ҟৗݕ஌ͷجૅͱ࣮ફ  ϓϩάϥϚͷͨΊͷ਺ֶษڧձ!෱Ԭ  

ࣗݾ঺հ Խֶͷम࢜߸Λऔಘ ௽ాʢͭΔͨʣ 5XJUUFS
!UTVSVCFF ΤϯδχΞྺϲ݄ ফ๷࢜ʹͳΔʢফ๷ୂɾٹٸୂɾՐࡂௐࠪ൝ʣ *5ΤϯδχΞʹస৬ʢ೥݄ʙʣ ʻܦྺʼ ܦྺ 

໨࣍ ʙجૅฤʙ l ҟৗݕ஌ͱ͸ʁ l ҟৗݕ஌ͷԠ༻ྫ l ҟৗσʔλྫ l ҟৗݕ஌ͷΞϓϩʔν l ౷ܭతҟৗݕ஌ͷߟ͑ํ ʙ࣮ફฤʙ l ϗςϦϯάཧ࿦ʹΑΔҟৗݕ஌ l 1ZUIPOʹΑΔ࣮૷ 

ҟৗݕ஌ͱ͸ʁ 

େଟ਺ͷσʔλͱ͸ৼΔ෣͍͕ ҟͳΔσʔλΛݕग़͢Δٕज़ 

େଟ਺ͷσʔλͱ͸ৼΔ෣͍͕ ҟͳΔσʔλΛݕग़͢Δٕज़ σʔλϚΠχϯά نଇੑ ҟৗ σʔλͷࢁ 

ҟৗݕ஌ͷԠ༻ྫ 

ҟৗݕ஌ͷԠ༻ྫ ίϯϐϡʔλ΢Πϧε΍%PT߈ܸͷૣظൃݟ ηΩϡϦςΟ෼໺ ނো༧ஹݕ஌ ػց෼໺ ྲྀߦͷݕ஌ɾ৽τϐοΫͷൃݟɾ ϢʔβߦಈͷมԽݕ஌ ϚʔέςΟϯά෼໺ 

ҟৗσʔλྫ 

ҟৗσʔλྫ̍ 

ҟৗσʔλྫ̍ ҟৗʂ 

ҟৗσʔλྫ̍ ҟৗʂ if value > 120: print('ERROR!') JGจͰݕ஌Ͱ͖ͦ͏ʂ 

ҟৗσʔλྫ̎ 

ҟৗσʔλྫ̎ Կ͔ҟৗ͕ى͖ͯΔ ҟৗʹ΋͍Ζ͍Ζ͋Δ 

ҟৗݕ஌ͷ෼ྨ ֎Ε஋ݕ஌ มԽ఺ݕ஌ ҟৗݕ஌ ٸܹͳৼΔ෣͍ͷมԽΛݕ஌ ࣌ܥྻϞσϧ ଞͱ͸େ͖͘ҟͳΔ஋Λݕ஌ ಠཱϞσϧ 

ҟৗݕ஌ͷ෼ྨ ֎Ε஋ݕ஌ มԽ఺ݕ஌ ҟৗݕ஌ ࠓճ͸ίονͷ࿩ʂ ٸܹͳৼΔ෣͍ͷมԽΛݕ஌ ࣌ܥྻϞσϧ ଞͱ͸େ͖͘ҟͳΔ஋Λݕ஌ ಠཱϞσϧ 

ҟৗݕ஌ͷΞϓϩʔν 

ҟৗݕ஌ͷΞϓϩʔν ஫ɿॏͳΔ෦෼΋͋Γ·͢ Ξϓϩʔνͷछྨ ख๏ྫ ϧʔϧϕʔεɾΞϓϩʔν ڑ཭ʹΑΔΞϓϩʔν ,ۙ๣๏ɺಛҟεϖΫτϧม׵๏ɺଞ ౷ܭతΞϓϩʔν ϗςϦϯάཧ࿦ɺΧʔωϧີ౓ਪఆ๏ɺଞ ػցֶशΞϓϩʔν αϙʔτϕΫλʔϚγϯʢ47.ʣɺ χϡʔϥϧωοτϫʔΫɺଞ 

