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Abstract This paper introduces a general framework of Semi-parametric TEnsor Factor Analysis (STEFA) that focuses on the methodology and theory of low-rank tensor decomposition with auxiliary covariates. Semi-parametric TEnsor Factor Analysis models extend tensor factor models by incorporating auxiliary covariates in the loading matrices. We propose an algorithm of iteratively projected singular value decomposition (IP-SVD) for the semi-parametric estimation. It iteratively projects tensor data onto the linear space spanned by the basis functions of covariates and applies singular value decomposition on matricized tensors over each mode. We establish the convergence rates of the loading matrices and the core tensor factor. The theoretical results only require a sub-exponential noise distribution, which is weaker than the assumption of sub-Gaussian tail of noise in the literature. Compared with the Tucker decomposition, IP-SVD yields more accurate estimators with a faster convergence rate. Besides estimation, we propose several prediction methods with new covariates based on the STEFA model. On both synthetic and real tensor data, we demonstrate the efficacy of the STEFA model and the IP-SVD algorithm on both the estimation and prediction tasks.
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Sketch-Based Tensor Decomposition for Non-Parametric Monitoring of Electrospinning Processes
Abstract Electrospinning is a promising process to fabricate functional parts from macrofibers and nanofibers of bio-compatible materials including collagen, polylactide (PLA), and polyacrylonitrile (PAN). However, the functionality of the produced parts highly rely on quality, repeatability, and uniformity of the electrospun fibers. Due to the variations in material composition, process settings, and ambient conditions, the process suffers from large variations. In particular, the fiber formation in the stable regime (i.e., Taylor cone and jet) and its propagation to the substrate plays the most significant role in the process stability. This work aims to designing a fast process monitoring tool from scratch for monitoring the dynamic electrospinning process based on the Taylor cone and jet videos. Nevertheless, this is challenging since the videos are of high frequency and high dimension, and the monitoring statistics may not have a parametric distribution. To achieve this goal, a framework integrating image analysis, sketch-based tensor decomposition, and non-parametric monitoring, is proposed. In particular, we use Tucker tensor-sketch (Tucker-TS) based tensor decomposition to extract the sparse structure representations of the videos. Additionally, the extracted monitoring variables are non-normally distributed, hence non-parametric bootstrap Hotelling T2 control chart is deployed to handle this issue during the monitoring. The framework is demonstrated by electrospinning a PAN-based polymeric solution. Finally, it is demonstrated that the proposed framework, which uses Tucker-TS, largely outperformed the computational speed of the alternating least squares (ALS) approach for the Tucker tensor decomposition, i.e., Tucker-ALS, in various anomaly detection tasks while keeping the comparable anomaly detection accuracy.
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- Award ID(s):
- 1846863
- PAR ID:
- 10212290
- Date Published:
- Journal Name:
- ASME 2020 15th International Manufacturing Science and Engineering Conference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Conference Paper:
- https://doi.org/10.1115/MSEC2020-8367
