Graph Regularized Nonnegative Matrix Factorization for Data Representation

By Deng Cai, Xiaofei He, Jiawei Han, Thomas S. Huang. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011

1,897 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/a58fd0822e57490a9d9a80bef460ba7087a17579

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In Computer Vision and Pattern Recognition

1. Dacheng Tao
2. Luc Van Gool
3. Ming-Hsuan Yang
4. Xiaogang Wang
5. Ling Shao
6. Yi Yang
7. Trevor Darrell
8. Jiashi Feng

Citations in the corpus

• Song recommendation with non-negative matrix factorization and graph total variation (2016, methodology): “In [10] this regularization is used along with a symmetric version of the KL divergence, however the latter has no analytic solution unlike the one we use in this work.”
• Ensemble manifold regularized sparse low-rank approximation for multiview feature embedding (2015, methodology): “the Regularized Nonnegative Matrix Factorization [17], the Non-negative Patch Alignment Framework [18], and the Regularized Low-Rank Matrix Approximation [19].”
• The Why and How of Nonnegative Matrix Factorization (2014, background): “…design and algorithmic implementation of refined NMF models for various applications is a very active area of research, e.g., graph regularized NMF [16], orthogonal NMF [24], tri-NMF [38, 85], semi and convex NMF [36], projective NMF [110], minimum volume NMF [93], and hierarchical NMF [86], to…”
• Unsupervised K-Means Clustering Algorithm (2020, methodology): “in Seeds, Flowmeter D, Wine and Waveform (version 1) are distributed in different ranges and data features in Australian (credit approval) are mixed feature types, we first preprocess data matrices using matrix factorization technique [35].”
• Group-Sparse Representation With Dictionary Learning for Medical Image Denoising and Fusion (2012, positive): “Recent works have shown that the graph-based method can preserve the geometrical structure effectively in manifold learning [23].”
• Piecewise Flat Embedding for Image Segmentation (2018, methodology): “GNMF [46] is another local method that proposes a graph regularized ob-jective function to take into account both the reconstruction loss and local pairwise variation cost.”
• Transfer Learning with Graph Co-Regularization (2012, background): “• can be either the Euclidian distance or the generalized KL-divergence [19], i.e., (x, x̂) = ‖x− x̂‖22, (x, x̂) = ∑ i ( xi log xi x̂i − xi + x̂i ) .”
• Algorithms for nonnegative matrix and tensor factorizations: a unified view based on block coordinate descent framework (2013, methodology): “In the data mining community, variants of NMF such as convex and semi-NMFs [25,75], orthogonal tri-NMF [26], and group-sparse NMF [56] have been proposed, and using NMF for clustering has been shown to be successful [12,57,63].”
• Salient Object Detection via Structured Matrix Decomposition (2017, methodology): “To this end, we introduce a Laplacian regularization based on the local invariance assumption [76]: if two adjacent image patches are similar with respect to their features, their representations should be close to each other in the subspace, and vise versa.”
• How to Learn a Graph from Smooth Signals (2016, methodology): “Cai et al. (2011) use the same term to regularize NMF, Jiang et al. (2013) for PCA and Kalofolias et al. (2014) for matrix completion.”
• Deep Collaborative Embedding for Social Image Understanding (2019, methodology): “Graph regularized NMF (GNMF) [51] explicitly exploits the local geometrical information as a regularization term added in NMF.”
• A Survey on Network Embedding (2017, methodology): “Given the set of clusters obtained from the ground truth and obtained from the algorithm, respectively, denoted by C 6 https://twitter.com/ 7 http://t.qq.com/ and C (cid:48) , the NMI can be defined as where H ( C ) is the entropy of C , and MI ( C, C (cid:48) ) is the mutual information metric of C ”
• Online Nonnegative Matrix Factorization With Robust Stochastic Approximation (2012, methodology): “These algorithms have been widely used to learn NMF and its extensions [8], [5], [14].”
• Nonnegative Matrix Factorization: A Comprehensive Review (2013, background): “[99], [98] modeled the manifold structure by constructing a nearest neighborhood graph on a scatter of data points.”
• Symmetric Nonnegative Matrix Factorization for Graph Clustering (2012, methodology): “We use the GNMF algorithm and the suggested parameters in [3].”
• Utilizing graph machine learning within drug discovery and development (2021, methodology): “One such approach is to use a graph’s structural information to regularize embeddings derived from the factorization of the feature matrix Xv [78, 79].”