ҟৗݕ஌ͷΞϓϩʔν ΞϓϩʔνʹΑΓඞཁͳٻΊΒΕΔ஌͕ࣝएׯҟͳΔ ஫ɿॏͳΔ෦෼΋͋Γ·͢ Ξϓϩʔνͷछྨ ख๏ྫ ϧʔϧϕʔεɾΞϓϩʔν ڑ཭ʹΑΔΞϓϩʔν ,ۙ๣๏ɺಛҟεϖΫτϧม׵๏ɺଞ ౷ܭతΞϓϩʔν ϗςϦϯάཧ࿦ɺΧʔωϧີ౓ਪఆ๏ɺଞ ػցֶशΞϓϩʔν αϙʔτϕΫλʔϚγϯʢ47.ʣɺ χϡʔϥϧωοτϫʔΫɺଞ ࠓճ͸ίϨʂ 

ͭ·Γࠓճ͸ɺ ʮ౷ܭతҟৗݕ஌ʹΑΔ ֎Ε஋ݕ஌ʯ ͷ࿩Ͱ͢ 

౷ܭతҟৗݕ஌ͷ ߟ͑ํ 

౷ܭతҟৗݕ஌ͷߟ͑ํ ඪຊநग़ ඪຊ ਅͷ෼෍ ౷ܭతҟৗݕ஌Ͱ͸ɺ؍ଌσʔλ͕͋Δಛఆͷ֬཰Ϟσϧ ֬཰෼෍ ͔Βੜ੒͞Ε͍ͯΔͱԾఆ͢Δɻ ฼ूஂ ਖ਼ৗ࣌ͷ ෼෍ ֶश σʔλ͔Βਖ਼ৗͱͳΔϞσϧΛͭ͘Γɺ͔ͦ͜Β֎ΕΔ΋ͷΛҟৗͱ͢Δɻ 

ೖྗσʔλ ֬཰Ϟσϧ ͷֶश είΞܭࢉ ग़ྗ  ؍ଌσʔλ͔Βσʔλੜ੒ͷ֬཰ϞσϧΛֶश ᶃ ະ஌ύϥϝʔλΛؚΉ֬཰෼෍ΛԾఆ ᶄ σʔλ͔Βະ஌ύϥϝʔλΛਪఆ  ֶशͨ͠ϞσϧΛجʹɺҟৗ౓߹͍ΛείΞϦϯά  ᮢ஋ͷઃఆ ᶃ ᶄ ᶅ ౷ܭతҟৗݕ஌ͷجຊεςοϓ 

ʙ࣮ફฤʙ ϗςϦϯάཧ࿦ʹΑΔ ҟৗݕ஌ 

༻͍Δσʔλ %BWJTσʔλɿਓͷੑผɺଌఆͨ͠਎௕ɾମॏɺ ͓Αͼࣗݾਃࠂͷ਎௕ɾମॏσʔλ IUUQTWJODFOUBSFMCVOEPDLHJUIVCJP3EBUBTFUTEBUBTFUTIUNM 

༻͍Δσʔλ %BWJTσʔλɿਓͷੑผɺଌఆͨ͠਎௕ɾମॏɺ ͓Αͼࣗݾਃࠂͷ਎௕ɾମॏσʔλ IUUQTWJODFOUBSFMCVOEPDLHJUIVCJP3EBUBTFUTEBUBTFUTIUNM มྔͷཧ࿦Λͬ͘͡Γ΍Γ·͢ ଌఆମॏͷΈʂ 

σʔλͷՄࢹԽ ਓͷମॏσʔλͷ෼෍ 

σʔλͷՄࢹԽ ਓͷମॏσʔλͷ෼෍ ֎Ε஋ ౷ܭֶతʹ٬؍తͳਫ४Ͱݕ஌͢Δʹ͸ʁ ֎Ε஋ ౷ܭతҟৗݕ஌ 

ೖྗσʔλ ֬཰Ϟσϧ ͷֶश είΞܭࢉ ग़ྗ ᶃ ᶄ ᶅ ࠶ܝ ౷ܭతҟৗݕ஌ͷجຊεςοϓ  ؍ଌσʔλ͔Βσʔλੜ੒ͷ֬཰ϞσϧΛֶश ᶃ ະ஌ύϥϝʔλΛؚΉ֬཰෼෍ΛԾఆ ᶄ σʔλ͔Βະ஌ύϥϝʔλΛਪఆ  ֶशͨ͠ϞσϧΛجʹɺҟৗ౓߹͍ΛείΞϦϯά  ᮢ஋ͷઃఆ 

