Low-Dimensional Polytope Approximation and Its Applications to Nonnegative Matrix Factorization

2008 ◽  
Vol 30 (3) ◽  
pp. 1131-1155 ◽  
Author(s):  
Moody T. Chu ◽  
Matthew M. Lin
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Nonnegative Matrix ◽  
Polytope Approximation ◽  
Low Dimensional

The flexible recruitment of muscle synergies depends on the required force-generating capability

2014 ◽  
Vol 112 (2) ◽  
pp. 316-327 ◽  
Author(s):  
Shota Hagio ◽  
Motoki Kouzaki
Keyword(s):  
Central Nervous System ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Isometric Force ◽  
Nonnegative Matrix ◽  
Muscle Synergies ◽  
Joint Angles ◽  
Activation Patterns ◽  
The Central Nervous System ◽  
Low Dimensional

To simplify redundant motor control, the central nervous system (CNS) may modularly organize and recruit groups of muscles as “muscle synergies.” However, smooth and efficient movements are expected to require not only low-dimensional organization, but also flexibility in the recruitment or combination of synergies, depending on force-generating capability of individual muscles. In this study, we examined how the CNS controls activations of muscle synergies as changing joint angles. Subjects performed multidirectional isometric force generations around right ankle and extracted the muscle synergies using nonnegative matrix factorization across various knee and hip joint angles. As a result, muscle synergies were selectively recruited with merging or decomposition as changing the joint angles. Moreover, the activation profiles, including activation levels and the direction indicating the peak, of muscle synergies across force directions depended on the joint angles. Therefore, we suggested that the CNS selects appropriate muscle synergies and controls their activation patterns based on the force-generating capability of muscles with merging or decomposing descending neural inputs.

scholarly journals Robust Structure Preserving Nonnegative Matrix Factorization for Dimensionality Reduction

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Bingfeng Li ◽  
Yandong Tang ◽  
Zhi Han
Keyword(s):  
Dimensionality Reduction ◽  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Noisy Data ◽  
Nonnegative Matrix ◽  
Structure Preserving ◽  
Structure Preservation ◽  
Significant Performance ◽  
Linear Dimensionality Reduction ◽  
Low Dimensional

As a linear dimensionality reduction method, nonnegative matrix factorization (NMF) has been widely used in many fields, such as machine learning and data mining. However, there are still two major drawbacks for NMF: (a) NMF can only perform semantic factorization in Euclidean space, and it fails to discover the intrinsic geometrical structure of high-dimensional data distribution. (b) NMF suffers from noisy data, which are commonly encountered in real-world applications. To address these issues, in this paper, we present a new robust structure preserving nonnegative matrix factorization (RSPNMF) framework. In RSPNMF, a local affinity graph and a distant repulsion graph are constructed to encode the geometrical information, and noisy data influence is alleviated by characterizing the data reconstruction term of NMF withl2,1-norm instead ofl2-norm. With incorporation of the local and distant structure preservation regularization term into the robust NMF framework, our algorithm can discover a low-dimensional embedding subspace with the nature of structure preservation. RSPNMF is formulated as an optimization problem and solved by an effective iterative multiplicative update algorithm. Experimental results on some facial image datasets clustering show significant performance improvement of RSPNMF in comparison with the state-of-the-art algorithms.

Cross-scene hyperspectral image classification based on DWT and manifold-constrained subspace learning

2017 ◽  
Vol 15 (06) ◽  
pp. 1750062 ◽  
Author(s):  
Minchao Ye ◽  
Wenbin Zheng ◽  
Huijuan Lu ◽  
Xianting Zeng ◽  
Yuntao Qian
Keyword(s):  
Matrix Factorization ◽  
Nonnegative Matrix Factorization ◽  
Hyperspectral Image ◽  
Nonnegative Matrix ◽  
Subspace Learning ◽  
Manifold Regularization ◽  
Scene Classification ◽  
3D Wavelet Transform ◽  
Feature Subspace ◽  
Low Dimensional

Hyperspectral image (HSI) classification draws a lot of attentions in the past decades. The classical problem of HSI classification mainly focuses on a single HSI scene. In recent years, cross-scene classification becomes a new problem, which deals with the classification models that can be applied across different but highly related HSI scenes sharing common land cover classes. This paper presents a cross-scene classification framework combining spectral–spatial feature extraction and manifold-constrained feature subspace learning. In this framework, spectral–spatial feature extraction is completed using three-dimensional (3D) wavelet transform while manifold-constrained feature subspace learning is implemented via multitask nonnegative matrix factorization (MTNMF) with manifold regularization. In 3D wavelet transform, we drop some coefficients corresponding to high frequency in order to avoid data noise. In feature subspace learning, a common dictionary (basis) matrix is shared by different scenes during the nonnegative matrix factorization, indicating that the highly related scenes should share than same low-dimensional feature subspace. Furthermore, manifold regularization is applied to force the consistency across the scenes, i.e. all pixels representing the same land cover class should be similar in the low-dimensional feature subspace, though they may be drawn from different scenes. The experimental results show that the proposed method performs well in cross-scene HSI datasets.

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