Contaminated Images Recovery by Implementing Non-negative Matrix Factorisation

• URL: http://arxiv.org/abs/2211.04247v4
• Date: Mon, 1 May 2023 11:01:32 GMT
• Title: Contaminated Images Recovery by Implementing Non-negative Matrix Factorisation
• Authors: Pengwei Yang, Chongyangzi Teng and Jack George Mangos
• Abstract summary: We theoretically examine the robustness of the traditional NMF, HCNMF, and L2,1-NMF algorithms and execute sets of experiments to demonstrate the robustness on ORL and Extended YaleB datasets. Due to the computational cost of these approaches, our final models, such as the HCNMF and L2,1-NMF model, fail to converge within the parameters of this work.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Non-negative matrix factorisation (NMF) has been extensively applied to the problem of corrupted image data. Standard NMF approach minimises Euclidean distance between data matrix and factorised approximation. The traditional NMF technique is sensitive to outliers since it utilises the squared error of each data point, despite the fact that this method has proven effective. In this study, we theoretically examine the robustness of the traditional NMF, HCNMF, and L2,1-NMF algorithms and execute sets of experiments to demonstrate the robustness on ORL and Extended YaleB datasets. Our research indicates that each algorithm requires a different number of iterations to converge. Due to the computational cost of these approaches, our final models, such as the HCNMF and L2,1-NMF model, fail to converge within the iteration parameters of this work. Nonetheless, the experimental results illustrate, to some extent, the robustness of the aforementioned techniques.

Related papers

• Stratified-NMF for Heterogeneous Data [8.174199227297514]
  We propose a modified NMF objective, Stratified-NMF, that simultaneously learns strata-dependent statistics and a shared topics matrix. We apply our method to three real world datasets and empirically investigate their learned features.
  arXiv  Detail & Related papers  (2023-11-17T00:34:41Z)
• Unitary Approximate Message Passing for Matrix Factorization [90.84906091118084]
  We consider matrix factorization (MF) with certain constraints, which finds wide applications in various areas. We develop a Bayesian approach to MF with an efficient message passing implementation, called UAMPMF. We show that UAMPMF significantly outperforms state-of-the-art algorithms in terms of recovery accuracy, robustness and computational complexity.
  arXiv  Detail & Related papers  (2022-07-31T12:09:32Z)
• Adaptive Weighted Nonnegative Matrix Factorization for Robust Feature Representation [9.844796520630522]
  Nonnegative matrix factorization (NMF) has been widely used to dimensionality reduction in machine learning. Traditional NMF does not properly handle outliers, so that it is sensitive to noise. This paper proposes an adaptive weighted NMF, which introduces weights to emphasize the different importance of each data point.
  arXiv  Detail & Related papers  (2022-06-07T05:27:08Z)
• SymNMF-Net for The Symmetric NMF Problem [62.44067422984995]
  We propose a neural network called SymNMF-Net for the Symmetric NMF problem. We show that the inference of each block corresponds to a single iteration of the optimization. Empirical results on real-world datasets demonstrate the superiority of our SymNMF-Net.
  arXiv  Detail & Related papers  (2022-05-26T08:17:39Z)
• Log-based Sparse Nonnegative Matrix Factorization for Data Representation [55.72494900138061]
  Nonnegative matrix factorization (NMF) has been widely studied in recent years due to its effectiveness in representing nonnegative data with parts-based representations. We propose a new NMF method with log-norm imposed on the factor matrices to enhance the sparseness. A novel column-wisely sparse norm, named $ell_2,log$-(pseudo) norm, is proposed to enhance the robustness of the proposed method.
  arXiv  Detail & Related papers  (2022-04-22T11:38:10Z)
• Co-Separable Nonnegative Matrix Factorization [20.550794776914508]
  Nonnegative matrix factorization (NMF) is a popular model in the field of pattern recognition. We refer to this NMF as a Co-Separable NMF (CoS-NMF) An optimization model for CoS-NMF is proposed and alternated fast gradient method is employed to solve the model.
  arXiv  Detail & Related papers  (2021-09-02T07:05:04Z)
• Feature Weighted Non-negative Matrix Factorization [92.45013716097753]
  We propose the Feature weighted Non-negative Matrix Factorization (FNMF) in this paper. FNMF learns the weights of features adaptively according to their importances. It can be solved efficiently with the suggested optimization algorithm.
  arXiv  Detail & Related papers  (2021-03-24T21:17:17Z)
• Entropy Minimizing Matrix Factorization [102.26446204624885]
  Nonnegative Matrix Factorization (NMF) is a widely-used data analysis technique, and has yielded impressive results in many real-world tasks. In this study, an Entropy Minimizing Matrix Factorization framework (EMMF) is developed to tackle the above problem. Considering that the outliers are usually much less than the normal samples, a new entropy loss function is established for matrix factorization.
  arXiv  Detail & Related papers  (2021-03-24T21:08:43Z)
• Algorithms for Nonnegative Matrix Factorization with the Kullback-Leibler Divergence [20.671178429005973]
  Kullback-Leibler (KL) divergence is one of the most widely used objective function for nonnegative matrix factorization (NMF) We propose three new algorithms that guarantee the non-increasingness of the objective function. We conduct extensive numerical experiments to provide a comprehensive picture of the performances of the KL NMF algorithms.
  arXiv  Detail & Related papers  (2020-10-05T11:51:39Z)
• Positive Semidefinite Matrix Factorization: A Connection with Phase Retrieval and Affine Rank Minimization [71.57324258813674]
  We show that PSDMF algorithms can be designed based on phase retrieval (PR) and affine rank minimization (ARM) algorithms. Motivated by this idea, we introduce a new family of PSDMF algorithms based on iterative hard thresholding (IHT)
  arXiv  Detail & Related papers  (2020-07-24T06:10:19Z)
• Sparse Separable Nonnegative Matrix Factorization [22.679160149512377]
  We propose a new variant of nonnegative matrix factorization (NMF) Separability requires that the columns of the first NMF factor are equal to columns of the input matrix, while sparsity requires that the columns of the second NMF factor are sparse. We prove that, in noiseless settings and under mild assumptions, our algorithm recovers the true underlying sources.
  arXiv  Detail & Related papers  (2020-06-13T03:52:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.