Results 1  10
of
198
MaximumMargin Matrix Factorization
 Advances in Neural Information Processing Systems 17
, 2005
"... We present a novel approach to collaborative prediction, using lownorm instead of lowrank factorizations. The approach is inspired by, and has strong connections to, largemargin linear discrimination. We show how to learn lownorm factorizations by solving a semidefinite program, and discuss ..."
Abstract

Cited by 264 (21 self)
 Add to MetaCart
(Show Context)
We present a novel approach to collaborative prediction, using lownorm instead of lowrank factorizations. The approach is inspired by, and has strong connections to, largemargin linear discrimination. We show how to learn lownorm factorizations by solving a semidefinite program, and discuss generalization error bounds for them.
Fast maximum margin matrix factorization for collaborative prediction
 In Proceedings of the 22nd International Conference on Machine Learning (ICML
, 2005
"... Maximum Margin Matrix Factorization (MMMF) was recently suggested (Srebro et al., 2005) as a convex, infinite dimensional alternative to lowrank approximations and standard factor models. MMMF can be formulated as a semidefinite programming (SDP) and learned using standard SDP solvers. However, cu ..."
Abstract

Cited by 248 (6 self)
 Add to MetaCart
(Show Context)
Maximum Margin Matrix Factorization (MMMF) was recently suggested (Srebro et al., 2005) as a convex, infinite dimensional alternative to lowrank approximations and standard factor models. MMMF can be formulated as a semidefinite programming (SDP) and learned using standard SDP solvers. However, current SDP solvers can only handle MMMF problems on matrices of dimensionality up to a few hundred. Here, we investigate a direct gradientbased optimization method for MMMF and demonstrate it on large collaborative prediction problems. We compare against results obtained by Marlin (2004) and find that MMMF substantially outperforms all nine methods he tested. 1.
Restricted Boltzmann machines for collaborative filtering
 In Machine Learning, Proceedings of the Twentyfourth International Conference (ICML 2004). ACM
, 2007
"... Most of the existing approaches to collaborative filtering cannot handle very large data sets. In this paper we show how a class of twolayer undirected graphical models, called Restricted Boltzmann Machines (RBM’s), can be used to model tabular data, such as user’s ratings of movies. We present eff ..."
Abstract

Cited by 220 (12 self)
 Add to MetaCart
Most of the existing approaches to collaborative filtering cannot handle very large data sets. In this paper we show how a class of twolayer undirected graphical models, called Restricted Boltzmann Machines (RBM’s), can be used to model tabular data, such as user’s ratings of movies. We present efficient learning and inference procedures for this class of models and demonstrate that RBM’s can be successfully applied to the Netflix data set, containing over 100 million user/movie ratings. We also show that RBM’s slightly outperform carefullytuned SVD models. When the predictions of multiple RBM models and multiple SVD models are linearly combined, we achieve an error rate that is well over 6 % better than the score of Netflix’s own system. 1.
Sparse representation for color image restoration
 the IEEE Trans. on Image Processing
, 2007
"... Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted ..."
Abstract

Cited by 219 (30 self)
 Add to MetaCart
(Show Context)
Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The KSVD has been recently proposed for this task [1], and shown to perform very well for various grayscale image processing tasks. In this paper we address the problem of learning dictionaries for color images and extend the KSVDbased grayscale image denoising algorithm that appears in [2]. This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to stateoftheart results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper. EDICS Category: COLCOLR (Color processing) I.
Relational Learning via Collective Matrix Factorization
, 2008
"... Relational learning is concerned with predicting unknown values of a relation, given a database of entities and observed relations among entities. An example of relational learning is movie rating prediction, where entities could include users, movies, genres, and actors. Relations would then encode ..."
Abstract

Cited by 130 (4 self)
 Add to MetaCart
(Show Context)
Relational learning is concerned with predicting unknown values of a relation, given a database of entities and observed relations among entities. An example of relational learning is movie rating prediction, where entities could include users, movies, genres, and actors. Relations would then encode users ’ ratings of movies, movies ’ genres, and actors ’ roles in movies. A common prediction technique given one pairwise relation, for example a #users × #movies ratings matrix, is lowrank matrix factorization. In domains with multiple relations, represented as multiple matrices, we may improve predictive accuracy by exploiting information from one relation while predicting another. To this end, we propose a collective matrix factorization model: we simultaneously factor several matrices, sharing parameters among factors when an entity participates in multiple relations. Each relation can have a different value type and error distribution; so, we allow nonlinear relationships between the parameters and outputs, using Bregman divergences to measure error. We extend standard alternating projection algorithms to our model, and derive an efficient Newton update for the projection. Furthermore, we propose stochastic optimization methods to deal with large, sparse matrices. Our model generalizes several existing matrix factorization methods, and therefore yields new largescale optimization algorithms for these problems. Our model can handle any pairwise relational schema and a
SoRec: Social Recommendation Using Probabilistic Matrix Factorization
, 2008
"... Data sparsity, scalability and prediction quality have been recognized as the three most crucial challenges that every collaborative filtering algorithm or recommender system confronts. Many existing approaches to recommender systems can neither handle very large datasets nor easily deal with users ..."
Abstract

