Python ではじめるスパースモデリング

Transcript

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   Python ではじめるスパースモデリング 2018年5月19日 PyCon mini Osaka @ ヤフー株式会社 GFOオフィス

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   છాوࢤ ͦΊ͔ͩͨ͠ • גࣜձࣾϋΧϧε औక໾$50 • 1ZUIPO
   ྺ 
   ೥ • .BDIJOF
   -FBSOJOH
   .FFUVQ
   ,"/4"*

   ্ཱͪ͛ • IUUQTNMNLBOTBJDPOOQBTTDPN
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   ϋΧϧεͱ͸ • ϥΠϑαΠΤϯεɾ࢈ۀ෼໺ Y
   "* • εύʔεϞσϦϯάΛ࣠ͱͨ͠σʔλղੳ • ౦๺େֶɾେؔਅ೭।ڭत͕ΞυόΠβʔ

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   ຊ೔ͷΰʔϧ • εύʔεϞσϦϯάΛ஌ͬͯ΋Β͏ • 1ZUIPO
   ͰͷΞϧΰϦζϜ࣮૷ΛΈͯ΋Β͏ • ߟ͑ํɾಛ௃ʹڵຯΛ΋ͬͯ΋Β͏

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   εύʔεϞσϦϯάͱ͸

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   εύʔεϞσϦϯά • σʔλʹ಺ࡏ͢Δεύʔεੑʹண໨ͯ͠ɺࣄ৅ ΛϞσϧԽ͢Δख๏ • ୯ҰͷΞϧΰϦζϜΛࢦ͢Θ͚Ͱ͸ͳ͍ • ೥ࠒ͔Β׆ൃʹݚڀ͞Ε͍ͯΔ

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   σϞ • Χϝϥ͔Βͷը૾Λֶश • എܠΛਪఆ • ҠಈମΛݕग़

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   ػցֶशͷಋೖ࣌ͷ՝୊ • ࣗಈԽ͸͍͕ͨ͠ɺઆ໌੹೚͸͋Δ • σʔλऩूͷ࣌ؒ΍ίετ͕େ͖͍ • ϋʔυ΢ΣΞͷίετ͸཈͍͑ͨ

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   εύʔεϞσϦϯά΁ͷظ଴ • ೖྗಛ௃ྔͷதͷॏཁͳ΋ͷ͕Θ͔Δ • গྔͷ৘ใ͔Β΋ਪఆΛߦ͑Δ • (16
   ؀ڥҎ֎Ͱ΋ಈ࡞͢Δ

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    ઢܗճؼͰͷεύʔεϞσϦϯά • લఏ • ग़ྗ Z ͸ɺೖྗ Y
    ͷઢܗ݁߹ͱ؍ଌϊΠζЏͰදݱ͞ΕΔ • ೖྗ

    Y ͸ N ࣍ݩɺ؍ଌ͞Εͨ Z ͸ O ݸ͋Δͱ͢Δ ! = #$ %$ + ⋯ + #( %( + ) 㱺 Z Λ͍͍ײ͡ʹઆ໌͢Δ X Λ஌Γ͍ͨ
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    ઢܗճؼͰͷεύʔεϞσϦϯά • ղ͘΂͖໰୊ • ؍ଌ஋ Z ͱਪఆͨ͠ X ͔Βܭࢉ͞ΕΔ஋ͷೋ৐ޡࠩΛ࠷খԽ min

    1 2 & − () * 㱺 Z ͷαϯϓϧ਺͕ Y ͷ࣍ݩΑΓ΋খ͍͞৔߹͸ʁ
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    εύʔε੍໿ͷ௥Ճ • ະ஌਺ͷ਺ΑΓํఔࣜͷ਺͕গͳ͍࿈ཱํఔࣜ • Y
    ʹର͢Δεύʔεͳ੍໿Λ௥Ճͯ͠ղ͘ • ʮͳΔ΂͘গͳ͍ Y Ͱ৚݅Λຬͨ͢ʯ 㱺ʮͳΔ΂͘ଟ͘ͷ

    X Λ 
    ʹ͢Δʯ • ૉ௚ʹ΍Δͱɺ૊Έ߹Θͤ࠷దԽ໰୊㽊
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    -
    ϊϧϜ࠷దԽ • ੍໿৚݅Λ؇࿨ • ʮX ͷઈର஋ͷ૯࿨ΛͳΔ΂͘খ͘͢͞Δʯ • ؇࿨ͯ͠΋େҬత࠷దղ͕ಘΒΕΔ • ਺஋తʹղ͘͜ͱ͕Ͱ͖Δ

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    • -FBTU
    "CTPMVUF
    4ISJOLBHF
    BOE
    4FMFDUJPO
    0QFSBUPS ͷུ • -
    ϊϧϜΛਖ਼ଇԽ߲ͱͯ͠௥Ճͨ͠໨తؔ਺ -BTTP min 1 2

