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Factorization Machine. I’m Jerry. Factorization Machine. Factorization Methods. Factorization Machine. Support Vector Machine. Factorization Model. User Features. Ratings. Item Feature. Support Vector Machine (SVM). D = {(x i , y i ) | x i ∈R P , y i ∈{-1, 1}} i = 1~n

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Factorization Machine


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    1. FactorizationMachine I’mJerry

    2. FactorizationMachine FactorizationMethods

    3. FactorizationMachine SupportVectorMachine

    4. FactorizationModel UserFeatures Ratings ItemFeature

    5. SupportVectorMachine(SVM) D={(xi,yi)|xi∈RP,yi∈{-1,1}}i=1~n Line: y(x) = w‧x+b=0 Forallyi=1,y(xi) = w‧xi+b≧1 Forallyi=-1,y(xi) = w‧xi+b≦-1 Minimize|w|

    6. SupportVectorMachine(SVM)

    7. RecommenderGroup YUNOUSESVM?

    8. “Y U NO USE SVM?” Real Value V.S. Classification Sparsity

    9. y(x) = w‧x+b= wu + wi+b

    10. ActuallyWeDoUseSVM OnEnsemble

    11. Ensemblemodels User Item Model2 Model1 Model3

    12. Ensemblemodels User Item Model2 Model1 Model3 x y

    13. Ensemblemodels User Item Model2 Model1 Model3 + + + =

    14. Predictionsontrainset Trainsetanswer

    15. Predictionsontrainset Trainsetanswer ModelWeights SVM

    16. Predictionsontrainset Trainsetanswer ModelWeights SVM ModelWeights Predictionsontestset

    17. Predictionsontrainset Trainsetanswer ModelWeights SVM ModelWeights Predictionsontestset FinalPrediction

    18. SVMCalculates“weight”offeatures

    19. FactorizationMachine • OriginalSVM: • y(x)=w‧x+b=b+Σwixi • FactorizationMachine: • y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    20. FactorizationMachine i=0 j=i+1 Interactionbetweenvariables • OriginalSVM: • y(x)=w‧x+b=b+Σwixi • FactorizationMachine: • y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    21. (vi‧vj)? W

    22. (vi‧vj)? W

    23. (vi‧vj)? W ?

    24. (vi‧vj)? W CFMatrix

    25. (vi‧vj)? W V VT = k

    26. (vi‧vj)? W V VT = i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    27. (vi‧vj)? W V VT = i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    28. (vi‧vj)? W V VT = i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    29. (vi‧vj)? W V VT = =vA‧vTI i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    30. (vi‧vj)? W V VT = =vA‧vTI i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    31. (vi‧vj)? W V VT = =vA‧vTI i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    32. (vi‧vj)? W V VT = Factorization i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    33. (vi‧vj)? W V VT = Machine Factorization i=0 j=i+1 y(x)=b+Σwixi+ΣΣ(vi‧vj)xixj

    34. FactorizationMachine

    35. W

    36. FMV.S.SVM SVMfailswithsparsity FMlearnwithsgd,SVMlearnwithdual

    37. FMV.S.SVM PolynomialkernelSVM ComparetoFM: Wi,jareallindependenttoeachother.

    38. FMV.S.MF • MF: • y( x ) = b+ wu+ wi+ vu‧vi • SVD++: • y( x ) = b + wu + wi + vu‧vi+(1/√|Nu|)Σvi‧vl • ClaimsthatFMismoregeneral

    39. Thanks!