Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
A Degeneracy Framework for Graph Similarity: グラ...
Search
OpenJNY
November 04, 2018
Technology
0
220
A Degeneracy Framework for Graph Similarity: グラフ類似度のための縮退フレームワーク
OpenJNY
November 04, 2018
Tweet
Share
More Decks by OpenJNY
See All by OpenJNY
Linux Networking Tools: 101
openjny
63
17k
BERT の解剖学: interpret-text による自然言語処理 (NLP) モデル解釈
openjny
11
3k
NSG フローログを支える技術 - NVF Advanced Flow Logging
openjny
1
770
グラフ分析ナイト - グラフデータ分析 入門編
openjny
2
930
Sports Analyst Meetup #5 LT - 目指せPGAツアー賞金王
openjny
1
1.1k
Representation Learning for Scale-free Networks: スケールフリーネットワークに対する表現学習
openjny
0
53
Handbook of Knowledge Representation - Chapter 2: Satisfiability Solvers
openjny
0
120
Other Decks in Technology
See All in Technology
XP matsuri 2024 - 銀河英雄伝説に学ぶ
kawaguti
PRO
3
500
Interfacing Kernel C APIs from Rust
ennael
PRO
0
210
マーケットプレイス版Oracle WebCenter Content For OCI
oracle4engineer
PRO
2
200
Amazon BedrockとPR-Agentでコードレビュー自動化に挑戦・実際に運用してみた
diggymo
0
560
【shownet.conf_】ShowNet 2024 ~ Inter * Network ~
shownet
PRO
0
380
「ばん・さく・つき・たー!」にならないためにSHIROBAKOから 学んだこと
ysknsid25
3
180
Hazard pointers with reference counter
ennael
PRO
0
110
Causal Impactを用いたLINE Pay UIの効果検証とABテスト実施への貢献
lycorptech_jp
PRO
3
490
ORM と向き合う
hoto17296
7
5.9k
