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階層クラスタリングにおける仮説検定
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saltcooky
May 23, 2020
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階層クラスタリングにおける仮説検定
saltcooky
May 23, 2020
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Transcript
֊ΫϥελϦϯάʹ͓͚ΔԾઆݕఆ !TBMUDPPLZ 5PLZP3 1
୭ !TBMUDPPLZ • 3ྺɿ͙Β͍͔ͳ • ۈઌɿݪ॓ʹ͋Δ*5ܥͷձࣾ • ࣄ༰ɿ3%తͳ෦ॺͰ ɹɹɹ3Λͬͨσʔλੳ͞Μ ৽ਓݚमͷ"*ߨ࠲ͷ४උ
• झຯɿϑΝογϣϯඒज़ؗ८Γ 2
༰ΛҰݴͰ ίϩφΟϧεͷܥ౷ੳʹར༻͞Ε͍ͯΔ ΫϥελϦϯάʹ͓͚Δ౷ܭతԾઆݕఆΛհ 3 5IFTQFDJFT4FWFSFBDVUFSFTQJSBUPSZTZOESPNFSFMBUFEDPSPOBWJSVTDMBTTJGZJOHO$P7BOEOBNJOHJU4"34$P7
ΫϥελϦϯάͷؾʹͳΔ͜ͱ σʔλ͕গ͠มΘ͚ͬͨͩͰΫϥελܗͷํ͕มԽ͢Δ ࠓಘΒΕ͍ͯΔσʔλͷΫϥελɺਅͷΫϥελ͔ʁ 4 ಘΒΕ͍ͯΔ σʔληοτ" ಘΒΕ͍ͯͳ͍ σʔληοτ# σʔλ͕ҰͭมԽͱ Ϋϥελͷܗ͕มԽ
͢ΔՄೳੑ͕͋Δ ಘΒΕ͍ͯΔΫϥελʹ ॴଐ͍ͯ͠Δσʔλ ຊʹಉ͡Ϋϥελ͔ʁ
ϒʔτετϥοϓ๏ʹΑΔݕఆ ͭͷର ͷҨࢠ ʹΑΓܗ͞ΕΔथܗਤ ܥ౷थ ௨Γ 5
ը૾Ҿ༻(Ұ෦վม) http://stat.sys.i.kyoto-u.ac.jp/titech/multiboot-j.html
ϒʔτετϥοϓ๏ʹΑΔݕఆ w /ݸͷઆ໌ม Ҩࢠྻ ͷσʔλ͔ΒॏෳΛڐ͠ɺ/ݸͷઆ໌มΛ ϦαϯϓϦϯάͯ͠ϒʔτετϥοϓඪຊΛੜ w ϦαϯϓϦϯάͨ͠σʔλΛ༻͍ͯथܗਤΛ࡞͢Δ w ͜ΕΛ#ճ܁Γฦ͢͜ͱͰಘΒΕͨ#ݸͷथܗਤಘΒΕ·͢
6 $ $ 5 ( ( 5 ( 5 ( ( ( ( $ ( 5 ( ( $ ( 5 $ $ 5 ( ( 5 ( 5 ( ( ( ( $ ( 5 ( ( $ ( 5 $ $ 5 ( ( 5 ( 5 ( ( ( ( $ ( 5 ( ( $ ( 5
7 ϒʔτετϥοϓ๏ʹΑΔथܗਤΛ/ݸ࡞͢Δ͜ͱͰɺ֤थܗਤ͕ಘΒ ΕΔ֬Λਪఆ͢Δ͜ͱ͕Ͱ͖Δɻ ը૾Ҿ༻(Ұ෦վม) http://stat.sys.i.kyoto-u.ac.jp/titech/multiboot-j.html ϒʔτετϥοϓ๏ʹΑΔݕఆ
ϒʔτετϥοϓ๏ʹΑΔݕఆ 8 4IJNPEBJSB)BTFHBXBݕఆ थܗਤͷ#4๏ʹΑΔݕఆͰɺݕग़ͷِӄੑ͕ଟ͘ͳͬͯ͠·͏ͨΊɺ ଟॏൺֱʹΑΔӨڹΛิਖ਼ͨ͠ݕఆ ը૾Ҿ༻(Ұ෦վม) http://stat.sys.i.kyoto-u.ac.jp/titech/multiboot-j.html
Ϛϧνεέʔϧϒʔτετϥοϓ "QQSPYJNBUFMZ6OCJBTFEݕఆ ϦαϯϓϦϯάΛ/͔Β༷ʑͳΛͱΔ/`ʹ͢ΔϚϧνεέʔϧϒʔτ ετϥοϓ๏ʹΑΔݕఆ 4)ݕఆͳͲΑΓෆภͳਪఆΛߦ͏͜ͱ͕Ͱ͖Δ 9 $ $ 5
( ( 5 ( 5 ( ( ( ( $ ( 5 ( ( $ ( 5 $ $ 5 5 $ $ 5 ( ( 5 ( 5 ( ( ( ( $ ( 5 ( ( $ ( 5 $ $ 5 5 $ $ 5 ( ( 5 ( 5 ( ( ( ( $ ( 5 ( ( $ ( 5 $ $ 5 5
Ϛϧνεέʔϧϒʔτετϥοϓ 10 ͳͥϚϧνεέʔϧʹ͢Δ͜ͱͰෆภͳਪఆΛߦ͏͜ͱ͕Ͱ͖Δͷ͔ زԿֶతʹߟ͑ΔͱϚϧνεέʔϧʹ͢Δ͜ͱͰɺԾઆͷۭؒͷܗঢ়Λ ௨ৗͷݕఆʹ͚ۙͮΔ͜ͱ͕Ͱ͖Δ ৄ͘͠ࢀߟจݙ UݕఆͳͲ ܥ౷थʹ͓͚Δݕఆ ը૾Ҿ༻ https://www.ism.ac.jp/editsec/toukei/pdf/50-1-033.pdf
3ͰͬͯΈΔ 11 ./*45ͷσʔλ͔Β ͷσʔλΛݸͣͭϥϯμϜʹऔಘ
3ͰͬͯΈΔ 12 3Ͱ"6ݕఆΛߦ͏ͨΊʹQWDMVTUύοέʔδΛར༻͢Δ ɹlibrary(pvclust) ɹlibrary(parallel) ɹcl <- makeCluster(detectCores()) #ฒྻԽͷ͓·͡ͳ͍ ɹ
