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Tensor decomposition for dimension reduction

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Abstract Tensor data are data with multiway array structure. They are often very high dimensional and are routinely encountered in many scientific fields. Dimension reduction is the technique of reducing the number of underlying variables for compressed data representation and for model parsimony. Tensor dimension reduction aims for reducing the tensor data dimension while keeping data's tensor structure. This article is categorized under: Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical and Graphical Methods of Data Analysis > Dimension Reduction Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data
Fibers and unfolding matrices
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Using best Rank‐(r1, …, rD) decomposition for multilinear dimension reduction. The face images are taken from the Olivetti dataset (https://cs.nyu.edu/ roweis/data.html), and their original versions are from AT&T Laboratories Cambridge (https://www.cl.cam.ac.uk/research/dtg/attarchive/facedatabase.html)
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Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning
Statistical and Graphical Methods of Data Analysis > Analysis of High Dimensional Data
Statistical and Graphical Methods of Data Analysis > Dimensional Reduction
Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

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