Non-negative Matrix Factorization on Manifold

By Deng Cai, Xiaofei He, Xiaoyun Wu, Jiawei Han. 2008 Eighth IEEE International Conference on Data Mining, 2008

436 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/5132c4dc71d19017e2feb98d107cc330cad0b7a2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Vision and Pattern Recognition

1. Dacheng Tao
2. Xuelong Li
3. Luc Van Gool
4. Yi Yang
5. Thomas S. Huang
6. Deng Cai
7. Jie Zhou
8. Ming-Hsuan Yang

Citations in the corpus

• MGAE: Marginalized Graph Autoencoder for Graph Clustering (2017, methodology): “When considering integrating both node content and network information, early methods in [1, 8] apply a nonnegative matrix factorization (NMF) strategy to decompose node content matrix and use graph structure as regularization terms.”
• Graph Regularized Nonnegative Matrix Factorization for Data Representation (2011, methodology): “Motivated by recent progress in matrix factorization and manifold learning [2], [5], [6], [7], in this paper we propose a novel algorithm, called Graph regularized Nonnegative Matrix Factorization (GNMF), which explicitly considers the local invariance.”
• 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.”
• Semantically Smooth Knowledge Graph Embedding (2015, background): “Manifold learning has been widely applied in many di ff erent areas, from dimensionality reduction (Belkin and Niyo-91 gi, 2001; Cai et al., 2008) and semi-supervised learning (Zhou et al., 2004; Zhu and Niyogi, 2005) to recommender systems (Ma et al., 2011) and community question answering (Wang et…”
• Constrained Nonnegative Matrix Factorization for Image Representation (2012, background): “Recently, Cai et al. [1] proposed a Graph regularized NMF (GNMF) approach to encode the geometrical information of the data space.”
• Manifold Regularized Discriminative Nonnegative Matrix Factorization With Fast Gradient Descent (2011, methodology): “Here, we evaluate the performance of the proposed MD-NMF comparing with six representative algorithms, which are NMF [24], PCA [18], LNMF [26], GNMF [12], DNMF [47], and NGE [44], on four popular face image datasets including YALE [6], ORL [36], UMIST [19], and CMU PIE [19].”
• Learning the Shared Subspace for Multi-task Clustering and Transductive Transfer Classification (2009, methodology): “In our future work, we will extend our method to take into account geometric structure as in [34] [38].”
• Network-based stratification of tumor mutations (2013, methodology): “For NBS we use a variant of NMF that encourages the selection of gene sets supporting each subtype according to high network connectivity (NetNMF) 58 .”
• Graph Regularized Sparse Coding for Image Representation (2011, background): “This assumption is usually referred to as manifold assumption [20], [39], which plays an essential role in developing various kinds of algorithms including dimensionality reduction algorithms [20], clustering algorithms [40], [41] and semisupervised learning algorithms [33], [42].”
• Robust nonnegative matrix factorization using L21-norm (2011, background): “also can be extended by making a combination with Laplacian embedding [2, 11].”
• Locally Consistent Concept Factorization for Document Clustering (2011, background): “Please see [15], [26] for other NMF extensions.”
• SSE: Semantically Smooth Embedding for Knowledge Graphs (2017, background): “Our approach further imposes constraints on the geometric structure of the embedding space, which exists intrinsically but is overlooked in previouswork.”