Download Master`s Thesis Project for 1 or 2 students: Movie recommendation

Master’s Thesis Project for 1 or 2 students:
Movie recommendation system
using Clustered Low Rank Approximations
and Temporal Analysis
Berkant Savas
Depatment of Mathematics
Linköping University
May 4, 2012
In the last five years The Netflix Prize chalange [1, 10] has attracted attention from many
researchers and hobby programmers. The online movie rental company Netflix provided over 100
million ratings from 480,189 users on 17,770 movies. The challenge was to improve the recommender
system of Netwlix with 10% and the winner would be awarded $1,000,000. The recommender
system may be seen as a missing data estimation problem, where the known movie ratings are
stored in a user × movie matrix A. For example, if user i has rated movie j with the rating 4, then
A(i, j) = aij = 4. The use of low rank approximation of
A ≈ U ΣV T
has turned out to yield good performance [8, 9]. The above low rank approximation is computed
only over the know entries of A.
Recently, a new approach called clustered low rank matrix approximations has been proposed
[11]. The benefits of the clustered approach are faster low rank computations, more accurate and
more memory efficient approximations, than traditional low rank approximations, e.g. approximation obtained by the singular value decomposition (SVD).
In the Master’s thesis project temporal analysis and the clustered low rank approximation
approach will be applied to the missing value estimation of the Netflix problem. Since the given
rating matrix A is rectangular it will be considered as a bipartite graph and co-clustering [3, 5, 2] will
be applied to obtain a clustering of the users and a clustering of the movies. After the co-clustering
step (and reordering of the users/movies according to cluster belonging) the rating matrix may be
partitioned as


A11 · · · A1m

..  ,
..
A =  ...
.
. 
Au1 · · ·
Aum
where u denotes the number of user cluster, m denotes the number of movie clusters, and Aij
contains the ratings from users in cluster i and movies in cluster j. The rating matrix A will be
approximated by computing low rank approximations of individual blocks Aij that are sufficiently
dense. The project consist of the flowing parts.
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1. Analyze the Netflix data set in various respects and in particular with respect to temporal
dynamics.
2. Learn about and use state of the art methods for large scale graph clustering [4, 7] and
co-clustering.
3. Learn about low rank approximations and the clustered low rank approximation of matrices
[6, 11].
4. Learn about low rank approximation of matrices with missing entries.
5. Implement a missing data estimation method using temporal analysis and clustered low rank
approximation with missing values.
6. Investigate the effect of various parameters, e.g., ranks of the approximation, number of movie
clusters, number of user clusters, on the performance of the method.
7. Compare the performance of the developed method with performance of standard/simple
missing values estimation methods.
References
[1] J. Bennett and S. Lanning. The netflix prize. In KDD Cup and Workshop in conjunction with KDD,
2007.
[2] M. Deodhar, G. Gupta, J. Ghosh, H. Cho, and I. S. Dhillon. A scalable framework for discovering
coherent co-clusters in noisy data. In Proceedings of the 26th Annual International Conference on
Machine Learning, ICML ’09, pages 241–248, New York, NY, USA, 2009. ACM.
[3] I. S. Dhillon. Co-clustering documents and words using bipartite spectral graph partitioning. In Proceedings of the 7th ACM SIGKDD International conference on Knowledge Discovery and Data Mining,
pages 269–274, New York, NY, USA, 2001. ACM.
[4] I. S. Dhillon, Y. Guan, and B. Kulis. Weighted graph cuts without eigenvectors: A multilevel approach.
IEEE Trans. Pattern Anal. Mach. Intell., 29(11):1944–1957, 2007.
[5] I. S. Dhillon, S. Mallela, and D. S. Modha. Information-theoretic co-clustering. In Proceedings of
the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, KDD ’03,
pages 89–98, New York, NY, USA, 2003. ACM.
[6] G. H. Golub and C. F. Van Loan. Matrix Computations. Johns Hopkins Studies in the Mathematical
Sciences. Johns Hopkins University Press, Baltimore, MD, third edition, 1996.
[7] George Karypis and Vipin Kumar. A fast and high quality multilevel scheme for partitioning irregular
graphs. SIAM Journal on Scientific Computing, 20(1):359–392, 1998.
[8] Y. Koren. Collaborative filtering with temporal dynamics. In Proceedings of the 15th ACM SIGKDD
international conference on Knowledge discovery and data mining, KDD ’09, pages 447–456, New York,
NY, USA, 2009. ACM.
[9] Y. Koren, R. Bell, and C. Volinsky. Matrix factorization techniques for recommender systems. Computer,
42:30–37, August 2009.
[10] S. Lohr. A $1 million research bargain for netflix, and maybe a model for others. The New York Times,
September 22:B1, 2009. September, 21.
[11] B. Savas and I. S. Dhillon. Clustered low rank approximation of graphs in information science applications. In Proceedings of the SIAM International Conference on Data Mining (SDM), pages 164–175,
2011.
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