Mathematical methods of Tensor Factorization applied to Recommender Systems Giuseppe Ricci, PhD Student in Computer Science University of Study of Bari “A. Moro” Advances in DataBases and Information Systems PhD Consortium, Genoa, 01 Septembre 2013 Semantic Web Access and Personalization research group http:// www.di.uniba.it/~swap Dipartimento di Informatica
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Mathematical methods of Tensor Factorization applied to
Recommender Systems Giuseppe Ricci, PhD Student in Computer Science
University of Study of Bari A. Moro Advances in DataBases and
Information Systems PhD Consortium, Genoa, 01 Septembre 2013
Semantic Web Access and Personalization research group
http://www.di.uniba.it/~swap Dipartimento di Informatica
Information Overload & Recommender Systems On internet
today, an overabundance of information can be accessed, making it
difficult for users to process and evaluate options and make
appropriate choices. Recommender Systems (RS) are techniques for
information filtering which play an important role in e- commerce,
advertising, e-mail filtering, etc.
What do RS do exactly? Predict how much you may like a certain
product/service Compose a list of N best items for you Compose a
list of N best users for a certain product/service Explain why
these items are recommended to you Adjust the prediction and
recommendation based on your feedback (ratings) and other people I1
I2 I3 I4 I5 I6 I7 I8 I9 U1 1 5 4 U2 4 2 5 U3 4 5 U4 5 2 4 A 1 3 1 3
1 4 5 8 user-item matrix
Matrix Factorization Matrix Factorization (MF) techniques fall
in the class of collaborative filtering (CF) methods latent factor
models: similarity between users and items is induced by some
factors hidden in the data Latent factor models build a matrix of
users and items and each element is associated with a vector of
characteristics MF techniques represent users and items by vectors
of features derived from ratings given by users for the items seen
or tried Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix
factorization techniques for recommender systems. IEEE Computer,
42(8):30-37, 2009.
Matrix Factorization U set of users, D set of items, R rating
matrix. MF aims to factorize R into two matrices P and Q such that
their product approximates R: P row: strength of the association
between user and k latent features. Q column: strength of the
association between an item and the latent features. Once these
vectors are discovered, recommendations are calculated using the
expression of A MF used in literature: Singular Value Decomposition
(SVD): introduced by Simon Funk in the NetFlix Prize has the
objective of reducing the dimensionality, i. e. the rank, of the
user-item matrix capture latent relationships between users and
items T T ij i jR P Q r p q ijr
SVD Different SVD algorithms were used in RS literature: in
[15], the authors uses a small SVD obtained retaining only k