Using underapproximations for sparse nonnegative matrix factorization
Pattern Recognition
Shape Analysis of Elastic Curves in Euclidean Spaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graph Regularized Nonnegative Matrix Factorization for Data Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Nonnegative Matrix Factorization with Earth Mover's Distance Metric for Image Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast coordinate descent methods with variable selection for non-negative matrix factorization
Proceedings of the 17th ACM SIGKDD international conference on Knowledge discovery and data mining
Group coordinate descent algorithms for nonconvex penalized regression
Computational Statistics & Data Analysis
Improving a Lagrangian decomposition for the unconstrained binary quadratic programming problem
Computers and Operations Research
Non-negative matrix factorization as a feature selection tool for maximum margin classifiers
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Ensemble Manifold Regularization
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Neural Networks
Non-Negative Patch Alignment Framework
IEEE Transactions on Neural Networks
Beyond cross-domain learning: Multiple-domain nonnegative matrix factorization
Engineering Applications of Artificial Intelligence
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Non-negative matrix factorization (NMF) has been widely used as a data representation method based on components. To overcome the disadvantage of NMF in failing to consider the manifold structure of a data set, graph regularized NMF (GrNMF) has been proposed by Cai et al. by constructing an affinity graph and searching for a matrix factorization that respects graph structure. Selecting a graph model and its corresponding parameters is critical for this strategy. This process is usually carried out by cross-validation or discrete grid search, which are time consuming and prone to overfitting. In this paper, we propose a GrNMF, called MultiGrNMF, in which the intrinsic manifold is approximated by a linear combination of several graphs with different models and parameters inspired by ensemble manifold regularization. Factorization metrics and linear combination coefficients of graphs are determined simultaneously within a unified object function. They are alternately optimized in an iterative algorithm, thus resulting in a novel data representation algorithm. Extensive experiments on a protein subcellular localization task and an Alzheimer's disease diagnosis task demonstrate the effectiveness of the proposed algorithm.