Rubyはなぜ「たのしい」のか? / Why is Ruby a programmers' best friend? #tqrk15
expajp
4
1.7k
第45回 MLOps 勉強会 - ML Test Score を用いた機械学習システムの定量的なアセスメント
masatakashiwagi
3
210
スクラム導入の舞台裏:QAエンジニアがスクラムマスターになるまで
bubo1201
0
120
Featured
See All Featured
実際に使うSQLの書き方 徹底解説 / pgcon21j-tutorial
soudai
167
48k
Performance Is Good for Brains [We Love Speed 2024]
tammyeverts
1
240
Templates, Plugins, & Blocks: Oh My! Creating the theme that thinks of everything
marktimemedia
26
2k
Put a Button on it: Removing Barriers to Going Fast.
kastner
58
3.4k
Keith and Marios Guide to Fast Websites
keithpitt
408
22k
Robots, Beer and Maslow
schacon
PRO
157
8.2k
Side Projects
sachag
452
42k
How to train your dragon (web standard)
notwaldorf
87
5.6k
From Idea to $5000 a Month in 5 Months
shpigford
380
46k
Refactoring Trust on Your Teams (GOTO; Chicago 2020)
rmw
30
2.6k
How to name files
jennybc
77
98k
How To Stay Up To Date on Web Technology
chriscoyier
786
250k
Transcript
"%FHFOFSBDZ'SBNFXPSLGPS (SBQI4JNJMBSJUZ ౦ژۀେֶҪ্ݚ. ࢁޱॱ . άϥϑྨࣅͷͨΊͷॖୀϑϨʔϜϫʔΫ
จʹ͍ͭͯ
"CPVU1BQFS ‣ ஶऀใ w ΤίʔϧɾϙϦςΫχʔΫʢ¬DPMFQPMZUFDIOJRVFʣͱ Ξςωେֶͷڞಉݚڀ ‣ *+*$"*Ͱ࠾ ‣ બΜͩཧ༝
w άϥϑΧʔωϧʹ ڵຯ͕͋ͬͨ
ΧʔωϧͱͳΜͧ ‣ ΧʔωϧؔʢLFSOFMGVODUJPOʣσʔλಉ࢜ͷྨࣅΛଌΔؔ w ڭࢣ͋ΓֶशͷҝͷػցֶशΞϧΰϦζϜʹɺڭࢣσʔλͱͷۙ͞ͷใ͚ͩΛཔΓ ʹֶशɾ༧ଌΛߦ͏ͷʢFHαϙʔτϕΫτϧϚγϯʣ w ਓؒಉ༷ɿະͳͷʹରͯ͠ɺྨࣅ͕ߴ͍طใͰਪ ‣ ਖ਼֬ʹɺΧʔωϧؔɹɹɹɹɹɹɹɹɹɺ࣍ͷ݅Λຬͨؔ͢
