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Breaking the curse of dimensionality based on tensor train: models and algorithms

Abstract : Massive and heterogeneous data processing and analysis have been clearly identified by the scientific community as key problems in several application areas. It was popularized under the generic terms of "data science" or "big data". Processing large volumes of data, extracting their hidden patterns, while preforming prediction and inference tasks has become crucial in economy, industry and science. Treating independently each set of measured data is clearly a reductive approach. By doing that, "hidden relationships" or inter-correlations between the datasets may be totally missed. Tensor decompositions have received a particular attention recently due to their capability to handle a variety of mining tasks applied to massive datasets, being a pertinent framework taking into account the heterogeneity and multi-modality of the data. In this case, data can be arranged as a D-dimensional array, also referred to as a D-order tensor. In this context, the purpose of this work is that the following properties are present: (i) having a stable factorization algorithms (not suffering from convergence problems), (ii) having a low storage cost (i.e., the number of free parameters must be linear in D), and (iii) having a formalism in the form of a graph allowing a simple but rigorous mental visualization of tensor decompositions of tensors of high order, i.e., for D> 3. Therefore, we rely on the tensor train decomposition (TT) to develop new TT factorization algorithms, and new equivalences in terms of tensor modeling, allowing a new strategy of dimensionality reduction and criterion optimization of coupled least squares for the estimation of parameters named JIRAFE. This methodological work has had applications in the context of multidimensional spectral analysis and relay telecommunications systems.
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Contributor : Yassine Zniyed <>
Submitted on : Thursday, February 27, 2020 - 3:59:11 PM
Last modification on : Wednesday, October 14, 2020 - 3:56:58 AM


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Yassine Zniyed. Breaking the curse of dimensionality based on tensor train: models and algorithms. Mathematical Physics [math-ph]. Paris-Saclay, 2019. English. ⟨tel-02493183⟩



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