Tensor methods for hyperspectral data analysis: a space object material identification study

Zhang, Qiang; Wang, Han; Plemmons, Robert J.; Pauca, V. Paúl

doi:10.1364/josaa.25.003001

Cited by 89 publications

(70 citation statements)

References 39 publications

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“…See Figure 1 for an illustration of 3-D tensor factorization. Similar to NMF, we also see a quick development of NTF algorithms [12,15] and their applications in recent years. In this research, we exploit the nonnegative tensor factorization of multidimensional climate data in order to capture patterns/signals not possible with traditional 2-way factor analysis.…”

Section: Introductionmentioning

confidence: 94%

A Parallel Nonnegative Tensor Factorization Algorithm for Mining Global Climate Data

Zhang

Berry

Lamb

et al. 2009

Lecture Notes in Computer Science

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Abstract. Increasingly large datasets acquired by NASA for global climate studies demand larger computation memory and higher CPU speed to mine out useful and revealing information. While boosting the CPU frequency is getting harder, clustering multiple lower performance computers thus becomes increasingly popular. This prompts a trend of parallelizing the existing algorithms and methods by mathematicians and computer scientists. In this paper, we take on the task of parallelizing the Nonnegative Tensor Factorization (NTF) method, with the purposes of distributing large datasets into each cluster node and thus reducing the demand on a single node, blocking and localizing the computation at the maximal degree, and finally minimizing the memory use for storing matrices or tensors by exploiting their structural relationships. Numerical experiments were performed on a NASA global sea surface temperature dataset and result factors were analyzed and discussed.

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Section: Introductionmentioning

confidence: 94%

A Parallel Nonnegative Tensor Factorization Algorithm for Mining Global Climate Data

Zhang

Berry

Lamb

et al. 2009

Lecture Notes in Computer Science

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“…One also talks about the number of ways or modes [1]. In this paper, due to the considered applications, including fluorescence spectroscopy [2][1] and hyperspectral imaging [3], we focus on real positive 3-way arrays denoted by T = (t ijk ) ∈ R I×J×K , admitting the following trilinear decom-…”

Section: Problem Statementmentioning

confidence: 99%

Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

Royer

Comon

Thirion-Moreau

2011

2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…Sparse and non-negative tensor models have recently been the subject of many works in various fields of applications like computer vision [21,22], image compression [23], hyperspectral imaging [24], music genre classification [25] and audio source separation [26], multi-channel EEG (electroencephalography) and network traffic analysis [27], fluorescence analysis [28], data denoising and image classification [29], among many others. Two nonnegative tensor models have been more particularly studied in the literature, the so-called non-negative tensor factorization (NTF), i.e., PARAFAC models with non-negativity constraints on the matrix factors, and non-negative Tucker decomposition (NTD), i.e., Tucker models with non-negativity constraints on the core tensor and/or the matrix factors.…”

Section: Introductionmentioning

confidence: 99%

Overview of constrained PARAFAC models

Favier

Almeida

2014

EURASIP J. Adv. Signal Process.

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In this paper, we present an overview of constrained parallel factor (PARAFAC) models where the constraints model linear dependencies among columns of the factor matrices of the tensor decomposition or, alternatively, the pattern of interactions between different modes of the tensor which are captured by the equivalent core tensor. Some tensor prerequisites with a particular emphasis on mode combination using Kronecker products of canonical vectors that makes easier matricization operations, are first introduced. This Kronecker product-based approach is also formulated in terms of an index notation, which provides an original and concise formalism for both matricizing tensors and writing tensor models. Then, after a brief reminder of PARAFAC and Tucker models, two families of constrained tensor models, the co-called PARALIND/CONFAC and PARATUCK models, are described in a unified framework, for Nth-order tensors. New tensor models, called nested Tucker models and block PARALIND/CONFAC models, are also introduced. A link between PARATUCK models and constrained PARAFAC models is then established. Finally, new uniqueness properties of PARATUCK models are deduced from sufficient conditions for essential uniqueness of their associated constrained PARAFAC models.Keywords: Constrained PARAFAC; PARALIND/CONFAC; PARATUCK; Tensor models; Tucker models 1 Review IntroductionTensor calculus was introduced in differential geometry, at the end of the nineteenth century, and then tensor analysis was developed in the context of Einstein's theory of general relativity, with the introduction of index notation, the so-called Einstein summation convention, at the beginning of the twentieth century, which allows to simplify and shorten physics equations involving tensors. Index notation is also useful for simplifying multivariate statistical calculations, particularly those involving cumulant tensors [1]. Generally speaking, tensors are used in physics and differential geometry for characterizing the properties of a physical system, representing fundamental laws of physics, and defining geometrical objects whose components are functions. When these functions are defined over a continuum of points of a mathematical space, the tensor forms what is called a tensor field, a generalization of vector field used to solve problems involving curved surfaces or spaces, as it is the case of After the first tensor developments by mathematicians and physicists, the need of analyzing collections of data matrices that can be seen as three-way data arrays gave rise to three-way models for data analysis, with the pioneering works of Tucker in psychometrics [3], and Harshman in phonetics [4], who proposed what is now referred to as the Tucker and parallel factor (PARAFAC) decompositions, respectively. The PARAFAC decomposition was independently proposed by Carroll and Chang [5] under the name canonical decomposition (CANDE-COMP) and then called CANDECOMP/PARAFAC (CP) in [6]. For a history of the development of multi-way models in the context ...

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Tensor methods for hyperspectral data analysis: a space object material identification study

Cited by 89 publications

References 39 publications

A Parallel Nonnegative Tensor Factorization Algorithm for Mining Global Climate Data

A Parallel Nonnegative Tensor Factorization Algorithm for Mining Global Climate Data

Nonnegative 3-way tensor factorization via conjugate gradient with globally optimal stepsize

Overview of constrained PARAFAC models

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