̍
؍ଌσʔλ͔Βσʔλੜ੒ͷ֬཰ϞσϧΛֶश ˞σʔλͷதʹ͸ҟৗͳ؍ଌσʔλؚ͕·Ε͍ͯͳ͍͔ɺ ؚ·Ε͍ͯͨͱͯ͠΋ͦͷӨڹ͸ແࢹͰ͖ΔͱԾఆ ؍ଌσʔλ͕ݸ͋Δͱ͖ɺσʔλΛ·ͱΊͯͱ͍͏ه߸Ͱද͢ɻ ᶃ ະ஌ύϥϝʔλΛؚΉ֬཰෼෍ΛԾఆ ɿฏۉ 2ɿ෼ࢄ ֬཰Ϟσϧ ʹ ਖ਼ن෼෍ΛԾఆ ϗςϦϯάཧ࿦ 

ᶄ σʔλ͔Βະ஌ύϥϝʔλΛਪఆ ฏۉ、෼ࢄ2Λ؍ଌσʔλ͔Βਪఆ ࠷໬ਪఆ ܭࢉͷ౎߹্ɺ໬౓ؔ਺ͷࣗવର਺Λͱͬͨର਺໬౓ؔ਺Λ࠷େԽ͢Δɻ ̍
؍ଌσʔλ͔Βσʔλੜ੒ͷ֬཰ϞσϧΛֶश ؍ଌσʔλ͕ޓ͍ʹಠཱ 

ͱͨ͠৔߹ɺର਺໬౓໬౓ؔ਺͸ɺ ࠷େԽ͢ΔύϥϝʔλΛٻΊΔͨΊɺͱͰͦΕͧΕภඍ෼ͯ͠θϩͱ͓͘ ̍
؍ଌσʔλ͔Βσʔλੜ੒ͷ֬཰ϞσϧΛֶश 

ฏۉɾ෼ࢄͷਪఆ஋ͱͯ͠ɺ؍ଌσʔλͷඪຊฏۉɾඪຊ෼ࢄΛ ࠾༻͢Δ͜ͱΛҙຯ͍ͯ͠Δ ֶशࡁΈ֬཰Ϟσϧʢ༧ଌ෼෍ʣ ͕ಘΒΕΔɻ ˞ਪఆ஋Ͱ͋Δ͜ͱΛ໌ࣔ͢ΔͨΊʮ? ϋοτ ʯΛ͚ͭͨɻ ̍
؍ଌσʔλ͔Βσʔλੜ੒ͷ֬཰ϞσϧΛֶश 

ֶ̎शͨ͠ϞσϧΛجʹɺҟৗ౓߹͍ΛείΞϦϯά ҟৗ౓ͷఆٛͱͯ͠ɺ ෛͷର਺໬౓Λ࠾༻ ৽ͨͳ؍ଌ஋(ʹର͢Δҟৗ౓(() ͸ɺ ୈ߲͸؍ଌσʔλ(ʹґଘ͠ͳ͍ͷͰແࢹ͢ΔɻશମʹΛ͔͚Δͱɺ ඪຊฏۉ͔ΒͷͣΕͷେ͖͞ ΋ͱ΋ͱ͹Β͖ͭͷେ͖͍΋ͷ͸ଟগͷ ͣΕͰ΋ଟΊʹݟΔ ෼ࢠɿ ෼฼ɿ ҟৗ౓ ௚ײʹ͍ۙʂ 

