Getting to the core of PARAFAC2, a nonnegative approach

Benthem, Mark Hilary Van; Keller, Timothy; Gillispie, Gregory D.; DeJong, Stephanie A.

doi:10.1016/j.chemolab.2020.104127

Cited by 9 publications

(10 citation statements)

References 14 publications

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“…The design of Fast-Higashi is based on a tensor decomposition model, called core-PARAFAC2 [29], and is generalized to simultaneously model multiple 3-way tensors that share only a single dimension (single cells). The core-PARAFAC2 model is usually used to analyze multimodal data where observations may not be aligned along one of its modes.…”

Section: Methodsmentioning

confidence: 99%

Ultrafast and interpretable single-cell 3D genome analysis with Fast-Higashi

Zhang

Zhou

2022

Preprint

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Single-cell Hi-C (scHi-C) technologies can probe three-dimensional (3D) genome structures in single cells and their cell-to-cell variability. However, existing scHi-C analysis methods are hindered by the data quality and the complex 3D genome patterns. The lack of computational scalability and interpretability poses further challenges for large-scale scHi-C analysis. Here, we introduce Fast-Higashi, an ultrafast and interpretable method based on tensor decomposition that can jointly identify cell identities and chromatin meta-interactions. Fast-Higashi is able to simultaneously model multiple tensors with unmatched features of different sizes. A new partial random walk with restart (Partial RWR) algorithm in Fast-Higashi efficiently mitigates data sparseness. Extensive evaluations on real scHi-C datasets demonstrate the advantage of Fast-Higashi over existing methods for embedding, leading to improved delineation of rare cell types and better reconstruction of developmental trajectories. Fast-Higashi can directly infer chromatin meta-interactions, identify 3D genome features that define distinct cell types, and help elucidate cell type-specific connections between genome structure and function. Moreover, Fast-Higashi can be generalized to incorporate other single-cell omics data. Fast-Higashi provides a highly efficient and interpretable scHi-C analysis solution that is applicable to a broad range of biological contexts.

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Section: Methodsmentioning

confidence: 99%

Ultrafast and interpretable single-cell 3D genome analysis with Fast-Higashi

Zhang

Zhou

2022

Preprint

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“…For the applications where all the modes are required to be non-negative, this flexible PARAFAC2 algorithm will be of great value. Furthermore, a core based PARAFAC algorithm has also been proposed recently with a possibility of imposing non-negativity constraints [ 66 ]. However, strict non-negativity cannot be guaranteed in this algorithm since the transformation matrixes operate on orthogonal factor matrixes.…”

Section: Multi-way Modelsmentioning

confidence: 99%

Multi-Way Analysis Coupled with Near-Infrared Spectroscopy in Food Industry: Models and Applications

Guo

Kharbach

et al. 2021

Foods

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Near-infrared spectroscopy (NIRS) is a fast and powerful analytical tool in the food industry. As an advanced chemometrics tool, a multi-way analysis shows great potential for solving a wide range of food problems and analyzing complex spectroscopic data. This paper describes the representative multi-way models which were used for analyzing NIRS data, as well as the advances, advantages and limitations of different multi-way models. The applications of a multi-way analysis in NIRS for the food industry in terms of food process control, quality evaluation and fraud, identification and classification, prediction and quantification, and image analysis are also reviewed. It is evident from this report that a multi-way analysis is presently an attractive tool for modeling complex NIRS data in the food industry while its full potential is far from reached. The combination of a multi-way analysis with NIRS will be a promising practice for turning food data information into operational knowledge, conducting reliable food analyses and improving our understanding about food systems and food processes. To the best of our knowledge, this is the first paper that systematically reports the advances on models and applications of a multi-way analysis in NIRS for the food industry.

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“…Data generation For the unimodality constraint, we generated shifting B k factor matrices similar to the approach in [47]. The components were generated as Gaussian probability density functions with zero mean and standard deviations drawn uniformly between 0.5 and 1, sampled on 50 linearly spaced points on the interval [−10, 10].…”

Section: Setup 3: Unimodality Constraintsmentioning

confidence: 99%

“…Additionally, constraints and regularization can improve the interpretability of components obtained from CP models [11,22], and the non-evolving modes of PARAFAC2 models [3]. Recently, there have been studies demonstrating the benefits of constraining the evolving mode of PARAFAC2 as well [27,17,3,47]; however, all current methods are limited in terms of the type of constraints they can impose.…”

Section: Introductionmentioning

confidence: 99%

“…The strength of this regularization increases with the iterations, thus ensuring that the components follow the PARAFAC2 constraint. Other notable approaches include LogPar [49], which uses another regularization penalty based on PARAFAC2 to improve the uniqueness properties of regularized coupled non-negative matrix factorization for binary data, and CANDELINC2, which uses a scheme based on CANDELINC (Canonical Decomposition with Linear Constraints) [15,9,30] to obtain mostly non-negative PARAFAC2 components [47].…”

Section: Introductionmentioning

confidence: 99%

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An AO-ADMM approach to constraining PARAFAC2 on all modes

Roald,

Schenker,

Calhoun

et al. 2021

Preprint

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Analyzing multi-way measurements with variations across one mode of the dataset is a challenge in various fields including data mining, neuroscience and chemometrics. For example, measurements may evolve over time or have unaligned time profiles. The PARAFAC2 model has been successfully used to analyze such data by allowing the underlying factor matrices in one mode (i.e., the evolving mode) to change across slices. The traditional approach to fit a PARAFAC2 model is to use an alternating least squares-based algorithm, which handles the constant cross-product constraint of the PARAFAC2 model by implicitly estimating the evolving factor matrices. This approach makes imposing regularization on these factor matrices challenging. There is currently no algorithm to flexibly impose such regularization with general penalty functions and hard constraints. In order to address this challenge and to avoid the implicit estimation, in this paper, we propose an algorithm for fitting PARAFAC2 based on alternating optimization with the alternating direction method of multipliers (AO-ADMM). With numerical experiments on simulated data, we show that the proposed PARAFAC2 AO-ADMM approach allows for flexible constraints, recovers the underlying patterns accurately, and is computationally efficient compared to the state-of-the-art. We also apply our model to a realworld chromatography dataset, and show that constraining the evolving mode improves the interpretability of the extracted patterns.

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Getting to the core of PARAFAC2, a nonnegative approach

Cited by 9 publications

References 14 publications

Ultrafast and interpretable single-cell 3D genome analysis with Fast-Higashi

Ultrafast and interpretable single-cell 3D genome analysis with Fast-Higashi

Multi-Way Analysis Coupled with Near-Infrared Spectroscopy in Food Industry: Models and Applications

An AO-ADMM approach to constraining PARAFAC2 on all modes

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