• Corpus ID: 13438152

Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition

  title={Tensor Networks for Latent Variable Analysis. Part I: Algorithms for Tensor Train Decomposition},
  author={A. Phan and Andrzej Cichocki and Andr{\'e} Uschmajew and Petr Tichavsk{\'y} and Gheorghe Luta and Danilo P. Mandic},
Decompositions of tensors into factor matrices, which interact through a core tensor, have found numerous applications in signal processing and machine learning. A more general tensor model which represents data as an ordered network of sub-tensors of order-2 or order-3 has, so far, not been widely considered in these fields, although this so-called tensor network decomposition has been long studied in quantum physics and scientific computing. In this study, we present novel algorithms and… 
Tensor Networks for Latent Variable Analysis: Novel Algorithms for Tensor Train Approximation
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Nonnegatively Constrained Tensor Network for Classification Problems
  • R. Zdunek, Krzysztof Fonał
  • Computer Science
    2019 Eleventh International Conference on Ubiquitous and Future Networks (ICUFN)
  • 2019
A new computational algorithm is proposed for extracting low-rank and nonnegative 2D features, and it is demonstrated that this approach outperforms the fundamental and state-of-the art methods for dimensionality reduction and classification problems.
Learning Tensor Train Representation with Automatic Rank Determination from Incomplete Noisy Data
A fully Bayesian treatment of TT decomposition is employed to enable automatic rank determination, and theoretical evidence is established for adopting a Gaussian-product-Gamma prior to induce sparsity on the slices of the TT cores, so that the model complexity is automatically determined even under incomplete and noisy observed data.
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