Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria

Yokota, Tatsuya; Lee, Namgil; Cichocki, Andrzej

doi:10.1109/tsp.2016.2620965

Cited by 64 publications

(43 citation statements)

References 29 publications

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“…At the same time, this low-rank representation should be rich enough to include all dimensions of the original HI tensor that contain relevant information. Therefore, although the literature presents many rank estimation strategies (see [39] and references therein), in this work we exploit the rank bounds discussed in Section II-E to approximate the "useful rank" of a tensor by the number of the largest singular values of their matricized versions required to represent most of the tensor energy.…”

Section: F Estimating Tensor Ranksmentioning

confidence: 99%

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Imbiriba

Borsoi

Bermudez

2020

IEEE Trans. Geosci. Remote Sensing

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Traditional hyperspectral unmixing methods neglect the underlying variability of spectral signatures often observed in typical hyperspectral images (HI), propagating these missmodeling errors throughout the whole unmixing process. Attempts to model material spectra as members of sets or as random variables tend to lead to severely ill-posed unmixing problems. Although parametric models have been proposed to overcome this drawback by handling endmember variability through generalizations of the mixing model, the success of these techniques depend on employing appropriate regularization strategies. Moreover, the existing approaches fail to adequately explore the natural multidimensinal representation of HIs. Recently, tensor-based strategies considered low-rank decompositions of hyperspectral images as an alternative to impose low-dimensional structures on the solutions of standard and multitemporal unmixing problems . These strategies, however, present two main drawbacks: 1) they confine the solutions to low-rank tensors, which often cannot represent the complexity of real-world scenarios; and 2) they lack guarantees that endmembers and abundances will be correctly factorized in their respective tensors. In this work, we propose a more flexible approach, called ULTRA-V, that imposes low-rank structures through regularizations whose strictness is controlled by scalar parameters. Simulations attest the superior accuracy of the method when compared with state-of-the-art unmixing algorithms that account for spectral variability.

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Section: F Estimating Tensor Ranksmentioning

confidence: 99%

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Imbiriba

Borsoi

Bermudez

2020

IEEE Trans. Geosci. Remote Sensing

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“…. , N. Rank of the Tucker decompositions can be determined using information criteria [227], or through the number of dominant eigenvalues when an approximation accuracy of the decomposition or a noise level is given (see Algorithm 8).…”

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confidence: 99%

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions

Cichocki

Lee

Oseledets

et al. 2016

FNT in Machine Learning

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371

342

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Modern applications in engineering and data science are increasingly based on multidimensional data of exceedingly high volume, variety, and structural richness. However, standard machine learning algorithms typically scale exponentially with data volume and complexity of cross-modal couplings - the so called curse of dimensionality - which is prohibitive to the analysis of large-scale, multi-modal and multi-relational datasets. Given that such data are often efficiently represented as multiway arrays or tensors, it is therefore timely and valuable for the multidisciplinary machine learning and data analytic communities to review low-rank tensor decompositions and tensor networks as emerging tools for dimensionality reduction and large scale optimization problems. Our particular emphasis is on elucidating that, by virtue of the underlying low-rank approximations, tensor networks have the ability to alleviate the curse of dimensionality in a number of applied areas. In Part 1 of this monograph we provide innovative solutions to low-rank tensor network decompositions and easy to interpret graphical representations of the mathematical operations on tensor networks. Such a conceptual insight allows for seamless migration of ideas from the flat-view matrices to tensor network operations and vice versa, and provides a platform for further developments, practical applications, and non-Euclidean extensions. It also permits the introduction of various tensor network operations without an explicit notion of mathematical expressions, which may be beneficial for many research communities that do not directly rely on multilinear algebra. Our focus is on the Tucker and tensor train (TT) decompositions and their extensions, and on demonstrating the ability of tensor networks to provide linearly or even super-linearly (e.g., logarithmically) scalable solutions, as illustrated in detail in Part 2 of this monograph

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“…Assuming that the beamformed noise N in (25) follows an i.i.d. Gaussian distribution and is independent of Y, we adopt a minimum description length (MDL) method to estimate the number of signal path components L [32], [33].…”

Section: Proposed Algorithmmentioning

confidence: 99%

Tensor-Based Channel Estimation for Millimeter Wave MIMO-OFDM With Dual-Wideband Effects

Lin

Jin

Matthaiou

et al. 2020

IEEE Trans. Commun.

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We consider the channel estimation problem in millimeter wave (mmWave) multiple-input multipleoutput orthogonal frequency division multiplexing (MIMO-OFDM) systems with hybrid analog-digital architectures. Leveraging the spatial-and frequency-wideband (dual-wideband) effects in massive MIMO scenarios, we derive a spatial-frequency channel model with dual-wideband effects that incorporates the multipath parameters, i.e., time delay, complex gain, angle of departure/arrival. We adopt a successive beam training scheme and formulate the training OFDM signal as a third-order low-rank tensor fitting a canonical polyadic (CP) model with factor matrices containing the channel parameters. Exploiting the Vandermonde nature of factor matrices, we propose a structured CP decomposition-based channel estimation strategy aided by the spatial smoothing method, where two dedicated algorithms with particular tensor modeling and parameter recovery operations are developed. The proposed scheme leverages standard linear algebra, and, hence, avoids the random initialization problem and iterative procedure. An analysis of the uniqueness condition of CP decomposition is also pursued. Simulation results indicate that the proposed strategy achieves enhanced estimation performance, which outperforms the traditional approaches in terms of accuracy, robustness and complexity.

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Robust Multilinear Tensor Rank Estimation Using Higher Order Singular Value Decomposition and Information Criteria

Cited by 64 publications

References 29 publications

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Low-Rank Tensor Modeling for Hyperspectral Unmixing Accounting for Spectral Variability

Tensor Networks for Dimensionality Reduction and Large-scale Optimization: Part 1 Low-Rank Tensor Decompositions

Tensor-Based Channel Estimation for Millimeter Wave MIMO-OFDM With Dual-Wideband Effects

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