Low-Rank and Sparse Matrix Completion for Recommendation

Zhao, Zhi Lin; Huang, Ling; Wang, Chang Dong; Lai, Jian; Yu, Philip S.

doi:10.1007/978-3-319-70139-4_1

Cited by 16 publications

(9 citation statements)

References 17 publications

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“…While original for the sparse spike estimation problem, it must be noted that the study of nonconvex optimization schemes for linear inverse problems has gained attraction recently for different kinds of low-dimensional models. For low-rank matrix estimation, a smooth parametrization of the problem is possible and it has been shown that a RIP guarantees the absence of spurious minima [3,30]. In [29], a model for phase recovery with alternated projections and smart initialization is considered.…”

Section: Related Workmentioning

confidence: 99%

The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem

Traonmilin

Aujol

2020

Inverse Problems

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The sparse spike estimation problem consists in estimating a number of off-thegrid impulsive sources from under-determined linear measurements. Information theoretic results ensure that the minimization of a non-convex functional is able to recover the spikes for adequately chosen measurements (deterministic or random). To solve this problem, methods inspired from the case of finite dimensional sparse estimation where a convex program is used have been proposed. Also greedy heuristics have shown nice practical results. However, little is known on the ideal non-convex minimization method. In this article, we study the shape of the global minimum of this non-convex functional: we give an explicit basin of attraction of the global minimum that shows that the non-convex problem becomes easier as the number of measurements grows. This has important consequences for methods involving descent algorithms (such as the greedy heuristic) and it gives insights for potential improvements of such descent methods.

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Section: Related Workmentioning

confidence: 99%

The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem

Traonmilin

Aujol

2020

Inverse Problems

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“…Ning et al [47] proposed a sparse linear method, which multiplies the sparse aggregation and scoring matrices to obtain the prediction matrix. Zhao et al [57] proposed a low-rank and sparse matrix completion (LSMC) algorithm and verified that LSMC could be used to recommend products to users in food and movie datasets. LSMC relies only on the original interaction matrix to learn lowrank and sparse matrices.…”

Section: Low-rank and Sparse Matrix Factorizationmentioning

confidence: 99%

Paper Recommendation Using SPECTER with Low-Rank and Sparse Matrix Factorization

2024

KSII TIIS

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“…Zhao and Udell (2020b) propose to impute missing data by learning a Gaussian copula model from incomplete observation and shows empirically the resulting imputation achieves stateof-the-art performance. Following this line of work, Zhao and Udell (2020a) develop a low rank Gaussian copula that scales well to large datasets, and Zhao, Landgrebe, Shekhtman, and Udell (2022) extend the model to online imputation of a streaming dataset using online model updates. This article introduces an additional methodological advance by extending the Gaussian copula model to support truncated variables.…”

Section: Introductionmentioning

confidence: 99%

gcimpute: A Package for Missing Data Imputation

Zhao,

Udell

2024

J. Stat. Soft.

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This article introduces the Python package gcimpute for missing data imputation. Package gcimpute can impute missing data with many different variable types, including continuous, binary, ordinal, count, and truncated values, by modeling data as samples from a Gaussian copula model. This semiparametric model learns the marginal distribution of each variable to match the empirical distribution, yet describes the interactions between variables with a joint Gaussian that enables fast inference, imputation with confidence intervals, and multiple imputation. The package also provides specialized extensions to handle large datasets (with complexity linear in the number of observations) and streaming datasets (with online imputation). This article describes the underlying methodology and demonstrates how to use the software package.

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Low-Rank and Sparse Matrix Completion for Recommendation

Cited by 16 publications

References 17 publications

The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem

The basins of attraction of the global minimizers of the non-convex sparse spike estimation problem

Paper Recommendation Using SPECTER with Low-Rank and Sparse Matrix Factorization

gcimpute: A Package for Missing Data Imputation

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