Orthogonal Nonnegative Matrix Factorization: Multiplicative Updates on Stiefel Manifolds

Authors:
Jiho Yoo;Seungjin Choi
Affiliations:
Department of Computer Science, Pohang University of Science and Technology, Pohang, Korea 790-784;Department of Computer Science, Pohang University of Science and Technology, Pohang, Korea 790-784
Venue:
IDEAL '08 Proceedings of the 9th International Conference on Intelligent Data Engineering and Automated Learning
Year:
2008

Citing 6
Cited 7

Geometric optimization methods for adaptive filtering

Geometric optimization methods for adaptive filtering
The Geometry of Algorithms with Orthogonality Constraints

SIAM Journal on Matrix Analysis and Applications
Document clustering based on non-negative matrix factorization

Proceedings of the 26th annual international ACM SIGIR conference on Research and development in informaion retrieval
Relation between PLSA and NMF and implications

Proceedings of the 28th annual international ACM SIGIR conference on Research and development in information retrieval
Orthogonal nonnegative matrix t-factorizations for clustering

Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Document clustering using nonnegative matrix factorization

Information Processing and Management: an International Journal

Weighted Nonnegative Matrix Co-Tri-Factorization for Collaborative Prediction

ACML '09 Proceedings of the 1st Asian Conference on Machine Learning: Advances in Machine Learning
Efficient object detection using orthogonal NMF descriptor hierarchies

Proceedings of the 32nd DAGM conference on Pattern recognition
Quadratic nonnegative matrix factorization

Pattern Recognition
Supervised input space scaling for non-negative matrix factorization

Signal Processing
Matrix co-factorization on compressed sensing

IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Perceptually enhanced blind single-channel music source separation by Non-negative Matrix Factorization

Digital Signal Processing
A convergent algorithm for orthogonal nonnegative matrix factorization

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

Nonnegative matrix factorization (NMF) is a popular method for multivariate analysis of nonnegative data, the goal of which is decompose a data matrix into a product of two factor matrices with all entries in factor matrices restricted to be nonnegative. NMF was shown to be useful in a task of clustering (especially document clustering). In this paper we present an algorithm for orthogonal nonnegative matrix factorization, where an orthogonality constraint is imposed on the nonnegative decomposition of a term-document matrix. We develop multiplicative updates directly from true gradient on Stiefel manifold, whereas existing algorithms consider additive orthogonality constraints. Experiments on several different document data sets show our orthogonal NMF algorithms perform better in a task of clustering, compared to the standard NMF and an existing orthogonal NMF.