w ରশੑɿ w ਖ਼ఆੑɿ k : × → ℝ+ ∀x, y ∈ : k(x, y) = k(y, x) ∀n ∈ ℕ, x1 , …, xn ∈ : (Gij ) ≜ (k(xi , xj )) ∈ ℝn×n (άϥϜߦྻʢ(SBNNBUSJY (SBNJBOʣͱݺΕΔ ͕ਖ਼ఆߦྻ ͞Βʹݫີʹɺ͜Εʮਖ਼ఆΧʔωϧʯʮϚʔαʔΧʔ ωϧʯͱݺΕΔಛघͳΧʔωϧؔͰ͋Δ͕ɺඇৗʹศརͳ ͷͰҰൠతͳఆٛͱͳ͍ͬͯΔ
‣ άϥϑΧʔωϧάϥϑͷϖΞΛೖྗͱ͢ΔΧʔωϧؔ w ͭ·ΓɺάϥϑΧʔωϧͰάϥϑಉ࢜ͷྨࣅΛܭࢉ͢Δ͜ͱ͕Ͱ͖Δ ‣ ͳͥάϥϑΧʔωϧ͕ॏཁͳͷ͔ʁ w ੈͷதͷσʔλͷଟ͘ɺہॴతʹେҬతʹԿΒ͔ͷߏΛ͍࣋ͬͯΔ͜ͱ͕ଟ͘ɺ άϥϑϩεϨεͳσʔλදݱͷྑ͍ۙࣅ w
w w w w άϥϑΧʔωϧάϥϑΛೖྗͱͯ͠ѻ͑ΔΞϧΰϦζϜͷઃܭʹཱͭ άϥϑΧʔωϧͱʁ k( , ) = 100
άϥϑΧʔωϧͷԠ༻ྫ https://art.ist.hokudai.ac.jp/~takigawa/data/fpai94_takigawa.pdf
άϥϑΧʔωϧ͕͍ͬͯΔ͜ͱ k( , ) = ⟨ϕ( ), ϕ( )⟩ℋ =
100 ࠶ੜ֩ώϧϕϧτۭؒ 3,)4 σʔλۭؒʢू߹ʣ ℋ = (ℝd, ⟨ ⋅ , ⋅ ⟩ℋ ) ϕ : → ℋ ϕ( ) ϕ( ) ໌ࣔతʹಛྔΛੜʢJFࣸ૾ПΛఆٛʣͯ͠ྑ͍͕ɺΧʔωϧؔΛఆٛ͢Δ͜ͱͰɺରԠ͢Δ 3,)4ٴͼП͕ʢඇ໌ࣔతʹʣҰҙʹܾఆ͞ΕΔ͜ͱ͕ΒΕ͍ͯΔʢΧʔωϧτϦοΫʣɻ ಛϕΫτϧͷมʢҰൠʹඇઢܗࣸ૾ʣ Ұൠʹ࣍ݩEແݶେ ੵ ػցֶशք۾ͰಛۭؒʢGFBUVSFTQBDFʣͱݺΕΔͭ
ΧʔωϧؔͷΘΕ͔ͨ ‣ Χʔωϧ͕ؔྗΛൃش͢Δͷɿ w ಛϕΫτϧʢࣹӨ͢Δؔʣͷઃܭ͕͍͠ͱ͖ w ֶशΞϧΰϦζϜͰඞཁͳܭࢉ͕ɺಛۭؒͰͷσʔλಉ࢜ͷੵʢJFΧʔωϧؔͷग़ྗʣ ͷΈʹґଘ͢Δͱ͖ ‣ ·ͨɺΧʔωϧؔΛ͏ͱઢܗͳֶशΞϧΰϦζϜΛඇઢܗԽͰ͖Δʂ
w తؔΛࣜมܗͨ͠Γ࠷దԽͷରΛղ͘͜ͱͰɺಛϕΫτϧ͕ੵͷܗͰ͔͠ݱΕ ͳ͍ࣜͷΈͷΞϧΰϦζϜΛߏ͢Δ w ʲྫʳΧʔωϧԽLNFEPJET๏ɺΧʔωϧओੳʢ,FSOFM1$"ʣɺαϙʔτϕΫτϧϚγϯ ʢ47.ʣɺΧʔωϧԽϦοδճؼɺಈܘجఈؔωοτϫʔΫʢ3#'/FUXPSLʣɺFUD ̂ f(x) = ̂ w⊤ϕ(x) = ( N ∑ i=1 ̂ αi ϕ(xi ) ) ⊤ ϕ(x) = N ∑ i=1 ̂ αi k (x, xi) ಛʹάϥϑΧʔωϧ͜͜Ͱॏཁ
ຊʹΔ
͜ͷจͰఏҊ͢Δͷ ‣ άϥϑͷ֊ߏΛ໌ࣔతʹར༻͢Δ৽ͨͳάϥϑΧʔωϧΛఏҊ w ֊ߏΛௐΔͷʹL$PSFͱݺΕΔ֓೦Λ׆༻ w ఏҊ͢Δख๏ʢJFL$PSFϑϨʔϜϫʔΫʣɺطଘͷάϥϑΧʔωϧʹదԠՄೳͰ͋ Γɺ͞ΒʹҰൠͷάϥϑϚονϯάख๏ʹదԠͰ͖Δ w ͭ·Γɺ
ఏҊάϥϑΧʔωϧ طଘάϥϑΧʔωϧ ʷ L$PSFϑϨʔϜϫʔΫ ‣ ఏҊख๏Λ༻͍Δͱɺ47.Λ༻͍ͨάϥϑྨλεΫʹ͓͍ͯɺطଘ ͷάϥϑΧʔωϧΑΓฏۉBDDVSBDZ্͕ͨ͠
