A Deep Nonnegative Matrix Factorization Approach via Autoencoder for Nonlinear Fault Detection

Ren, Zelin; Zhang, Wensheng; Zhang, Zhizhong

doi:10.1109/tii.2019.2951011

Cited by 44 publications

(19 citation statements)

References 28 publications

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“…Others have examined NMF extensions on the basis of sparseness and other constraints for graphical analysis [56] and deeply enhanced weighted NMF [57]. Even more recent work has leveraged NMF in the context of deep learning [58][59][60]. These newer techniques have not been used as extensively and have not been included here.…”

Section: Discussionmentioning

confidence: 99%

Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization

Maisog¹,

DeMarco

Devarajan

et al. 2021

Mathematics

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Non-negative matrix factorization is a relatively new method of matrix decomposition which factors an m × n data matrix X into an m × k matrix W and a k × n matrix H, so that X ≈ W × H. Importantly, all values in X, W, and H are constrained to be non-negative. NMF can be used for dimensionality reduction, since the k columns of W can be considered components into which X has been decomposed. The question arises: how does one choose k? In this paper, we first assess methods for estimating k in the context of NMF in synthetic data. Second, we examine the effect of normalization on this estimate’s accuracy in empirical data. In synthetic data with orthogonal underlying components, methods based on PCA and Brunet’s Cophenetic Correlation Coefficient achieved the highest accuracy. When evaluated on a well-known real dataset, normalization had an unpredictable effect on the estimate. For any given normalization method, the methods for estimating k gave widely varying results. We conclude that when estimating k, it is best not to apply normalization. If the underlying components are known to be orthogonal, then Velicer’s MAP or Minka’s Laplace-PCA method might be best. However, when the orthogonality of the underlying components is unknown, none of the methods seemed preferable.

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Section: Discussionmentioning

confidence: 99%

Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization

Maisog¹,

DeMarco

Devarajan

et al. 2021

Mathematics

View full text Add to dashboard Cite

show abstract

“…(25), we also can prove the convergence under the updating rule of U in Eq. (26), so the objective function ( 25) is nonincreasing under the updating rules (26) and (27). Therefore, Algorithm 1 can be proved to be convergent under its iterative formulas in a similar way.…”

Section: Convergence Analysismentioning

confidence: 95%

“…Recently, Guo et al [26] proposed a Sparse Deep Nonnegative Matrix Factorization (SDNMF) algorithm for more accurate classification and better feature interpretation, which can learn localized features or generate more discriminative representations for samples in distinct classes by imposing L 1 -norm penalty on the columns of certain factors. Although these multi-layer structure methods [27], [28] can extract more latent hierarchical features than onelayer structure methods, they still have two shortcomings:…”

Section: Introductionmentioning

confidence: 99%

Sparse Dual Graph-Regularized Deep Nonnegative Matrix Factorization for Image Clustering

Guo

2021

IEEE Access

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Deep nonnegative matrix factorization (Deep NMF) as an emerging technique for image clustering has attracted more and more attention. This is because it can effectively reduce high-dimensional data and reveal the latent hierarchical information of the complex data. However, two limitations may still deteriorate their performances: (1) the local invariance of the input data is insufficiently explored, that is, the intrinsic geometrical structures of the original data in the data and feature spaces are not considered simultaneously; (2) the sparseness that can greatly improve the ability of learning parts is also ignored. In this paper, we propose a novel approach to address the above two problems, referred to as Sparse Dual Graph-regularized Deep Nonnegative Matrix Factorization (SDG Deep NMF), which can learn sparse and informative deep features while sufficiently exploring the local invariance of the data to discover valuable information underlying the input data. Specifically, SDG Deep NMF learns the informative deep features by performing the dual graph regularization in the deep NMF framework, which can respect the intrinsic geometrical structures of the input data in the data and feature spaces while mining the data information in hidden layers. Meanwhile, SDG Deep NMF also imposes sparse constraints on the basis matrix during the feature learning to improve the part-based learning capabilities. Moreover, we construct the objective function of SDG Deep NMF in the form of the Euclidean distance for convenience, the iterative updating scheme is chosen to optimize it. Comprehensive experiments on four benchmark datasets can demonstrate the effectiveness of the proposed approach in image clustering. INDEX TERMSDeep nonnegative matrix factorization, dual graph regularization, sparse constraints, image clustering.

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“…Bando et al ( 2018 ) proposed a deep variational NMF by interpreting the spectrogram of input data as the sum of a speech spectrogram and a non-negative noisy spectrogram, which is modeled as the variational prior distribution. Ren et al ( 2019 ) introduced an end-to-end deep NMF architecture with non-negative constraints and a factorization loss conducted on middle layers. Those deep NMFs can further learn non-linear correlations hidden in data.…”

Section: Preliminaries and Related Workmentioning

confidence: 99%

A Deep Non-negative Matrix Factorization Model for Big Data Representation Learning

et al. 2021

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Nowadays, deep representations have been attracting much attention owing to the great performance in various tasks. However, the interpretability of deep representations poses a vast challenge on real-world applications. To alleviate the challenge, a deep matrix factorization method with non-negative constraints is proposed to learn deep part-based representations of interpretability for big data in this paper. Specifically, a deep architecture with a supervisor network suppressing noise in data and a student network learning deep representations of interpretability is designed, which is an end-to-end framework for pattern mining. Furthermore, to train the deep matrix factorization architecture, an interpretability loss is defined, including a symmetric loss, an apposition loss, and a non-negative constraint loss, which can ensure the knowledge transfer from the supervisor network to the student network, enhancing the robustness of deep representations. Finally, extensive experimental results on two benchmark datasets demonstrate the superiority of the deep matrix factorization method.

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A Deep Nonnegative Matrix Factorization Approach via Autoencoder for Nonlinear Fault Detection

Cited by 44 publications

References 28 publications

Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization

Assessing Methods for Evaluating the Number of Components in Non-Negative Matrix Factorization

Sparse Dual Graph-Regularized Deep Nonnegative Matrix Factorization for Image Clustering

A Deep Non-negative Matrix Factorization Model for Big Data Representation Learning

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