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Matrix factorization with Binary Components
Motivated by an application in computational biology, we consider low-ra...
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A global optimization algorithm for sparse mixed membership matrix factorization
Mixed membership factorization is a popular approach for analyzing data ...
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The PRIMPing Routine -- Tiling through Proximal Alternating Linearized Minimization
Mining and exploring databases should provide users with knowledge and n...
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A Parallel and Efficient Algorithm for Learning to Match
Many tasks in data mining and related fields can be formalized as matchi...
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Adaptive Quantile Low-Rank Matrix Factorization
Low-rank matrix factorization (LRMF) has received much popularity owing ...
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Asymmetric Multiresolution Matrix Factorization
Multiresolution Matrix Factorization (MMF) was recently introduced as an...
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MatRec: Matrix Factorization for Highly Skewed Dataset
Recommender systems is one of the most successful AI technologies applie...
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Expectile Matrix Factorization for Skewed Data Analysis
Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and extreme data, least squares cannot explain their central tendency or tail distributions, yielding undesired estimates. In this paper, we propose expectile matrix factorization by introducing asymmetric least squares, a key concept in expectile regression analysis, into the matrix factorization framework. We propose an efficient algorithm to solve the new problem based on alternating minimization and quadratic programming. We prove that our algorithm converges to a global optimum and exactly recovers the true underlying low-rank matrices when noise is zero. For synthetic data with skewed noise and a real-world dataset containing web service response times, the proposed scheme achieves lower recovery errors than the existing matrix factorization method based on least squares in a wide range of settings.
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