On the Equivalence of Nonnegative Matrix Factorization and Spectral Clustering

By Chris H. Q. Ding, Xiaofeng He. 2005

1,040 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics, Optimization & Training

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Citations in the corpus

Efficient Content-Based Sparse Attention with Routing Transformers (2020, methodology): “This strategy draws inspiration from the application of k-means clustering to Non-negative Matrix Factorization (NMF) (Lee and Seung, 2001; Ding et al., 2005; Kim and Park, 2008), which is relevant to the sparsification of non-negative matrices like”
The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering (2006, methodology): “A very recent theoretical analysis [12] shows the equivalence of NMF and spectral clustering andK-means clustering.”
Deep Feature Factorization For Concept Discovery (2018, background): “Since NMF can be seen as performing clustering [8], we view a factor W j as a centroid of an activation cluster, which we show corresponds to coherent object or object-part.”
Sparse Nonnegative Matrix Factorization for Clustering (2008, background): “[6] claimed that symmetric NMF (A ≈ HH ) is equivalent to kernel K-means.”
Discriminative and Distinct Phenotyping by Constrained Tensor Factorization (2017, background): “This transformation is beneficial because it helps phenotypes to be more orthogonal (or distinct) by retaining B T orthogonality approximately 39 .”
An efficient and principled method for detecting communities in networks (2011, background): “A corresponding relaxation has been noted previously for a version of NMF and was shown to be related to spectral clustering [41, 42].”
Nonnegative Matrix Factorization: A Comprehensive Review (2013, methodology): “Further more, NMF is equivalent to k-means clustering when using Square of Euclidian Distance (SED) [44], [45], while tantamount to Probabilistic Latent Semantic Analysis (PLSA) when using Generalized Kullback-Leibler Divergence (GKLD) as the objective function [46], [47].”
Orthogonal nonnegative matrix t-factorizations for clustering (2006, methodology): “This corresponds to the simultaneous K-means clustering [9] of the rows and columns of X , where F is the cluster indicator matrix for clustering rows and G is the cluster indicator matrix for clustering columns.”
Constrained Nonnegative Matrix Factorization for Image Representation (2012, background): “Ding et al. [26] proposed a Semi-nonnegative Matrix Factorization algorithm where only one matrix factor is restricted to contain nonnegative entries, while it relaxes the constraint on the basis vectors.”
The Constrained Laplacian Rank Algorithm for Graph-Based Clustering (2016, background): “See (Ding and He 2005; Li and Ding 2006) for a discussion of the relations among these graph-based methods, and also the connections to non-negative matrix factorization.”
Open problems in the theory of completely positive and copositive matrices (2015, background): “More recent applications are in data mining and clustering [25], and in dynamical systems and control [48, 8].”
Federating Recommendations Using Differentially Private Prototypes (2020, background): “Non-negative matrix factorization (NMF) and spectral clustering have been shown to be equivalent (Ding et al., 2005).”
SVD based initialization: A head start for nonnegative matrix factorization (2008, methodology): “To do this, we consider matrices that admit the orthogonal nonnegative factorization described in [3,37].”
Convex and Semi-Nonnegative Matrix Factorizations (2010, methodology): “clustering ( 19 ), making use of the least square objectives o f NMF; as we emphasize in the”
A Semi-NMF-PCA Unified Framework for Data Clustering (2017, methodology): “(4) is usually solved by an alternately iterative algorithm, and in each iteration step, the intensive matrix multiplications are involved [13], [14], [15], [17].”