A consistent and flexible framework for deep matrix factorizations

Handschutter, Pierre De; Gillis, Nicolas

doi:10.1016/j.patcog.2022.109102

Cited by 10 publications

(4 citation statements)

References 30 publications

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“…Inspired by the work of [20,25], we combine the deep L p smooth symmetric matrix factorization model, as described in Section 2, with (3) to formulate a comprehensive loss function that incorporates weighted sums of the layer-wise contributions.…”

Section: Algorithm For Dssnmfmentioning

confidence: 99%

“…To minimize (4), the block coordinate descent (BCD) [15,20,25] is employed, necessitating the blockwise updating of the factor matrices. In this study, we utilize the fast projected gradient method (FPGM) [26] to update the factor matrices U l or V l .…”

Section: Algorithm For Dssnmfmentioning

confidence: 99%

“…where U l ∈ R m×r l + and V l ∈ R r l ×r l−1 + (l = 1, • • • , L) with r 0 = n. In scheme of (1) the dimension r l of each layer is the rank of the factorization at layer l, and r l (l = 1, • • • , L) are assumed to be decreasing, that is, [19,20] for more details.…”

Section: Introductionmentioning

confidence: 99%

“…These hyperparameters can be manually specifled by the user if there is existing prior knowledge about the network. In line with [20], we utilize the multilayer matrix factorization (MulMF) method to initialize the hierarchical factor matrices U (0) l and V (0) l . Specifically, the L-layer deep L p smooth symmetric nonnegative matrix factorization initializes the factors layer by layer, supplying the initial factor matrix before entering the DSSNMF procedure.…”

mentioning

confidence: 99%

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Hierarchical Object Part Learning Using Deep Lp Smooth Symmetric Non-Negative Matrix Factorization

Li,

Song,

et al. 2024

Symmetry

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Nowadays, deep representations have gained significant attention due to their outstanding performance in a wide range of tasks. However, the interpretability of deep representations in specific applications poses a significant challenge. For instances where the generated quantity matrices exhibit symmetry, this paper introduces a variant of deep matrix factorization (deep MF) called deep Lp smooth symmetric non-negative matrix factorization (DSSNMF), which aims to improve the extraction of clustering structures inherent in complex hierarchical and graphical representations in high-dimensional datasets by improving the sparsity of the factor matrices. We successfully applied DSSNMF to synthetic datasets as well as datasets related to post-traumatic stress disorder (PTSD) to extract several hierarchical communities. Specifically, we identified non-disjoint communities within the partial correlation networks of PTSD psychiatric symptoms, resulting in highly meaningful clinical interpretations. Numerical experiments demonstrate the promising applications of DSSNMF in fields like network analysis and medicine.

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Section: Algorithm For Dssnmfmentioning

confidence: 99%

Section: Algorithm For Dssnmfmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Hierarchical Object Part Learning Using Deep Lp Smooth Symmetric Non-Negative Matrix Factorization

Li,

Song,

et al. 2024

Symmetry

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Deep graph regularized nonnegative Tucker decomposition for image data analysis

Liao,

Bakar,

Liu

et al. 2024

Appl Intell

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Neural nonnegative matrix factorization for hierarchical multilayer topic modeling

Haddock,

Will,

Vendrow

et al. 2023

Sampl. Theory Signal Process. Data Anal.

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We introduce a new method based on nonnegative matrix factorization, Neural NMF, for detecting latent hierarchical structure in data. Datasets with hierarchical structure arise in a wide variety of fields, such as document classification, image processing, and bioinformatics. Neural NMF recursively applies NMF in layers to discover overarching topics encompassing the lower-level features. We derive a backpropagation optimization scheme that allows us to frame hierarchical NMF as a neural network. We test Neural NMF on a synthetic hierarchical dataset, the 20 Newsgroups dataset, and the MyLymeData symptoms dataset. Numerical results demonstrate that Neural NMF outperforms other hierarchical NMF methods on these data sets and offers better learned hierarchical structure and interpretability of topics.

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A consistent and flexible framework for deep matrix factorizations

Cited by 10 publications

References 30 publications

Hierarchical Object Part Learning Using Deep Lp Smooth Symmetric Non-Negative Matrix Factorization

Hierarchical Object Part Learning Using Deep Lp Smooth Symmetric Non-Negative Matrix Factorization

Deep graph regularized nonnegative Tucker decomposition for image data analysis

Neural nonnegative matrix factorization for hierarchical multilayer topic modeling

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