̏
ᮢ஋ͷઃఆ ҟৗ౓ͷᮢ஋Λઃఆ͢Δ͜ͱͰҟৗ൑ఆͰ͖Δʂ Ͱ΋ɺᮢ஋͸Ͱ͖Δ͚ͩ٬؍తج४ʹج͍ܾͮͯΊ͍ͨɾɾ ϗςϦϯάཧ࿦ͷҟৗ౓ ҟৗ౓͕ै͏֬཰෼෍Λɺ ໌ࣔతʹಋ͘͜ͱ͕Ͱ͖Δʂ ͭ·Γɺύʔηϯτ஋ʹΑΓҟৗ൑ఆΛߦ͏͜ͱ͕Ͱ͖Δʂ ྫ͑͹ ʮਓʹਓ͔͍͠ͳ͍ϨΞͩͬͨ͞Βҟৗͱ൑அ͠Α͏ʯ 

̏
ᮢ஋ͷઃఆ σʔλ਺͕े෼ʹେ͖͍࣌ɺҟৗ౓(()͸ࣗ༝౓ͷΧΠೋ৐෼෍ʹै͏ ɿඪ४ਖ਼ن෼෍(0, 1) ʹै͏֬཰ม਺ ࣗ༝౓OͷΧΠೋ৐෼෍ɿ ྫ͑͹ɺ(() = 2.0ͷ஋ ͕ى͜Γ͏Δ֬཰͸ʁ ࣗ༝౓ͷΧΠೋ৐෼෍ ͜͜Λੵ෼͢Δʂ 

1ZUIPOʹΑΔ࣮૷ 

࡞Γ͍ͨ΋ͷ ೖྗͱͯ͠ɺσʔλͱҟৗ౓ͷᮢ஋  Λ༩͑Δͱɺ ग़ྗͱͯ͠ɺҟৗ஋ͱͦͷΠϯσοΫε൪߸ Λฦؔ͢਺Λ࡞Δɻ ࢖༻ϥΠϒϥϦ /VN1Z 4DJ1Z ΧΠೋ৐෼෍ͷ ੵ෼஋ͷࢉग़ʹར༻ ࢖༻ݴޠ 1ZUIPO
 

import numpy as np from scipy import stat def hotelling_1d(data, threshold): """ Parameters ---------- data : Numpy array threshold : float Returns ------- List of tuples where each tuple contains index number and anomalous value. """ #Covert raw data into the degree of abnormality avg = np.average(data) var = np.var(data) data_abn = [(x - avg)**2 / var for x in data] #Set the threshold of abnormality abn_th = stats.chi2.interval(1-threshold, 1)[1] #Abnormality determination result = [] for (index, x) in enumerate(data_abn): if x > abn_th: result.append((index, data[index])) return result 

1ZUIPOʹΑΔ࣮૷ hotelling_1d(data, 0.01) #-> [(11, 166), (20, 119)] ᮢ஋ 
 

1ZUIPOʹΑΔ࣮૷ hotelling_1d(data, 0.01) #-> [(11, 166), (20, 119)] ᮢ஋ 
 

ϗςϦϯάཧ࿦ͷݶք ؍ଌσʔλಉ͕࢜ޓ͍ʹಠཱͰɺͦΕͧΕ͕୯Ұͷ ਖ਼ن෼෍ʹै͍ͬͯΔͱԾఆ͍ͯ͠ΔͨΊɺ ̍
ෳ਺ͷϞʔυ͕͋ΔΑ͏ͳෳࡶͳܥ΁ͷద༻͕ࠔ೉ ̎
஋͕ಈతʹมԽ͢Δ࣌ܥྻσʔλ΁ͷద༻͕ࠔ೉ 

·ͱΊ ϗςϦϯάཧ࿦Ͱ͸ɺ؍ଌσʔλΛਖ਼ن෼෍ ʹै͏ͱԾఆ͢Δɻ ఆٛͨ͠ҟৗ౓͕ɺΧΠೋ৐෼෍ʹै͏ͨΊɺ ΧΠೋ৐෼෍ʹج͖ͮܭࢉͨ͠ҟৗ౓ͷᮢ஋ ʹΑΓҟৗ൑ఆͰ͖Δɻ ଟ࣍ݩσʔλ΍࣌ܥྻσʔλͷҟৗݕ஌͸ ·ͨผͷػձʢ1Z'VLVPLBɺσʔλαΠΤϯε ษڧձʁʣʹ࿩͠·͢ʂ