άϥϑͷॖୀʢEFHFOFSBDZʣ ‣ ॖୀʢEFHFOFSBDZʣάϥϑʹର͢Δੑ࣭ w ແάϥϑ͕Lॖୀ LEFHFOFSBUF Ͱ͋Δͱɺҙͷ ෦άϥϑ͕ߴʑLͷ࣍ͷΛؚΉͱ͖Λ͍͏ ‣ LDPSF<4FJENBO>
w άϥϑ( 7 & ͷLDPSFͱɺશͯͷͷ͕࣍L Ҏ্Ͱ͋Δ(ͷ࠷େ༠ಋ෦άϥϑCk = (S, E(S)) ∀v ∈ S : degree(v) ≥ k ∀(u, v) ∈ E : u, v ∈ S ⟹ (u, v) ∈ E(S) ˢʮ4 㱪7 ʹΑΔ༠ಋ෦άϥϑ 4 & 4 ʯͷఆٛ ˢҙ༠ಋ෦άϥϑʹ͓͚Δ࣍ ؆୯ʹݴͬͯ͠·͏ͱɺ4ʹؔͳ͍ʢ4ʹͳ͍ϊʔυΛͬͯΔʣΤοδΛআͯ͠ಘΒΕΔ෦άϥϑ
LDPSFͷྫ ͱͷάϥϑͰ࣍ͷϊʔυʢC D V ʜʣ͋Δ͕ɺ ༠ಋ෦άϥϑ͚ͩͰ࣍Λୡ͢Δͷ͕ෆՄೳ DPSFଘࡏ͠ͳ͍
LDPSFղΞϧΰϦζϜ ‣ ࣍ͷখ͍͞ॱʹɺશͯͷϊʔυʹ ͍ͭͯௐ͍ͯ͘ w ࠓߏங͍ͯ͠ΔLDPSFΑΓ͕࣍খ͚͞ ΕͦΕΛLDPSF͔Βআ w ͯ͢ͷ͕࣍LҎ্ʹͳͬͨͷΛ֬ೝ͠ ͨΒLDPSFΛొ
‣ ܭࢉͷΦʔμʔ0 / . w /ϊʔυ w .Τοδ ઢܗ࣌ؒͰܭࢉՄೳͳͷͰɺޙड़ͷఏҊ ख๏Ͱ͜ͷܭࢉ͕ൺֱతϘτϧωοΫ ʹͳΓʹ͍͘
LDPSFͷಛ ‣ LDPSFͷಛɿ෦ू߹ੑ ‣ L͕େ͖͘ͳΔʹͭΕɺΑΓॏཁͳ ใΛؚΜͰ͍Δͱߟ͑ΒΕΔ w ྫ͑ιʔγϟϧωοτϫʔΫͰɺத৺త ਓͰߏ͞ΕΔίϛϡχςΟʔ͕֘ Cδ*(G)
⊆ … ⊆ C1 ⊆ C0 = G LDPSF͕ߏஙͰ͖Δ࠷େͷLάϥϑͷॖୀ άϥϑͷྨࣅLDPSF͝ͱͷྨࣅͰଌΔͷ͕ྑ͍ͷͰʁ
ఏҊख๏
ʲఏҊख๏ʳ$PSF7BSJBOUPG#BTF,FSOFM ‣ ϕʔεͱͳΔάϥϑΧʔωϧΛ༻ҙ͢Δ w ྫʣLϫΠεϑΝΠϥʔɾϦʔϚϯʢ8FJTGFJMFS-FINBOʣΧʔωϧ ‣ ༩͑ΒΕͨͭͷάϥϑʹରͯ͠ɺͦΕͧΕͷશLDPSFΛܭࢉ͢Δ w ྫʣ(ͷLDPSFT\$ $
$ $^ (`ͷLDPSFT\$` $` $`^ ‣ ಉ͡ϨϕϧͷLDPSFΛೖྗͱͨ͠άϥϑΧʔωϧͷग़ྗΛ͠߹ΘͤΔ w ྫʣL@D ( (` L $ $` L $ $` L $ $` L ɾ ɾ ͕άϥϑΧʔωϧ͡Όͳͯ͘ɺάϥϑͷϖΞ Λೖྗͱ͢Δҙͷؔʹར༻Ͱ͖Δ LDPSFϑϨʔϜϫʔΫ
$PNQVUBUJPOBM$PNQMFYJUZ ‣ LDPSFϑϨʔϜϫʔΫͷܭࢉෳࡶ͞ w ɹɹɿάϥϑͷϖΞΛೖྗͱ͢ΔؔʢFHάϥϑΧʔωϧʣͷܭࢉෳࡶ͞ w ɹɹɿೖྗάϥϑͷॖୀʢJFLDPSF͕ଘࡏ͢Δ࠷େͷLʣͷখ͍͞ํ ‣ Ұൠʹɺάϥϑͷॖୀͷ্ք࣍ͷͲͪΒ͔Ͱ༩͑ΒΕΔ w
άϥϑͷ࠷େ࣍ w ྡߦྻͷ࠷େݻ༗ ‣ ɹɹϊʔυΑΓेʹখ͍͞ʢɹɹɹɹʣ͜ͱ͕ଟ͍ͷͰɺLDPSF ϑϨʔϜϫʔΫʹཁ͢ΔՃܭࢉൺֱతͯ͘ࡁΉ c = A × δ* min A δ* min λmax λmax λmax ≪ n
