Improving "People You May Know" on Directed Social Graph

by Agata Naomichi

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©2019 Wantedly, Inc. ͜͜Ͱ͸Graphதͷ֤Nodeʹରͯ͠ʮϕΫτϧදݱʯΛ֫ಘ͢Δ͜ͱ ͭͳ͕͍ͬͯΔNodeͨͪ͸ۙ͘ɺͭͳ͕͍ͬͯͳ͍Nodeͨͪ͸ԕ͘ͳΔΑ͏ʹֶश͢Δ ʮྨࣅ౓ʯ͸Cosineྨࣅ౓΍಺ੵͰఆٛ͢Δ Graph Embeddings? A B C similarity(A, B) = ⃗ a ⋅ ⃗ b similarity(A, C) = ⃗ a ⋅ ⃗ c

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©2019 Wantedly, Inc. ෳࡶͳؔ܎ΛදݱͰ͖Δʢ͜ͱ͕ظ଴͞ΕΔʣ άϥϑͱ͍͏ෳࡶͳσʔλߏ଄ͷ৘ใΛ࣍ݩϕΫτϧͱͯ͠ѻ͑ͨΒ͏Ε͍͠ʂ ʢยํ޲ͷΤοδ΋ؚΊΔͱʣ਺ԯΤοδͷάϥϑ͕γϯϓϧͳදݱʹམͱ͠ࠐΊΔ ਪનީิͷݕࡧ͕ߴ଎ʹ࣮ݱͰ͖Δ શ୳ࡧ͢Δͱͯ͠΋಺ੵΛऔΔ͚ͩ ʢଞͷλεΫ΁ͷԠ༻ʣ ಘΒΕͨembeddingsΛdownstream tasksͷೖྗʹ͔ͭ͑Δ Link Prediction΋ downstream tasksͷͻͱͭ ͳͥGraph EmbeddingsΛ͔ͭ͏ͷ͔

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©2019 Wantedly, Inc. ਪનͷશମ૾ Embeddings ۙ๣఺୳ࡧ ճؼϞσϧ ਪન ϢʔβͷϖΞ͔Βʮͭͳ͕Δ཰ʯΛ༧ଌ͢ΔϞσϧ ಛ௃ྔͱ֤ͯ͠ϢʔβͷϕΫτϧදݱΛ࢖͏ ͦͷ΄͔ͷ৘ใʢ࣍਺΍ڞ௨ͷͭͳ͕Γ਺ͳͲʣΛಛ௃ྔͱ͔ͯͭ͠͏͜ͱ΋Ͱ͖Δ ͳͯ͘΋embeddingͷ಺ੵͷେ͖͞ॱʹιʔτ্ͯ͠ҐΛਪન͢Δํ๏͕ͱΕΔ ͋ͬͨ΄͏͕ਫ਼౓͕Α͔ͬͨ ֬཰ͱͯ͠ղऍͰ͖ΔΑ͏ʹͳΔͷͰѻ͍΍͍͢

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©2019 Wantedly, Inc. ΍ͬͯΈͨ ·ͣ͸૒ํ޲ͷͭͳ͕ΓͷΈΛ׆༻ֶͯ͠शͨ͠ γϯϓϧͳDeepWalk Graph ্ΛϥϯμϜ΢ΥʔΫͯ͠ಘͨ Node ྻ͔Β Word2Vec ͱಉ͡Α͏ͳํ๏ Ͱֶश ਪનΛग़ͤΔϢʔβ͕;͑ͨ͜ͱͰɺैདྷͷ໿2ഒͷͭͳ͕ΓΛͭͬͨ͘ʂ %FFQ8BMLPOMJOFMFBSOJOHPGTPDJBMSFQSFTFOUBUJPOT<#1SP[[J ,%%>

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©2019 Wantedly, Inc. ͭͳ͕ΓͷछྨΛͲ͏දݱ͢Δ͔ ͦ͜Ͱɺ"͔Β#ʹରͯ͠Sͱ͍͏Τοδ͕͋Δͱ͖ɺͦΕΛ࣍ͷΑ͏ʹදݱ͢Δ score(A, r, B) = ⃗ a ⋅ fr ( ⃗ b ) score(B, r, A) = ⃗ b ⋅ fr ( ⃗ a ) ͸Τοδͷछྨ͝ͱʹఆٛ͞ΕΔϕΫτϧΛม׵͢Δؔ਺ fr A B r fr ͸খ͘͞ͳΔΑ͏ʹ΋ֶश ⃗ a ⋅ fr ( ⃗ b ) ͸େ͖͘ ⃗ b ⋅ fr ( ⃗ a )

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©2019 Wantedly, Inc. ࠓճ͸Complex EmbeddingsΛࢀߟʹ࣍ͷΑ͏ͳม׵Λߦͬͨ $PNQMFY&NCFEEJOHTGPS4JNQMF-JOL1SFEJDUJPO<55SPVJMMPO *$.-> real, imag = embedding[:dim // 2], embedding[dim // 2:] concat(real * W_real - imag * W_imag, real * W_imag + image * W_real) W_real, W_imag͸ֶश͞ΕΔύϥϝʔλ ͭͳ͕ΓͷछྨΛͲ͏දݱ͢Δ͔

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©2019 Wantedly, Inc. ࠓճͷ࣮ݧͰͷදݱҰํ௨ߦ A͞Μ B͞Μ ⃗ a ⋅ f( ⃗ b ) ⃗ b ⋅ f( ⃗ a ) - dstଆΛม׵ A → B ͸positive͔ͭB → A ͸negativeΛ  දݱͰ͖ΔΑ͏ʹ͢Δ ⃗ a ⋅ f( ⃗ b ) Λେ͖͘ʢA → B͸Ұํ௨ߦʣ ⃗ b ⋅ f( ⃗ a ) Λখ͘͞ʢ# → A͸ଘࡏ͠ͳ͍ʣ ⃗ a ⋅ ⃗ b Λখ͘͞ʢA ͱ B͸૒ํ޲ͭͳ͕ΓͰ͸ͳ͍ʣ

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©2019 Wantedly, Inc. ͦͷଞͷ࣮ݧ͜Ε͔Β ͍Ζ͍Ζ΍ͬͯΈ͚ͨͲྑ͍݁Ռ͕ಘΒΕͳ͔࣮ͬͨݧͨͪʜ ʮ໊ࢗܦ༝ʯʮϦΫΤετܦ༝ʯͱ͍ͬͨ৘ใ΋Τοδͷϥϕϧͱͯ͠ѻͬͯΈΔ ϦΫΤετͷReject΋Τοδͱͯ͠ѻͬͯΈΔ ৽͘͠ਪન͕ग़ͤΔΑ͏ʹͳͬͨϢʔβʹߜͬͨධՁ͕Ͱ͖͍ͯͳ͍ ୯ํ޲ͷΤοδ΋͔ͭ͏Α͏ʹͳͬͨ͜ͱͰɺ࣍਺ͷখ͍͞Ϣʔβ΋ଟؚ͘Ήάϥϑ ʹͳͬͨ ΄͔ͷλεΫ΁ͷԠ༻

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