Nonnegative Matrix Factorization models for knowledge extraction from biomedical and other real world data

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Flavia Esposito ◽  
Nicoletta Del Buono ◽  
Laura Selicato
Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1187
Author(s):  
Peitao Wang ◽  
Zhaoshui He ◽  
Jun Lu ◽  
Beihai Tan ◽  
YuLei Bai ◽  
...  

Symmetric nonnegative matrix factorization (SNMF) approximates a symmetric nonnegative matrix by the product of a nonnegative low-rank matrix and its transpose. SNMF has been successfully used in many real-world applications such as clustering. In this paper, we propose an accelerated variant of the multiplicative update (MU) algorithm of He et al. designed to solve the SNMF problem. The accelerated algorithm is derived by using the extrapolation scheme of Nesterov and a restart strategy. The extrapolation scheme plays a leading role in accelerating the MU algorithm of He et al. and the restart strategy ensures that the objective function of SNMF is monotonically decreasing. We apply the accelerated algorithm to clustering problems and symmetric nonnegative tensor factorization (SNTF). The experiment results on both synthetic and real-world data show that it is more than four times faster than the MU algorithm of He et al. and performs favorably compared to recent state-of-the-art algorithms.


2020 ◽  
Vol 34 (04) ◽  
pp. 5420-5427
Author(s):  
Qiao Maoying ◽  
Yu Jun ◽  
Liu Tongliang ◽  
Wang Xinchao ◽  
Tao Dacheng

Nonnegative matrix factorization (NMF) has been widely employed in a variety of scenarios due to its capability of inducing semantic part-based representation. However, because of the non-convexity of its objective, the factorization is generally not unique and may inaccurately discover intrinsic “parts” from the data. In this paper, we approach this issue using a Bayesian framework. We propose to assign a diversity prior to the parts of the factorization to induce correctness based on the assumption that useful parts should be distinct and thus well-spread. A Bayesian framework including this diversity prior is then established. This framework aims at inducing factorizations embracing both good data fitness from maximizing likelihood and large separability from the diversity prior. Specifically, the diversity prior is formulated with determinantal point processes (DPP) and is seamlessly embedded into a Bayesian NMF framework. To carry out the inference, a Monte Carlo Markov Chain (MCMC) based procedure is derived. Experiments conducted on a synthetic dataset and a real-world MULAN dataset for multi-label learning (MLL) task demonstrate the superiority of the proposed method.


2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Feiqiong Chen ◽  
Guopeng Li ◽  
Shuaihui Wang ◽  
Zhisong Pan

Many real-world datasets are described by multiple views, which can provide complementary information to each other. Synthesizing multiview features for data representation can lead to more comprehensive data description for clustering task. However, it is often difficult to preserve the locally real structure in each view and reconcile the noises and outliers among views. In this paper, instead of seeking for the common representation among views, a novel robust neighboring constraint nonnegative matrix factorization (rNNMF) is proposed to learn the neighbor structure representation in each view, and L2,1-norm-based loss function is designed to improve its robustness against noises and outliers. Then, a final comprehensive representation of data was integrated with those representations of multiviews. Finally, a neighboring similarity graph was learned and the graph cut method was used to partition data into its underlying clusters. Experimental results on several real-world datasets have shown that our model achieves more accurate performance in multiview clustering compared to existing state-of-the-art methods.


Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Xiangguang Dai ◽  
Chuandong Li ◽  
Biqun Xiang

We present a novel method, called graph sparse nonnegative matrix factorization, for dimensionality reduction. The affinity graph and sparse constraint are further taken into consideration in nonnegative matrix factorization and it is shown that the proposed matrix factorization method can respect the intrinsic graph structure and provide the sparse representation. Different from some existing traditional methods, the inertial neural network was developed, which can be used to optimize our proposed matrix factorization problem. By adopting one parameter in the neural network, the global optimal solution can be searched. Finally, simulations on numerical examples and clustering in real-world data illustrate the effectiveness and performance of the proposed method.


2016 ◽  
Vol 22 ◽  
pp. 219
Author(s):  
Roberto Salvatori ◽  
Olga Gambetti ◽  
Whitney Woodmansee ◽  
David Cox ◽  
Beloo Mirakhur ◽  
...  

2020 ◽  
Author(s):  
Jersy Cardenas ◽  
Gomez Nancy Sanchez ◽  
Sierra Poyatos Roberto Miguel ◽  
Luca Bogdana Luiza ◽  
Mostoles Naiara Modroño ◽  
...  

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