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Enhancing Matrix Factorization Through Initialization for Implicit Feedback Databases

This paper presents an advanced approach to matrix factorization (MF) tailored for implicit feedback databases. We explore the significance of initialization methods, including naive and SimFactor approaches, emphasizing their impact on model accuracy. Through empirical experiments using real-world datasets, we demonstrate that context-aware similarity preservation significantly enhances MF performance. Our findings suggest that leveraging additional metadata and contextual information leads to better feature representation, which is crucial for improvement in recommendation systems.

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Enhancing Matrix Factorization Through Initialization for Implicit Feedback Databases

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  1. Enhancing Matrix Factorization Through Initialization forImplicit Feedback Databases Balázs Hidasi Domonkos Tikk Gravity R&D Ltd. Budapest University of Technology and Economics CaRR workshop, 14th February 2012, Lisbon

  2. Outline • Matrixfactoriztion • Initializationconcept • Methods • Naive • SimFactor • Results • Discussion

  3. MatrixFactorization • CollaborativeFiltering • One of the most commonapproaches • Approximatestheratingmatrixasproduct of low-rankmatrices Items R P Q ≈ Users

  4. Matrixfactorization • Initialize P and Q withsmallrandomnumbers • Teach P and Q • AlternatingLeastSquares • GradientDescent • Etc. • Transformsthedatato a featurespace • Separatelyforusers and items • Noisereduction • Compression • Generalization

  5. Implicit feedback • No ratings • User-iteminteractions (events) • Muchnoisier • Presence of an event mightnot be positivefeedback • Absence of an event doesnotmeannegativefeedback • No negativefeedback is available! • More commonproblem • MF for implicit feedback • Less accurateresultsduetonoise • Mostly ALS is used • Scalabilityproblems (ratingmatrix is dense)

  6. Concept • Good MF model • The featurevectors of similarentitiesaresimilar • Ifdata is toonoisy similarentitieswon’t be similarbytheirfeatures • Start MF from a „good” point • Featurevectorsimilaritiesare OK • Data is more thanjustevents • Metadata • Infoaboutitems/users • Contextualdata • Inwhatcontextdidtheeventoccured • Canweincorporatethosetohelp implicit MF?

  7. Naiveapproach • Describeitemsusinganydatawehave (detailedlater) • Long, sparsevectorsforitemdescription • Compressthesevectorstodensefeaturevectors • PCA, MLP, MF, … • Length of desiredvectors = Numberoffeaturesin MF • Usethesefeaturesas starting points

  8. Naiveapproach • Compression and alsonoisereduction • Doesnotreallycareaboutsimilarities • Butoftenfeaturesimilaritiesarenotthatbad • If MF is used • Half of theresults is thrown out Descriptors Descriptorfeatures Description of items Itemfeatures ≈ Items

  9. SimFactoralgorithm • Trytopreservesimilaritiesbetter • Starting from an MF of itemdescription • Similarities of items: DD’ • Somemetricsrequiretransformationon D Descriptors Descriptorsfeatures Description of items (D) Itemfeatures ≈ Items Description of items (D’) Itemsimilarities (S) Description of items (D) =

  10. SimFactoralgorithm • Similarityapproximation • Y’Y  KxKsymmetric • Eigendecomposition Itemfeatures (X’) Itemsimilarities (S) Itemfeatures (X) Descriptorsfeatures (Y’) ≈ Descriptorsfeatures (Y) Itemfeatures (X’) Itemsimilarities (S) Itemfeatures (X) Y’Y ≈

  11. SimFactoralgorithm • λ diagonal λ = SQRT(λ) * SQRT(λ) • X*U*SQRT(λ) = (SQRT(λ)*U’*X’)’=F • F is MxKmatrix • S  F * F’  Fusedforinitialization Y’Y U λ U’ = Itemfeatures (X’) Itemsimilarities (S) Itemfeatures (X) U SQRT (λ) SQRT (λ) U’ ≈ F’ Itemsimilarities (S) F ≈

  12. Creatingthedescriptionmatrix • „Any” dataabouttheentity • Vector-spacereprezentation • ForItems: • Metadatavector (title, category, description, etc) • Eventvector (whoboughttheitem) • Context-statevector (inwhichcontextstatewasitbought) • Context-event (inwhichcontextstatewhoboughtit) • ForUsers: • Allaboveexceptmetadata • Currently: Chooseonesourcefor D matrix • Contextused: seasonality

  13. Experiments: Similaritypreservation • Real life dataset: online grocery shopping events • SimFactorapproximatessimilaritiesbetter

  14. Experiments: Initialization • Usingdifferentdescriptionmatrices • And bothnaiveandSimFactorinitialization • Baseline: random init • Evaluationmetric: recall@50

  15. Experiments: Grocery DB • Upto 6% improvement • Best methodsuseSimFactor and usercontextdata

  16. Experiments: „Implicitized” MovieLens • Keeping 5 starratings implicit events • Upto 10% improvement • Best methodsuseSimFactor and itemcontextdata

  17. Discussion of results • SimFactoryieldsbetterresultsthannaive • Contextinformationyieldsbetterresultsthanotherdescriptions • Contextinformationseparateswellbetweenentities • Grocery: Usercontext • People’sroutines • Differenttypes of shoppingsindifferenttimes • MovieLens: Itemcontext • Differenttypes of movieswatchedondifferenthours • Context-basedsimilarity

  18. Whycontext? • Groceryexample • Correlationbetweencontextstatesbyusers low • Whycancontextawarealgorithms be efficient? • Differentrecommendationsindifferentcontextstates • Contextdifferentiateswellbetweenentities • Easiersubtasks

  19. Conclusion & Futurework • SimFactor Similaritypreservingcompression • Similaritybased MF initialization: • Descriptionmatrixfromanydata • ApplySimFactor • Use output asinitialfeaturesfor MF • Contextdifferentitatesbetweenentitieswell • Futurework: • Mixed descriptionmatrix (multipledatasources) • Multipledescriptionmatrix • Usingdifferentcontextinformation • Usingdifferentsimilaritymetrics

  20. Thanksforyourattention! For more of my recommender systems related research visit my website: http://www.hidasi.eu

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