The Relationships Among Various Nonnegative Matrix Factorization Methods for Clustering

By Tao Li, Chris H. Q. Ding. Industrial Conference on Data Mining, 2006

348 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/12e46e8bebeb36875d19bc6d61cde3531bb39ca5

How researchers see this paper

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

In Artificial Intelligence

1. Feiping Nie
2. Xuelong Li
3. Deng Cai
4. Jiawei Han
5. Xiaofei He
6. Thomas S. Huang
7. Heng Huang
8. Dacheng Tao

In Computer Vision and Pattern Recognition

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

Citations in the corpus

• Non-negative Matrix Factorization on Manifold (2008, background): “For more discussions on the relationship between various NMF extensions, please refer [17], [12], [6].”
• 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].”
• Efficient agglomerative hierarchical clustering (2015, methodology): “…computed, various partitional clustering algorithms have been developed and representative ones include spectral clustering (Luxburg, 2007; Ng, Jordan, & Weiss, 2001), graph-partitioning based (Dhillon, Guan, & Kulis, 2004), and non-negative matrix factorization based approaches (Li & Ding, 2006).”
• Clustering and projected clustering with adaptive neighbors (2014, methodology): “More recently, the Nonnegative Matrix Factorization (NMF) has been used as the relaxation technique for clustering with excellent performance [12, 16].”
• Constrained Nonnegative Matrix Factorization for Image Representation (2012, methodology): “Among matrix factorization methods, Nonnegative Matrix Factorization (NMF) [2], [3] specializes in that it enforces the constraint that the factor matrices must be nonnegative, i.e., all elements must be equal to or greater than zero.”
• A Semi-NMF-PCA Unified Framework for Data Clustering (2017, methodology): “A comparison of several NMF algorithms with various databases was performed by Li and Ding [24].”
• 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.”