Relational Learning as Collective Matrix Factorization

author: Ajit Singh, The Auton Lab, School of Computer Science, Carnegie Mellon University
published: Feb. 14, 2008,   recorded: February 2008,   views: 10001


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We present a unified view of matrix factorization models, including singular value decompositions, non-negative matrix factorization, probabilistic latent semantic indexing, and generalizations of these models to exponential families and non-regular Bregman divergences. One can model relational data as a set of matrices, where each matrix represents the value of a relation between two entity-types. Instead of a single matrix, relational data is represented as a set of matrices with shared dimensions and tied low-rank representation. Our example domain is augmented collaborative filtering, where both user ratings and side information about items are available. To predict the value of a relation, we extend Bregman matrix factorization to a set of related matrices. Using an alternating minimization scheme, we show the existence of a practical Newton step. The use of stochastic second-order methods for large matrices is also covered.

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Reviews and comments:

Comment1 Fawad, July 4, 2008 at 11:54 p.m.:

Unfortunately, the slides are poorly designed and the talk too fast. You should simplify the talk and try to spend some time and really explain each slide instead of running through them which makes it quite hard to follow.

I am a PhD student working on document clustering/ classification (also worked on PCA and SVD) and even I am finding it hard to follow the talk.

Very interesting topic that I always wanted to find a lecture.

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