    & − () * + , ( - 㱺 ਖ਼ଇԽύϥϝʔλЕͰεύʔε੍໿ͷޮ͖Λௐ੔
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    छʑͷΞϧΰϦζϜ • ࠲ඪ߱Լ๏ $PPSEJOBUF
    %FTDFOU • ࠷খ֯ճؼ -FBTU
    "OHMF
    3FHSFTTJPO • ൓෮ॖখᮢ஋ΞϧΰϦζϜ *45"

    • ަޓํ޲৐਺๏ "%..
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    ྫɿ࠲ඪ߱Լ๏ͷΞϧΰϦζϜ 1. #$ % = 1, … , ) ΛॳظԽ

    2. + #$ = , - . /0 . 1 , 2 Ͱߋ৽ 3($) = 6 − 8 9:$ ; 9 #9 ͱ͠ɺ, ͸ೈᮢ஋࡞༻ૉͱ͢Δ 3. ऩଋ৚݅·Ͱ܁Γฦ͠
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    ೈᮢ஋࡞༻ૉ • ஋Λθϩʹ͚ۙͮΔ࡞༻Λ࣋ͭ S ", $ = & " −

    $, (" ≥ $) 0, (−$ < " < $) " + $, (" ≤ −$)
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    ྫɿ࠲ඪ߱Լ๏ͷ࣮૷ྫ #  def soft_threshold(X, thresh): return np.where(np.abs(X) <= thresh,

    0, X - thresh * np.sign(X)) # 
     w_cd = np.zeros(n_features) for _ in range(n_iter): for j in range(n_features): w_cd[j] = 0.0 r_j = y - np.dot(X, w_cd) w_cd[j] = soft_threshold(np.dot(X[:, j], r_j) / n_samples, alpha)
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    ࣮ߦ݁Ռ ೖྗಛ௃ྔͷ࣍ݩ͸  
    ඇθϩཁૉ͸ 
    αϯϓϧ਺͸

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    ͦͷଞͷ࣮૷ • TDJLJUMFBSO • ࠲ඪ߱Լ๏ͱ࠷খ֯ճؼ • IUUQTDJLJUMFBSOPSHTUBCMFNPEVMFTHFOFSBUFETLMFBSOMJOFBS@NPEFM-BTTPIUNM • IUUQTDJLJUMFBSOPSHTUBCMFNPEVMFTHFOFSBUFETLMFBSOMJOFBS@NPEFM-BTTP-BSTIUNM •

    TQNJNBHF • ަޓํ޲৐਺๏ • IUUQTHJUIVCDPNIBDBSVTTQNJNBHFCMPCEFWFMPQNFOUTQNJNBHFMJOFBS@NPEFMBENNQZ
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    TQNJNBHF • εύʔεϞσϦϯά༻ϥΠϒϥϦ • ը૾ղੳʹ༻͍ΒΕΔΞϧΰϦζϜΛத৺ʹ • TDJLJUMFBSO
    ΠϯλʔϑΣʔεʹ४ڌ • IUUQTHJUIVCDPNIBDBSVTTQNJNBHF

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    ը૾ॲཧ΁ͷద༻ • جຊΞΠσΟΞ • ը૾͔ΒύονΛ੾Γग़͢ • ύονΛಉαΠζͷࣙॻجఈͷઢܕ݁߹Ͱදݱ͢Δ • ը૾શମΛදݱ͢ΔͨΊࣙॻ΋ֶश͢Δ

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    ը૾ॲཧ΁ͷద༻ :
    ը૾ "
    ࣙॻ ! "# $# 9
    ܎਺

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    ࣙॻʹΑΔ࠶ߏ੒ Y
    ύον جఈͰͷ࠶ߏ੒݁Ռ

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    ྫɿࣙॻֶशͱ࠶ߏ੒ #  
    patches = extract_simple_patches_2d(img, patch_size) #

      patches = patches.reshape(patches.shape[0], -1).astype(np.float64) intercept = np.mean(patches, axis=0) patches -= intercept patches /= np.std(patches, axis=0) #   model = MiniBatchDictionaryLearning(n_components=n_basis, alpha=1, n_iter=n_iter, n_jobs=1) model.fit(patches) #  reconstructed_patches = np.dot(code, model.components_) reconstructed_patches = reconstructed_patches.reshape(len(patches), *patch_size) reconstructed = reconstruct_from_simple_patches_2d(reconstructed_patches, img.shape)
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    ܽଛิ׬΁ͷద༻ ܽଛ஋Λߟྀͨࣙ͠ॻֶशʹΑΔ৘ใ෮ݩ ը૾ :
    ʹର͠ྼԽ࡞༻ૉ .
    ͕͔͔Δͱߟ͑ͯॲཧΛߦ͏

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    ·ͱΊ

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    εύʔεϞσϦϯάͱ͸ • ೖྗಛ௃ྔͷதͷॏཁͳ΋ͷ͕Θ͔Δ • গྔͷ৘ใͰ΋͸͡ΊΔ͜ͱ͕Ͱ͖Δ • طଘ࣮૷Λ࢖ͬͯؾܰʹࢼͤΔ • TDJLJUMFBSO
    ΍ TQNJNBHF

    • ຊ೔ͷ಺༰ ˠ IUUQTHJUJPWQY2