ɹ# આ໌ม͕ߦɺର͕ྻͷঢ়ଶʹ͢ΔͨΊʹసஔ ɹmnist_df_t <- ɹɹɹɹmnist_df %>% ɹɹɹɹdplyr::select(-label) %>% ɹɹɹɹt() ɹcolnames(mnist_df_t) <- mnist_df$label ɹsa <- 9^seq(-1,1,length=13)ɹ# ϚϧνεέʔϧϒʔτετϥοϓͷεέʔϧྻΛੜ ɹmnist_boot <- pvclust(data = mnist_df_t, ɹ r = 1/sa, ɹ nboot = 2000, ɹ method.hclust = "ward.D2", ɹɹɹɹɹɹɹɹɹɹɹɹɹparallel = cl)
3ͰͬͯΈΔ 13 ݁ՌΛ֬ೝ ɹ> mnist_boot ɹCluster method: ward.D2 ɹDistance :
euclidean ɹEstimates on edges: ɹ si au bp se.si se.au se.bp v c pchi ɹ1 0.999 1.000 0.999 0.000 0.000 0.000 -3.175 0.156 0.000 ɹ2 0.979 0.990 0.971 0.001 0.001 0.001 -2.117 0.221 0.000 ɹ3 0.579 0.801 0.759 0.004 0.002 0.001 -0.775 0.073 0.000 ɹ4 0.392 0.718 0.655 0.003 0.002 0.001 -0.487 0.089 0.000 ɹ5 0.771 0.900 0.852 0.004 0.002 0.002 -1.151 0.105 0.000 ɹ6 0.112 0.634 0.455 0.003 0.002 0.001 -0.119 0.231 0.000 ɹ7 0.213 0.795 0.323 0.004 0.002 0.002 -0.182 0.641 0.000 ɹ8 0.532 0.770 0.755 0.004 0.002 0.001 -0.716 0.025 0.000 ɹ9 0.266 0.779 0.394 0.004 0.002 0.002 -0.250 0.520 0.000 ɹ10 0.915 0.969 0.878 0.003 0.001 0.002 -1.518 0.354 0.183 ɹ11 0.223 0.757 0.397 0.004 0.002 0.001 -0.211 0.471 0.000 ɹ12 0.229 0.704 0.475 0.003 0.002 0.001 -0.237 0.299 0.000 ɹ13 0.246 0.752 0.409 0.004 0.002 0.001 -0.235 0.464 0.017 ɹ14 0.229 0.691 0.492 0.003 0.002 0.001 -0.239 0.258 0.000
3ͰͬͯΈΔ 14 ݁ՌΛՄࢹԽͯ͠ΈΔ QΛ༗ҙͱ͢Δ ɹplot(mnist_boot, cex=0.5, cex.pv=0.5)ɹ# σϯυϩάϥϜͷϓϩοτ ɹpvrect(mnist_boot,
alpha = 0.9, pv = “au") # p-value >= 0.9 Λғ͏ ༗ҙ ͦͷଞ ༗ҙ ͦͷଞ
3ͰͬͯΈΔ 15 ݁ՌΛՄࢹԽͯ͠ΈΔ ɹplot(mnist_boot, cex=0.5, cex.pv=0.5)ɹ# σϯυϩάϥϜͷϓϩοτ ɹpvrect(mnist_boot, alpha =
0.9, pv = “au") # p-value >= 0.9 Λғ͏ ڑ͍͕ۙ ༗ҙͰͳ͍
؆୯ʹ·ͱΊ w֊ΫϥελϦϯάʹ͓͚Δϒʔτετϥοϓ๏Λ༻͍ͨ ԾઆݕఆΛհ wϦαϯϓϦϯάΛϚϧνεέʔϧ ༷ʑͳΛͱΔ ʹ͢Δ ͜ͱͰෆภͳݕఆΛߦ͏͜ͱ͕Ͱ͖Δ w3ͰQWDMVTUύοέʔδͷQWDMVTUؔΛ༻͍Δ͜ͱͰ࣮ ߦ͢Δ͜ͱͰ͖Δ 16
ࢀߟ ϒʔτετϥοϓ๏ʹΑΔΫϥελੳͷόϥπΩධՁ IUUQTXXXJTNBDKQFEJUTFDUPVLFJQEGQEG Ϛϧνεέʔϧϒʔτετϥοϓͷۙཧ ɹIUUQTXXXUFSSBQVCDPKQKPVSOBMTKKTTKQEGQEG ϚϧνεςοϓʹϚϧνεέʔϧɾϒʔτετϥοϓ๏Լฏӳण ɹIUUQTUBUTZTJLZPUPVBDKQUJUFDINVMUJCPPUKIUNM Ϛϧνεέʔϧϒʔτετϥοϓ๏ʹΑΔΫϥελϦϯάͷ༗ҙࠩݕఆ ɹIUUQTTBMUDPPLZIBUFOBCMPHDPNFOUSZNVMUJTDBMF@CPPUTUSBQ 17
&/% 18 &OKPZ