Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition

Zhang, Chenyu; Han, Rungang; Zhang, Anru; Voyles, Paul M.

doi:10.1016/j.ultramic.2020.113123

Cited by 27 publications

(17 citation statements)

References 49 publications

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“…Additional applications of tensor block model include hypergraph clustering (Ke et al, 2019;Chien et al, 2019), collaborative filtering (Zhang et al, 2020b) and signal detection in 3D/4D imaging (Zhang et al, 2020a), among others. While clustering analysis is prevalent in discovering heterogeneous patterns in usual multivariate data, it has unique challenges when the data is organized as a multi-way tensor.…”

Section: High-order Tensor Clusteringmentioning

confidence: 99%

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

Han¹,

Luo²,

Wang³

et al. 2020

Preprint

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High-order clustering aims to identify heterogeneous substructure in multiway dataset that arises commonly in neuroimaging, genomics, and social network studies. The non-convex and discontinuous nature of the problem poses significant challenges in both statistics and computation. In this paper, we propose a tensor block model and the computationally efficient methods, high-order Lloyd algorithm (HLloyd) and high-order spectral clustering (HSC), for highorder clustering in tensor block model. The convergence of the proposed procedure is established, and we show that our method achieves exact clustering under reasonable assumptions. We also give the complete characterization for the statistical-computational trade-off in high-order clustering based on three different signal-to-noise ratio regimes. Finally, we show the merits of the proposed procedures via extensive experiments on both synthetic and real datasets.

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Section: High-order Tensor Clusteringmentioning

confidence: 99%

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

Han¹,

Luo²,

Wang³

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

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“…Advancements in in situ transmission electron microscopy (TEM) enable direct observation of these complicated processes, but the extraction of quantitative information from images remains challenging . Recent research has combined rapid automated image analysis using machine learning with advanced microscopy techniques to study a variety of materials with remarkable detail and precision. − Here, we quantify the evolution of a model catalyst system at high temperature using in situ TEM and automated image analysis. Developing an analytical model for particle growth, we can ascertain the size-dependence of particle growth rates in nonconservative systems and the influence of local and long-range particle interactions.…”

mentioning

confidence: 99%

Quantifying Competitive Degradation Processes in Supported Nanocatalyst Systems

2021

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The stability of supported metal nanoparticles determines the activity and lifetime of heterogeneous catalysts. Catalysts can destabilize through several thermodynamic and kinetic pathways, and the competition between these mechanisms complicates efforts to quantify and predict the overall evolution of supported nanoparticles in reactive environments. Pairing in situ transmission electron microscopy with unsupervised machine learning, we quantify the destabilization of hundreds of supported Au nanoparticles in real-time to develop a model describing the observed particle evolution as a competition between evaporation and surface diffusion. Data mining of particle evolution statistics allows us to determine physically reasonable values for the model parameters, quantify the particle size at which the Gibbs− Thomson pressure accelerates the evaporation process, and explore how individual particle interactions deviate from the meanfield model. This approach can be applied to a wide range of supported nanoparticle systems, allowing quantitative insight into the mechanisms that control their evolution in reactive environments.

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“…As introduced in Example 2.1, the goal of tensor PCA is to extract low-rank signal from a noisy tensor observation A ∈ R d 1 ×•••×dm . Tensor PCA has been proven effective in learning hidden components in Gaussian mixture models , denoising electron microscopy data (Zhang et al, 2020b) and in the inference of spatial and temporal patterns of gene regulation during brain development . Tensor PCA has been intensively studied from various aspects by both statistics and machine learning community resulting into a rich literature (e.g.…”

Section: Robust Sub-gaussian Tensor Pcamentioning

confidence: 99%

“…An mth-order tensor is a multilinear array with m ways, e.g., matrices are second order tensors. These multi-way structures often emerge when, to name a few, information features are collected from distinct domains Han et al, 2020;Bi et al, 2018;Zhang et al, 2020b;Wang and Zeng, 2019), the multi-relational interactions or higher-order interactions of entities are present (Ke et al, 2019;Jing et al, 2020;Kim et al, 2017;Paul and Chen, 2020;Luo and Zhang, 2020;Wang and Li, 2020;Ghoshdastidar and Dukkipati, 2017;Pensky and Zhang, 2019), or the higher-order moments of data are explored Sun et al, 2017;Hao et al, 2020). There is an increasing demand for effective methods to analyze large and complex tensorial datasets.…”

Section: Introductionmentioning

confidence: 99%

Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization

Cai¹,

Li²,

Dong³

2021

Preprint

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We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or heterogeneous signals that are unexplainable by the low-rank part. The framework is flexible covering both linear and non-linear models, and can easily handle continuous or categorical variables. We propose a fast algorithm by integrating the Riemannian gradient descent and a novel gradient pruning procedure. Under suitable conditions, the algorithm converges linearly and can simultaneously estimate both the low-rank and sparse tensors. The statistical error bounds of final estimates are established in terms of the gradient of loss function. The error bounds are generally sharp under specific statistical models, e.g., the robust tensor PCA and the community detection in hypergraph networks with outlier vertices. Moreover, our method achieves non-trivial error bounds for heavy-tailed tensor PCA whenever the noise has a finite 2 + ε moment. We apply our method to analyze the international trade flow dataset and the statistician hypergraph co-authorship network, both yielding new and interesting findings.

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Denoising atomic resolution 4D scanning transmission electron microscopy data with tensor singular value decomposition

Cited by 27 publications

References 49 publications

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

Exact Clustering in Tensor Block Model: Statistical Optimality and Computational Limit

Quantifying Competitive Degradation Processes in Supported Nanocatalyst Systems

Generalized Low-rank plus Sparse Tensor Estimation by Fast Riemannian Optimization

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