CUR Based Initialization Strategy for Non-Negative Matrix Factorization in  Application to Hyperspectral Unmixing

Sun, Li; Zhao, Gengxin; Du, Xinpeng

doi:10.4236/jamp.2016.44068

Cited by 7 publications

(4 citation statements)

References 6 publications

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“…The result obtained after decomposition is nonnegative and has good physical meaning, and the implementation process is simple and fast. As the name implies, NMF decomposes a nonnegative matrix into two nonnegative matrices, and the result of multiplying these two matrices is equal to the original matrix before decomposition [11]. The objective function is shown in…”

Section: Basic Content Of Nonnegative Matrix Factorizationmentioning

confidence: 99%

Integrated Classification Algorithm for Unbalanced Data Streams Based on Joint Nonnegative Matrix Factorization

Zhao

2022

Wireless Communications and Mobile Computing

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The purpose of this paper is to study the unbalanced data flow integration classification algorithm based on joint nonnegative matrix factorization, in order to solve the problem that the basic clustering results obtained from the original data set have some information loss, thereby reducing the effective information in the integration stage. In this paper, the accuracy of the unbalanced data and the detection time consumption are selected as the research object. Six data sets with imbalanced proportions of minority and majority samples are selected for experiments. Mathematical statistical analysis is first used to observe text classification, disease diagnosis, and network intrusion detection and the classification accuracy of majority class and minority class; the commonly used algorithm for unbalanced data is statistical analysis method. Comparing the univariate method for comprehensive classification of unbalanced data flow based on nonnegative matrix factorization with the unbalanced data algorithm, the observation has accurate rate and detects time-consuming changes. Among them, the comprehensive classification algorithm of unbalanced data flow is based on the classification of data, classifying the data, judging whether two data points belong to the same category, and determining their degree of balance. The research data shows that the unbalanced data flow integrated classification algorithm based on joint nonnegative matrix decomposition can reasonably evaluate the classification performance of the classifier for a few classes, and the detection speed is faster and saves more time. The experimental research shows that the algorithm combines the relationship matrix and information matrix from the original data set into a consensus function, uses NMF technology to obtain the membership matrix, effectively uses potential information, improves the accuracy rate of 69.73%, and shortens 71.65% of the time consumed.

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Section: Basic Content Of Nonnegative Matrix Factorizationmentioning

confidence: 99%

Integrated Classification Algorithm for Unbalanced Data Streams Based on Joint Nonnegative Matrix Factorization

Zhao

2022

Wireless Communications and Mobile Computing

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“…The initial endmember matrix is the column vector in the original matrix that is most similar to the spectrum vector of the actual surface feature. In this manner, the objective function can rapidly decrease in the initial stage of iteration, and the factorization results of the algorithm are effectively improved [2,3]. The second type of work is the NMF model with regular terms.…”

Section: Introductionmentioning

confidence: 99%

Minimum Volume Constraint with Perturbation for Non-negative Matrix Factorization

Sun,

Yang,

et al. 2024

J. Phys.: Conf. Ser.

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Nonnegative matrix factorization (NMF) has been applied in hyperspectral unmixing. The nonconvexity of the NMF’s cost function leads to solutions that are only locally optimal. Adding regularized terms to the NMF helps improve the solutions. In this study, we proposed a regularized NMF model, the regularized tern is the minimum volume constraint with perturbation. The NMF model is solved with multiplicative updated rules. Numerical results verified that adding a disturbance term to the minimum volume constraint effectively improves the spectral curve’s local accuracy while maintaining the original model’s advantages.

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“…Inspired by the column selection technique of CUR, [12] presented an initialization stage based on two measurements: the spectral angle distance (SAD), and the symmetrized Kullback-Leibler divergence. In addition, some studies have used hierarchical clustering, principle component analysis, independent component analysis, spherical k-means, fuzzy C-means, and vertex component analysis to produce a good initialization matrix that contains better localized basis vectors in U [15]- [17].…”

Section: Introductionmentioning

confidence: 99%

Enhancing Hyperspectral Unmixing With Two-Stage Multiplicative Update Nonnegative Matrix Factorization

et al. 2019

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Nonnegative matrix factorization (NMF) is a powerful tool for hyperspectral unmixing (HU). This method factorizes a hyperspectral cube into constituent endmembers and their fractional abundances. In this paper, we propose a two-stage nonnegative matrix factorization algorithm. During the first stage, k-means clustering is first employed to obtain the estimated endmember matrix. This matrix serves as the initial matrix for NMF during the second stage, where we design a new cost function for the purpose of refining the solutions of NMF. The two-stage NMF model is solved with multiplicative update rules, and the monotonic convergence of this algorithm is proven with an auxiliary function. Numerical tests demonstrate that our two-stage NMF algorithm can achieve accurate and stable solutions.INDEX TERMS Initialization, multiplicative update, nonnegative matrix factorization, hyperspectral unmixing.

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CUR Based Initialization Strategy for Non-Negative Matrix Factorization in Application to Hyperspectral Unmixing

Cited by 7 publications

References 6 publications

Integrated Classification Algorithm for Unbalanced Data Streams Based on Joint Nonnegative Matrix Factorization

Integrated Classification Algorithm for Unbalanced Data Streams Based on Joint Nonnegative Matrix Factorization

Minimum Volume Constraint with Perturbation for Non-negative Matrix Factorization

Enhancing Hyperspectral Unmixing With Two-Stage Multiplicative Update Nonnegative Matrix Factorization

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