Introduction Existing Work o Traditional MF methods: Can only model one matrix ·Example:LSl Joint Link-Content MF (LCMF): Can model both content and link matrices simultaneously Can only model Type I links lllustration: Link structure Result of LCMF =.8 =.5 -3 =.1 =,0 .0 .4 -.1 -.4 =.0 .4 =.1 . .3 3 =.4 3 =.4 .0 -.1 =.4 -.8 .4 Li and Yeung (CSE.HKUST) RRMF UCA12009 6/23
Introduction Existing Work Traditional MF methods: Can only model one matrix Example: LSI Joint Link-Content MF (LCMF): Can model both content and link matrices simultaneously Can only model Type I links Illustration: Link structure V1 V8 V6 V7 V4 V5 V2 V3 Result of LCMF -.8 -.5 .3 -.1 -.0 -.0 .4 .6 -.1 -.4 -.0 .4 .6 -.1 -.4 .3 -.2 .3 -.4 .3 .3 -.2 .3 -.4 .3 -.4 .5 .0 -.2 .6 -.4 .5 .0 -.2 .6 -.1 .1 -.4 -.8 -.4 Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 6 / 23
Introduction Our Contribution Relation regularized matrix factorization (RRMF): To model Type ll links Can also model Type I links by preprocessing the link structure ●Convergent o Linear time-complexity 日卡4日卡4三4至卡三80 Li and Yeung (CSE.HKUST) RRMF UCA120097/23
Introduction Our Contribution Relation regularized matrix factorization (RRMF): To model Type II links Can also model Type I links by preprocessing the link structure Convergent Linear time-complexity Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 7 / 23
Relation Regularized Matrix Factorization Model Formulaton Notations Content matrix:X-n x m Xi:content feature vector for instance i o Adjacency matrix:A-n x n Aij =1 if there is a relation between instances i and j,and otherwise Aij=0;Aii=0 Note:This specification of A is only suitable for Type Il links.We will introduce the strategy to specify A for Type I links later. 4口4日+1艺4至卡三)Q0 Li and Yeung (CSE.HKUST) RRMF UCA120098/23
Relation Regularized Matrix Factorization Model Formulation Notations Content matrix: X − n × m Xi∗: content feature vector for instance i Adjacency matrix: A − n × n Aij = 1 if there is a relation between instances i and j, and otherwise Aij = 0; Aii = 0 Note: This specification of A is only suitable for Type II links. We will introduce the strategy to specify A for Type I links later. Li and Yeung (CSE, HKUST) RRMF IJCAI 2009 8 / 23