Relation Regularized Matrix Factorization Wu-Jun Li,Dit-Yan Yeung Department of Computer Science and Engineering Hong Kong University of Science and Technology Hong Kong,China IJCAI 2009 4口4日+立4至卡至及0 Li and Yeung (CSE.HKUST) RRMF UCA120091/23
Relation Regularized Matrix Factorization Wu-Jun Li, Dit-Yan Yeung Department of Computer Science and Engineering Hong Kong University of Science and Technology Hong Kong, China IJCAI 2009 Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 1 / 23
Contents Introduction Relation Regularized Matrix Factorization o Model Formulation ●Learning Convergence and Complexity Analysis Experiments Conclusion 4日4日+4立4至至只0 Li and Yeung (CSE.HKUST) RRMF UCA1200952/23
Contents 1 Introduction 2 Relation Regularized Matrix Factorization Model Formulation Learning Convergence and Complexity Analysis 3 Experiments 4 Conclusion Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 2 / 23
Introduction Matrix Factorization(MF) To project instances into a lower-dimensional latent space. X:n x m,with each row Xis denoting an instance X≈UVT U:n×D V:m×D D<m Ui*is the lower-dimensional representation of Xi 。Objective: To get a U which can remove the noise in X 。Example: Latent semantic indexing(LSI)for document analysis Li and Yeung (CSE.HKUST) RRMF UCA120093/23
Introduction Matrix Factorization (MF) To project instances into a lower-dimensional latent space. X : n × m, with each row Xi∗ denoting an instance X ≈ UVT U : n × D V : m × D D < m Ui∗ is the lower-dimensional representation of Xi∗ Objective: To get a U which can remove the noise in X Example: Latent semantic indexing (LSI) for document analysis Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 3 / 23
Introduction Relational Data Contain both content information and relation (link)structure. Examples: o Web pages:page content and hyperlinks o Research papers:paper content and citations Representation:two matrices o Content matrix o Link matrix 4口4日+1立4至卡三只0 Li and Yeung (CSE.HKUST) RRMF UCA120094/23
Introduction Relational Data Contain both content information and relation (link) structure. Examples: Web pages: page content and hyperlinks Research papers: paper content and citations Representation: two matrices Content matrix Link matrix Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 4 / 23
Introduction Semantics of Relations There exist at least two types of links with different semantics: o Type I Links:If two instances link to or are linked by one common instance,they will be most likely to belong to the same class. Example:Hyperlinks among web pages o Type ll Links:Two linked instances are most likely to belong to the same class. Example:Citations among research papers 4口4香+之卡要，三)Q0 Li and Yeung (CSE.HKUST) RRMF UCA120095/23
Introduction Semantics of Relations There exist at least two types of links with different semantics: Type I Links: If two instances link to or are linked by one common instance, they will be most likely to belong to the same class. V1 V2 V3 V1 V2 V3 Example: Hyperlinks among web pages Type II Links: Two linked instances are most likely to belong to the same class. V1 V2 V3 V1 V2 V3 V1 V2 V3 Example: Citations among research papers Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 5 / 23