DocumentCode :
2985166
Title :
Bounded Matrix Low Rank Approximation
Author :
Kannan, Ravindran ; Ishteva, M. ; Haesun Park
fYear :
2012
fDate :
10-13 Dec. 2012
Firstpage :
319
Lastpage :
328
Abstract :
Matrix lower rank approximations such as non-negative matrix factorization (NMF) have been successfully used to solve many data mining tasks. In this paper, we propose a new matrix lower rank approximation called Bounded Matrix Low Rank Approximation (BMA) which imposes a lower and an upper bound on every element of a lower rank matrix that best approximates a given matrix with missing elements. This new approximation models many real world problems, such as recommender systems, and performs better than other methods, such as singular value decompositions (SVD) or NMF. We present an efficient algorithm to solve BMA based on coordinate descent method. BMA is different from NMF as it imposes bounds on the approximation itself rather than on each of the low rank factors. We show that our algorithm is scalable for large matrices with missing elements on multi core systems with low memory. We present substantial experimental results illustrating that the proposed method outperforms the state of the art algorithms for recommender systems such as Stochastic Gradient Descent, Alternating Least Squares with regularization, SVD++, Bias-SVD on real world data sets such as Jester, Movie lens, Book crossing, Online dating and Netflix.
Keywords :
data mining; gradient methods; matrix algebra; bounded matrix low rank approximation model; coordinate descent method; data mining task; multicore systems; nonnegative matrix factorization; recommender systems; regularization; singular value decomposition; stochastic gradient descent; Approximation algorithms; Least squares approximation; Matrix decomposition; Recommender systems; Upper bound; Vectors; Low rank approximation; block; block coordinate de- scent method; bound constraints; matrix factorization; recommender systems; scalable algorithm;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Data Mining (ICDM), 2012 IEEE 12th International Conference on
Conference_Location :
Brussels
ISSN :
1550-4786
Print_ISBN :
978-1-4673-4649-8
Type :
conf
DOI :
10.1109/ICDM.2012.131
Filename :
6413891
Link To Document :
بازگشت