Limitations of matrix completion via trace norm minimization

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.

• Type: Journal
• Year: 2010
• Where: SIGKDD
• Authors: Xiaoxiao Shi, Philip S. Yu
• Keywords: Information Technology, Norm Minimization, SIGKDD 2010, Small Set, Trace Norm Minimization