Fast maximum margin matrix factorization for collaborative prediction
ICML '05 Proceedings of the 22nd international conference on Machine learning
Uncovering shared structures in multiclass classification
Proceedings of the 24th international conference on Machine learning
Classifying matrices with a spectral regularization
Proceedings of the 24th international conference on Machine learning
Consistency of Trace Norm Minimization
The Journal of Machine Learning Research
Improving maximum margin matrix factorization
Machine Learning
Convex multi-task feature learning
Machine Learning
An accelerated gradient method for trace norm minimization
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Fast nonparametric matrix factorization for large-scale collaborative filtering
Proceedings of the 32nd international ACM SIGIR conference on Research and development in information retrieval
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Social trust prediction using rank-k matrix recovery
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Matrix Recipes for Hard Thresholding Methods
Journal of Mathematical Imaging and Vision
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In recent years, compressive sensing attracts intensive attentions in the field of statistics, automatic control, data mining and machine learning. It assumes the sparsity of the dataset and proposes that the whole dataset can be reconstructed by just observing a small set of samples. One of the important approaches of compressive sensing is trace norm minimization, which can minimize the rank of the data matrix under some conditions. For example, in collaborative filtering, we are given a small set of observed item ratings of some users and we want to predict the missing values in the rating matrix. It is assumed that the users' ratings are affected by only a few factors and the resulting rating matrix should be of low rank. In this paper, we analyze the issues related to trace norm minimization and find an unexpected result that trace norm minimization often does not work as well as expected.