࣮ݧ
࣮ݧͷηοςΟϯά ‣ σʔληοτɿ w όΠΦΠϯϑΥϚςΟΫεͱιʔγϟϧ ωοτϫʔΫ༝དྷͷσʔληοτΛར༻ ‣ ྨɿ w 47.Λར༻ͯ͠ྨλεΫΛղ͘
w ύϥϝʔλGPME$7Ͱܾఆ ‣ ൺֱ͢ΔάϥϑΧʔωϧɿ w ϕʔεάϥϑΧʔωϧछʷఏҊϑϨʔ ϜϫʔΫͷ༗ແछྨ όΠΦΠϯϑΥ ιʔγϟϧωοτ https://ls11-www.cs.tu-dortmund.de/staff/morris/graphkerneldatasets
݁ՌʢฏۉBDDVSBDZͱͦͷࢄʣ ଠࣈͷࣈɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ
݁ՌʢฏۉBDDVSBDZͱͦͷࢄʣ ଠࣈͷࣈɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ όΠΦܥͷσʔλΑΓιʔγϟϧ ωοτܥͷσʔλͷํ͕ੑೳ্͕ ΈΒΕͨ ԾઆʮίΞ͕େ͖͍LDPSFͷ ΄͏͕ॏཁʯΛࢧ࣋͢Δ݁Ռ
݁ՌʢฏۉBDDVSBDZͱͦͷࢄʣ ଠࣈͷࣈɺUݕఆʢ༗ҙਫ ४ʣʹΑͬͯɺ$03&ϑϨʔ ϜϫʔΫͷੑೳ্͕༗ҙʹ ೝΊΒΕͨέʔεΛද͢ɻ (3Ͱݦஶʹੑೳ্͕ΈΒΕ ΔҰํ 8-Ͱ͍·͍ͪޮՌͳ͠ 8-֤ϊʔυͷۙΛཁ ͢ΔΑ͏ͳΧʔωϧͳͷ
ͰɺײతʹLDPSFͷ ֓೦ͱ͋·Γ૬ҧແ͠
None
࣮ߦ࣌ؒͷ૿େʹؔ͢Δߟ ‣ ϕʔεΧʔωϧͷ࣮ߦ࣌ؒʹର͢ΔɺLDPSF֦ு ͷ૬ର࣮ߦ࣌ؒΛࣔͨ͠ද ‣ *.%##*/"3:ͱ*.%#.6-5*Ͱඇৗʹ࣮ߦ ͕࣌ؒ͘ͳ͍ͬͯΔ͕ɺੑೳ্Λߟྀ͢Δͱ ܾͯ͠๏֎ͳͷͰͳ͍ʢͱओுʣ
ιʔγϟϧωοτϫʔΫͰੑೳ্͕ݦஶͳཧ༝ ‣ ωοτϫʔΫͷ͕࣍ҟͳΔ ‣ ͖ଇʹै͏ωοτϫʔΫɺΑΓத৺ͷLDPSFʹ༗ӹͳใ͕٧ ·͍ͬͯΔͱߟ͑ΕΔ
୯ҰLDPSFΛͬͨBDDVSBDZ ‣ ೖྗΛɺΦϦδφϧͷάϥϑͰͳ͘ɺ LDPSFͱஔ͖͑ͨ߹ͷBDDVSBDZ w LͷLDPSFάϥϑͦͷͷͳͷͰஔ͖ ͑͠ͳ͍ ‣ ؍ଌɿ w
ʲ$PSF(3ʳ୯ௐతʹখ͍͞LͰੑೳ্ w ʲ(3ʳL ͰɺΦϦδφϧͷάϥϑΛೖྗ ͤͨ͞߹ΑΓੑೳ͕ྑ͘ͳ͍ͬͯΔ ʢײʣඞཁ࠷ݶͷใ͕٧·͍ͬͯΔ࠷খͷ෦ άϥϑ͕͜ͷ͋ͨΓͳͷͰʁ IMDB-BINARYͰͷGRͱCore GR
·ͱΊ
·ͱΊ LDPSFղʹجͮ͘ϑϨʔϜϫʔΫ ‣ LDPSF࠷খ͕࣍LͰ͋Δ࠷େ༠ಋ෦άϥϑ ‣ LDPSF㱬 L DPSFͰ͋Δ͜ͱΛར༻ͯ͠ɺάϥϑͷ֊ߏ͝ͱʹൺֱΛߦ͏ϑϨʔϜϫʔΫΛఏҊ ‣
ຊจͰάϥϑΧʔωϧʹద༻͕ͨ͠ɺҙͷάϥϑϚονϯάΞϧΰϦζϜʹద༻Ͱ͖Δ ͜ͷϑϨʔϜϫʔΫʹΑͬͯɺάϥϑྨλεΫʹ͓͍ͯطଘͷά ϥϑΧʔωϧͷੑೳΛ্ͤͨ͞ ‣ ιʔγϟϧωοτϫʔΫͳͲͷɺεέʔϧϑϦʔωοτϫʔΫͰ༗ޮ ‣ LDPSFʹࣅͨ֓೦ͷطଘάϥϑΧʔωϧʹରͯ͠ޮՌ͍·͍ͪ