An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiclass Spectral Clustering
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
K-means clustering via principal component analysis
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Non-negative Matrix Factorization with Sparseness Constraints
The Journal of Machine Learning Research
Co-clustering by block value decomposition
Proceedings of the eleventh ACM SIGKDD international conference on Knowledge discovery in data mining
Nonsmooth Nonnegative Matrix Factorization (nsNMF)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Orthogonal nonnegative matrix t-factorizations for clustering
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiplicative updates for non-negative projections
Neurocomputing
Fast Projection-Based Methods for the Least Squares Nonnegative Matrix Approximation Problem
Statistical Analysis and Data Mining
Computational Statistics & Data Analysis
Non-negative matrix factorization with α-divergence
Pattern Recognition Letters
Nonnegative matrix factorization with quadratic programming
Neurocomputing
Mixed Membership Stochastic Blockmodels
The Journal of Machine Learning Research
Orthogonal Nonnegative Matrix Factorization: Multiplicative Updates on Stiefel Manifolds
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
ICDM '08 Proceedings of the 2008 Eighth IEEE International Conference on Data Mining
Convex and Semi-Nonnegative Matrix Factorizations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonnegative Matrix and Tensor Factorizations: Applications to Exploratory Multi-way Data Analysis and Blind Source Separation
Linear and nonlinear projective nonnegative matrix factorization
IEEE Transactions on Neural Networks
Projective nonnegative matrix factorization for image compression and feature extraction
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
IEEE Transactions on Neural Networks - Part 1
K-local hyperplane distance nearest neighbor classifier oriented local discriminant analysis
Information Sciences: an International Journal
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In Nonnegative Matrix Factorization (NMF), a nonnegative matrix is approximated by a product of lower-rank factorizing matrices. Most NMF methods assume that each factorizing matrix appears only once in the approximation, thus the approximation is linear in the factorizing matrices. We present a new class of approximative NMF methods, called Quadratic Nonnegative Matrix Factorization (QNMF), where some factorizing matrices occur twice in the approximation. We demonstrate QNMF solutions to four potential pattern recognition problems in graph partitioning, two-way clustering, estimating hidden Markov chains, and graph matching. We derive multiplicative algorithms that monotonically decrease the approximation error under a variety of measures. We also present extensions in which one of the factorizing matrices is constrained to be orthogonal or stochastic. Empirical studies show that for certain application scenarios, QNMF is more advantageous than other existing nonnegative matrix factorization methods.