Singular value decomposition and least squares solutions

By Gene H. Golub, C. Reinsch. 1970

Subfields: Statistical Learning Theory, Numerical Methods & Scientific Computing

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Citations in the corpus

Measuring Data (2022, methodology): “Such embeddings may be obtained for example by modeling co-occurrences between data instances through Singular Value Decomposition (Golub and Reinsch, 1970) or Word2Vec (Mikolov et al.”
SimLex-999: Evaluating Semantic Models With (Genuine) Similarity Estimation (2014, methodology): “As described by Landauer and Dumais (1997), we applied Singular Value Decomposition (SVD) (Golub and Reinsch, 1970) to the PMI-weighted VSM matrix, reducing the dimension of each concept representation to 300 (which yielded best re-sults after experimenting, as before, with 100-500 dimension vectors”
A practical tutorial on autoencoders for nonlinear feature fusion: Taxonomy, models, software and guidelines (2018, methodology): “The procedure to curate biological databases is very expensive, so usually machine learning methods such as SVD ( Singular Value Decomposition ) [145] are applied to help in the process.”
A Comprehensive Survey of Graph Embedding: Problems, Techniques, and Applications (2017, methodology): “odes [21]. Eq. 5 aims to ﬁnd an optimal rank-dapproximation of the proximity matrix W(dis the dimensionality of the embedding). One popular solution is to apply SVD (Singular Value Decomposition) on W[110]. Formally, W= P jVj i=1 ˙ iu iu c i T ˇ P d i=1 ˙ iu iu i T; (6) where f˙ 1 ;˙ 2; jV gare the ”
Computation of the Singular Value Decomposition (2006, background): “The developments for it can be found in [GK65], [GK68], [BG69], and [GR70].”
Deep autoencoder neural networks for gene ontology annotation predictions (2014, methodology): “Truncated Singular Value Decomposition (tSVD) [16] is a matrix factorization method that produces a low-rank approximation to a matrix.”
Transferability vs. Discriminability: Batch Spectral Penalization for Adversarial Domain Adaptation (2019, methodology): “In addition, in each min-batch iteration, (c) uses 0.342s while (d) uses 0.359s (Titan V), which shows that SVD does not cost much computation for feature matrix of a small batch.”
A Deep Matrix Factorization Method for Learning Attribute Representations (2015, methodology): “In Singular Value Decomposition (SVD) [16], the method that underlies Principal Component Analysis (PCA) [17], we factorize X into two factors: the loadings or bases Z ∈ p × k and the features or components H ∈ k × n , without imposing any sign restrictions on either our data or the resulting…”
Unsupervised Deep Homography: A Fast and Robust Homography Estimation Model (2017, background): “In addition, the gradients are easier to calculate than for SVD.”
Finding Approximate POMDP solutions Through Belief Compression (2011, unknown): “Related Work Many attempts have been made to use reachability analysis to constrain the set of beliefs for planning (Washington, 1997; Hauskrecht, 2000; Zhou & Hansen, 2001; Pineau, Gordon, & Thrun, 2003a). If the reachable set of beliefs is relatively small, then forward search to find this set is ”
Multi-source random excitation identification for stochastic structures based on matrix perturbation and modified regularization method (2019, methodology): “Callahna [15] proved that the regularization method is feasible and effective for the ill-posed problem based on singular value decomposition (SVD) technique used during the inversion of FRF matrix.”
Learning Grounded Meaning Representations with Autoencoders (2014, methodology): “In contrast, all bimodal models (SVD, kCCA, and SAE) are better than their unimodal equivalents and RNN-640.”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, unknown): “SVD can be used to solve metric equations and data reduction problems [59–62] .”