Projected Gradient Methods for Nonnegative Matrix Factorization

By Chih-Jen Lin. 2007

1,819 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Optimization & Training, Signal Processing

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Citations in the corpus

GAN Inversion: A Survey (2021, methodology): “DFF is the application of non-negative matrix factorization (NMF) [189], [190] to the ReLU feature activations of a pretrained neural network.”
Recommendations as Treatments: Debiasing Learning and Evaluation (2016, methodology): “Finally, note that other recommendation methods (e.g., Weimer et al., 2007; Lin, 2007) can in principle be adapted to propensity scoring as well.”
Don’t count, predict! A systematic comparison of context-counting vs. context-predicting semantic vectors (2014, methodology): “The latter were obtained by applying the Singular Value Decomposition (Golub and Van Loan, 1996) or Non-negative Matrix Factorization (Lee and Seung, 2000), Lin (2007) algorithm, with reduced sizes ranging from 200 to 500 in steps of 100.”
Multi-Step Regression Learning for Compositional Distributional Semantics (2013, methodology): “We use the Matlab implementation 2 of the projected gradient algorithm proposed in Lin (2007), which minimizes the squared error of Frobenius norm F ( W, H ) = (cid:107) X − W H 2 F .”
Online Learning for Matrix Factorization and Sparse Coding (2009, methodology): “As for dictionary learning, classical approaches for addressing this problem are batch algorithms, such as the multiplicative update rules of Lee and Seung (2001), or the projected gradient descent algorithm of Lin (2007).”
Constrained Nonnegative Matrix Factorization for Image Representation (2012, methodology): “Other than the multiplicative update method to find the matrix factors, others have suggested gradient descent algorithms [28] to solve the optimization problem.”
Generalized Low Rank Models (2014, methodology): “Hence a number of specialized algorithms and codes for fitting NNMF models are available [86, 91, 78, 80, 13, 79, 81].”
Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis (2009, methodology): “Other types of NMF algorithms, based for example on projected gradient or quasiNewton methods, have recently been designed to improve convergence of NMF with the Euclidean distance (Berry et al., 2007; Lin, 2007).”
Learning the Structural Vocabulary of a Network (2017, methodology): “…reduction to 20% of the input dimension (250 hidden units), the autoencoder achieved a 73.4% reconstruction accuracy, also outperforming other methods, including PCA + SVD, ICA (Hyvarinen & Oja, 2000), non-negative matrix factorization (Lin, 2007), and dictionary learning (Mairal et al., 2009).”
An analysis of the coherence of descriptors in topic modeling (2015, methodology): “We used the squared error NMF variant as provided by scikit-learn (Pedregosa et al., 2011), which is an implementation of the fast alternating least squares method proposed by Lin (2007).”
Scalable Temporal Latent Space Inference for Link Prediction in Dynamic Social Networks (2014, methodology): “st term), is also NP-hard. There exists a set of candidate approximate algorithms, including block coordinate descent [33], multiplicative update rule [34], projected non-negative least square method [17], quasi-newton method [36], and linear programming [21], which might be adopted here to solve Pr”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “Linear Projection-Based NMF (LPBNMF) suggested by Li and Zhang [69], where VV ¼ QQX and XX (cid:5) UUQX , can be regarded as the dual problem of Convex NMF.”
Coupled Nonnegative Matrix Factorization Unmixing for Hyperspectral and Multispectral Data Fusion (2012, positive): “In this case, the CNMF algorithm appears to be a projected gradient NMF [36], with the projection steps being (6) and (7), which is mathematically clear and simple to implement.”
Information Bottleneck Learning Using Privileged Information for Visual Recognition (2016, methodology): “We compute F with Algorithm 1, which is a projected gradient method [26] with Armijo’s condition”