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Fast and Low Memory Cost Matrix Factorization: Algorithm, Analysis, and Case Study
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DOI：10.1109/TKDE.2018.2882197.png)
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Abstract
En 中文
Matrix factorization has been widely applied to various applications. With the fast development of storage and internet technologies, we have been witnessing a rapid increase of data. In this paper, we propose new algorithms for matrix factorization with the emphasis on efficiency. In addition, most existing methods of matrix factorization only consider a general smooth least square loss. Differently, many real-world applications have distinctive characteristics. As a result, different losses should be used accordingly. Therefore, it is beneficial to design new matrix factorization algorithms that are able to deal with both smooth and non-smooth losses. To this end, one needs to analyze the characteristics of target data and use the most appropriate loss based on the analysis. We particularly study two representative cases of low-rank matrix recovery, i.e., collaborative filtering for recommendation and high dynamic range imaging. To solve these two problems, we respectively propose a stage-wise matrix factorization algorithm by exploiting manifold optimization techniques. From our theoretical analysis, they are both are provably guaranteed to converge to a stationary point. Extensive experiments on recommender systems and high dynamic range imaging demonstrate the satisfactory performance and efficiency of our proposed method on large-scale real data.
Keywords:
Imaging
Optimization
Recommender systems
Manifolds
Convergence
Minimization
Dynamic range
Matrix factorization
matrix recovery
efficient optimization
convergence guarantees
recommender systems
HDR imaging
batch image alignment
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