Cited by 126 (8 self)
 Add to MetaCart
(Show Context)
Data sparsity, scalability and prediction quality have been recognized as the three most crucial challenges that every collaborative filtering algorithm or recommender system confronts. Many existing approaches to recommender systems can neither handle very large datasets nor easily deal with users who have made very few ratings or even none at all. Moreover, traditional recommender systems assume that all the users are independent and identically distributed; this assumption ignores the social interactions or connections among users. In view of the exponential growth of information generated by online social networks, social network analysis is becoming important for many Web applications. Following the intuition that a person’s social network will affect personal behaviors on the Web, this paper proposes a factor analysis approach based on probabilistic matrix factorization to solve the data sparsity and poor prediction accuracy problems by employing both users ’ social network information and rating records. The complexity analysis indicates that our approach can be applied to very large datasets since it scales linearly with the number of observations, while the experimental results shows that our method performs much better than the stateoftheart approaches, especially in the circumstance that users have made few or no ratings.
Matrix completion from noisy entries
 Journal of Machine Learning Research
"... Abstract Given a matrix M of lowrank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the 'Netflix problem') to structurefrommotion and position ..."
Abstract

Cited by 124 (8 self)
 Add to MetaCart
Abstract Given a matrix M of lowrank, we consider the problem of reconstructing it from noisy observations of a small, random subset of its entries. The problem arises in a variety of applications, from collaborative filtering (the 'Netflix problem') to structurefrommotion and positioning. We study a low complexity algorithm introduced in [1], based on a combination of spectral techniques and manifold optimization, that we call here OPTSPACE. We prove performance guarantees that are orderoptimal in a number of circumstances.
Gaussian processes for ordinal regression
 Journal of Machine Learning Research
, 2004
"... We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation ..."
Abstract

Cited by 116 (4 self)
 Add to MetaCart
We present a probabilistic kernel approach to ordinal regression based on Gaussian processes. A threshold model that generalizes the probit function is used as the likelihood function for ordinal variables. Two inference techniques, based on the Laplace approximation and the expectation propagation algorithm respectively, are derived for hyperparameter learning and model selection. We compare these two Gaussian process approaches with a previous ordinal regression method based on support vector machines on some benchmark and realworld data sets, including applications of ordinal regression to collaborative filtering and gene expression analysis. Experimental results on these data sets verify the usefulness of our approach.
CubeSVD: A Novel Approach to Personalized Web Search
 In Proc. of the 14 th International World Wide Web Conference (WWW
, 2005
"... As the competition of Web search market increases, there is a high demand for personalized Web search to conduct retrieval incorporating Web users' information needs. This paper focuses on utilizing clickthrough data to improve Web search. Since millions of searches are conducted everyday, a se ..."
Abstract

Cited by 111 (3 self)
 Add to MetaCart
(Show Context)
As the competition of Web search market increases, there is a high demand for personalized Web search to conduct retrieval incorporating Web users' information needs. This paper focuses on utilizing clickthrough data to improve Web search. Since millions of searches are conducted everyday, a search engine accumulates a large volume of clickthrough data, which records who submits queries and which pages he/she clicks on. The clickthrough data is highly sparse and contains di#erent types of objects (user, query and Web page), and the relationships among these objects are also very complicated. By performing analysis on these data, we attempt to discover Web users' interests and the patterns that users locate information. In this paper, a novel approach CubeSVD is proposed to improve Web search. The clickthrough data is represented by a 3order tensor, on which we perform 3mode analysis using the higherorder singular value decomposition technique to automatically capture the latent factors that govern the relations among these multitype objects: users, queries and Web pages. A tensor reconstructed based on the CubeSVD analysis reflects both the observed interactions among these objects and the implicit associations among them. Therefore, Web search activities can be carried out based on CubeSVD analysis. Experimental evaluations using a realworld data set collected from an MSN search engine show that CubeSVD achieves encouraging search results in comparison with some standard methods.
Generalized Low Rank Approximations of Matrices
 MACHINE LEARNING
, 2004
"... We consider the problem of computing low rank approximations of matrices. The novelty of our approach is that the low rank approximations are on a sequence of matrices. Unlike the ..."
Abstract

Cited by 110 (6 self)
 Add to MetaCart
We consider the problem of computing low rank approximations of matrices. The novelty of our approach is that the low rank approximations are on a sequence of matrices. Unlike the