IEEE Signal Processing Magazine· 2015Q1
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis
- 1,384citations
- Q1SCImago
- 2015year
Short summary
Higher-order tensors (multiway arrays) offer a more versatile data analysis paradigm than traditional matrix models, enabling polynomial models with guaranteed uniqueness under mild conditions.
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Key points
- Tensors (multiway arrays) provide a fundamental shift beyond flat-view matrix models for data analysis.
- Tensor models are inherently polynomial and offer guaranteed uniqueness under mild conditions.
- Multilinear algebra underpins tensor decomposition techniques, enabling flexible constraint application.
- Tensor methods can extract more general latent components compared to matrix-based approaches.
AI-generated from the title and abstract; the full text is not read.
Abstract
The widespread use of multisensor technology and the emergence of big data sets have highlighted the limitations of standard flat-view matrix models and the necessity to move toward more versatile data analysis tools. We show that higher-order tensors (i.e., multiway arrays) enable such a fundamental paradigm shift toward models that are essentially polynomial, the uniqueness of which, unlike the matrix methods, is guaranteed under very mild and natural conditions. Benefiting from the power of multilinear algebra as their mathematical backbone, data analysis techniques using tensor decompositions are shown to have great flexibility in the choice of constraints which match data properties and extract more general latent components in the data than matrix-based methods.
The authors' abstract, as published at the source. IEEE Signal Processing Magazine, 2015 · DOI ↗
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Field: Computational Mathematics
Computational MathematicsMathematics