A Unified View of Matrix Factorization Models

By Ajit Paul Singh, Geoffrey J. Gordon. 2008

196 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Mechanics, Computational Theory and Mathematics

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Citations in the corpus

Modeling Consumer Preferences and Price Sensitivities from Large-Scale Grocery Shopping Transaction Logs (2017, methodology): “Matrix factorization techniques have been widely applied for recommender systems due to their accuracy and scalability [6, 16, 21, 35].”
Guaranteed Matrix Completion via Non-Convex Factorization (2014, methodology): “Such a matrix factorization model has long been used in PCA (principle component analysis) and many other applications [15].”
Exploiting compositionality to explore a large space of model structures (2012, background): “Srebro (2004) and Singh and Gordon (2008) each interpreted a variety of unsupervised learning algorithms as factorizing an input matrix into a product of two factors.”
Multimodal Data Fusion: An Overview of Methods, Challenges, and Prospects (2015, background): “, [16], [161], [163] and references therein.”
Structured sparsity through convex optimization (2011, background): “…all principal components, typically do not require the orthogonality of the components, and are referred to as matrix factorization problems (Singh and Gordon, 2008; Bach, Mairal and Ponce, 2008) in machine learning, and dictionary learning in signal processing (Olshausen and Field, 1996).”
Generative-Discriminative Basis Learning for Medical Imaging (2012, methodology): “Table I represents some examples of well-known methods that can be described by (1) (for more examples, see [25]).”
On Smoothing and Inference for Topic Models (2009, unknown): “Others have uni-ﬁed similar deterministic latent variable models [Welling et al., 2008a] and matrix factorization techniques [Singh and Gordon, 2008].”
Data Fusion by Matrix Factorization (2013, methodology): “For instance, SVD, non-negative matrix factorization and exponential family PCA all minimize Bregman divergence [19].”
Bayesian Inference for Nonnegative Matrix Factorisation Models (2009, background): “For NMF models, there exist many conditional independence relations, hence the Hessian matrix has a special block structure [12].”
Structured Sparse Principal Component Analysis (2009, background): “The synthesis interpretation leads to non-convex global formulations ([4, 11, 9, 12]) which estimate simultaneously all principal components, often drop the orthogonality constraints, and are referred to as matrix factorization problems ([13]) in machine learning, and dictionary learning in signal p”
Static and Dynamic Source Separation Using Nonnegative Factorizations: A unified view (2014, methodology): “…matrix factorization (NMF) [1] model, and it is conceptually similar to other well-known matrix factorizations such as principal component analysis , independent component analysis, sparse linear models, or even vector quantization, which can all be expressed using the same equation [2].”
Protein-protein interaction prediction via Collective Matrix Factorization (2010, methodology): “We first introduce matrix factorization (MF) [25] methods for an individual network.”
Poisson Noise Reduction with Non-local PCA (2012, methodology): “Some more specific details can be found in [39, 40] about matrix factorization for exponential families.”
Large-scale matrix factorization with distributed stochastic gradient descent (2011, background): “Speci.cally, low-rank matrix factorizations are effective tools for analyzing dyadic data in order to discover and quantify the interactions between two given entities.”
General Latent Feature Models for Heterogeneous Datasets (2017, methodology): “In particular, probabilistic matrix factorization models (Singh and Gordon, 2008) decompose the data as a product of a weight matrix and a feature matrix.”
Multi-relational matrix factorization using bayesian personalized ranking for social network data (2012, methodology): “Singh and Gordon [12, 13] propose a framework for multirelational factorization models.”
Generalized Low Rank Models (2014, methodology): “In [SG08], the authors offer a complete view of the state of the literature on matrix factorization as of 2008 in Table 1 of their paper.”
Collaborative competitive filtering: learning recommender using context of user choice (2011, background): “To design a concrete model [2, 21, 23], one needs to specify a distribution for the dependence.”
Outlier Detection for Text Data (2017, methodology): “It should be pointed out that NMF is similar to the generative models of text such as pLSI and LDA [10] [7] [21], though NMF often provides better interpretability.”