ᕧΜርͶͥͺ͹͔Νďᩆͩ ͡΁ጪᩆᨷᲩᕥĐ K = k(x1 , x1 ) k(x2 , x1 ) ⋯ k(xn , x1 ) k(x1 , x2 ) k(x2 , x2 ) ⋯ k(xn , x2 ) ⋮ ⋮ ⋱ ⋮ k(x1 , xn ) k(x2 , xn ) ⋯ k(xn , xn ) n ∑ i=1 n ∑ j=1 αi αj Kij ≥ 0 ⋯ (8)
  3. ΧʔωϧτϦοΫ ↟طͽᩆᨷᬰᕥΤຬͱͫͥͺ͞Ρ͝͵͸͖Νؔ਺Τᑿ͚΂f಺᧤΀ຌᒿ͞Ᏽ᠓ͽͼΝ ΀͹΁Ħďᤎ᷀΀ἦᥥ΀ζ⑲ξͽͶ͖͸Đ ↟ᴰ௃Ϟδύϰ΀಺᧤ͺͩ͸ᨷᤅͩͱΰ⑲ϒϰ΁|ᩆᨷᲩ}͹͔Ν ↟ᝂͽf᥅᣾΀ᩧᨷᲩؔ਺L Y Ys ͞ରশ L Y

    Ys L Ys Y ͹͔Ξ΂ͯΞ΁|ᴰ௃Ϟδύϰ΀಺ ᧤}͹͔Ν ↟ͥΞ΁ᦉᷯͽΚ͵͸΁዗ᷟᮈᡯ΀ᴰ௃Ϟδύϰ΀಺᧤͞ඦ୯ͼؔ਺ͽͼΝᦉᷯ͞ ͔Ν ↟ͶΐΜfᩆᨷᲩᕥΤΰ⑲ϒϰ΀ᨷᤅͺͫΞ΂ຌᒿᅗΤවΛͭΝͥͺ͞͹͟Ν ↟ͥΞΤ|ΰ⑲ϒϰύϯψδ}ͺ͖͘
  4. ֤Χʔωϧͷಛ௃ w ϊΠζΛ৐ͤͨਖ਼ݭ೾ʹର͢ΔϑΟο ςΟϯάΛ֤ΧʔωϧͰ࣮ࢪ w ্ஈͰ͸Y< >ͷൣғͷϑΟοςΟ ϯάΛ֬ೝ͍ͯ͠Δ͕େ͖ͳࠩҟ͸ ݟΒΕͳ͍ w

    ͔͠͠ɺԼஈͰ͸ֶशσʔλͷൣ ғ֎Λ༧ଌͤ͞Δͱɺଟ߲ࣜ͸ൃ ࢄํ޲ɺ3#'͸΁ऩଋ͢Δํ޲΁ ͱ޲͔͏ w IUUQTHJTUHJUIVCDPN LJDIJOPTVLFZ