Weighted Low-Rank Approximations

By Nati Srebro, Tommi S. Jaakkola. 2003

873 citations recorded by the source corpus.

Subfields: Numerical Methods & Scientific Computing, Algorithms & Complexity

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Citations in the corpus

Recovery guarantee of weighted low-rank approximation via alternating minimization (2016, background): “For a matrix A , let A i denote its i -th column, A j denote its j -th row, and A i,j denote the element in i -th row and j -th column.”
On the Effectiveness of Linear Models for One-Class Collaborative Filtering (2016, background): “The basic idea is to embed users and items into some shared latent space (Srebro and Jaakkola 2003; Koren, Bell, and Volinsky 2009).”
Explainable Recommendation: A Survey and New Perspectives (2018, methodology): “Representative matrix factorization methods include Singular Value Decomposition (SVD) (Koren, 2008; Koren et al., 2009; Srebro and Jaakkola, 2003), Non-negative Matrix Factorization (NMF) (Lee and Seung, 1999, 2001), Max-Margin Matrix Factorization (MMMF) (Rennie and Srebro, 2005; Srebro et al.”
Spectral Regularization Algorithms for Learning Large Incomplete Matrices (2010, positive): “The following seemingly small modification to (1), minimize ‖Z‖∗ subject to ∑ (i,j)∈Ω (Xij − Zij) 2 ≤ δ, (2) makes the problem convex [Faz02].”
In Search of the Real Inductive Bias: On the Role of Implicit Regularization in Deep Learning (2014, neutral): “This is in stark contrast to the dimensionality-constrained low-rank situation, where the limiting factor is the number of hidden units, and local minima are abundant (Srebro & Jaakkola, 2003).”
Learning One-hidden-layer Neural Networks with Landscape Design (2017, methodology): “The optimization landscape has also been analyzed for other machine learning problems, including SVD/PCA phase retrieval/synchronization, orthogonal tensor decomposition, dictionary learning, matrix completion, matrix sensing [BH89, SJ13, GHJY15, SQW15, BBV16, GLM16, BNS16, GJZ17].”
SoRec: social recommendation using probabilistic matrix factorization (2008, methodology): “Recently, several matrix factorization methods [15, 17, 18, 23] have been proposed for collaborative filtering.”
Algorithmic Regularization in Over-parameterized Matrix Sensing and Neural Networks with Quadratic Activations (2017, background): “Such a phenomenon was already known for the PCA problem and recently shown for phase retrieval, robust PCA, and random tensor decomposition as well (e.g., see [36, 15, 3, 14, 13, 39] and references therein).”
Blind source separation problem in GPS time series (2016, methodology): “In this work, we use the PCA technique incorporated in the PCA-based inversion method software (PCAIM, Kositsky and Avouac 2010), which exploits the Srebro and Jaakkola (2003) decomposition algorithm, allowing the user to take into account missing data while performing the decomposition of the data…”
Transfer learning in heterogeneous collaborative filtering domains (2013, methodology): “These solutions have also been applied in collaborative filtering [24,22,7,44,48,53,29,10,27].”
Probabilistic factor models for web site recommendation (2011, background): “Recently, due to its efficiency in dealing with large datasets, several low-dimensional matrix approximation methods [1, 13, 21, 22, 23, 26] have been proposed.”
Probabilistic Models for Incomplete Multi-dimensional Arrays (2009, methodology): “Along the direction of SVD decomposition, Srebro and Jaakkola (2003) studied the weighted low-rank approximation problems on incomplete observational matrices.”
Bayesian exponential family projections for coupled data sources (2010, methodology): “Following Srebro and Jaakkola (2003), we use conjugate gradients, which has in our experiments turned out to be sufficiently robust.”
Weighted Nuclear Norm Minimization with Application to Image Denoising (2014, methodology): “Low rank matrix approximation methods can be generally categorized into two categories: the low rank matrix factorization (LRMF) methods [25, 2, 16, 13] and the nuclear norm minimization (NNM) methods [14, 4, 27, 3, 20, 19, 21, 11].”
Learning Multiscale Sparse Representations for Image and Video Restoration (2008, background): “This problem is known as a weighted rank-one approximation matrix (see [40]).”
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery (2018, background): “Both of these two categories have a variety of extensions as proposed in [5], [6], [19], [30], [61].”
Incorporating Phrase-level Sentiment Analysis on Textual Reviews for Personalized Recommendation (2015, background): “Copyrights for components of this work owned by others than the author(s) must be honored.”