Tensor Regression with Applications in Neuroimaging Data Analysis

Zhou, Hua; Li, Lexin; Zhu, Hongtu

doi:10.1080/01621459.2013.776499

Cited by 444 publications

(579 citation statements)

References 41 publications

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“…The aforementioned concept can be extended in case of tensor inputs, X ∈ R p1×···×p D , [21]. In this way, we have that…”

Section: Tensor-based Logistic Regressionmentioning

confidence: 99%

“…In contrast to [21], in this paper, a multi-class classification problem is investigated using tensor-based logistic regression models of multiple outputs. In addition, the rank-1 canonical decomposition property is also applied, apart from high-order linear, to non-linear classifiers, which is not a straightforward process.…”

Section: A Our Contributionmentioning

confidence: 99%

“…Our work is motivated from [21] which proposes a single linear output tensor regression model for binary classification. In contrast to [21], in this paper, a multi-class classification problem is investigated using tensor-based logistic regression models of multiple outputs.…”

Section: A Our Contributionmentioning

confidence: 99%

“…In particular, Zhou et al [21] and Tan et. al [22] have introduced a linear model using tensor-based regression with applications in neuro-imaging data analysis [21] and for classification [22].…”

Section: Introductionmentioning

confidence: 99%

“…Tensor-based machine learning models are promising alternatives for hyperspectral data classification [21], [22]. In particular, Zhou et al [21] and Tan et.…”

Section: Introductionmentioning

confidence: 99%

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Tensor-Based Classification Models for Hyperspectral Data Analysis

Makantasis

Doulamis

Nikitakis

2018

IEEE Trans. Geosci. Remote Sensing

116

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Abstract-In this paper, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which satisfy the rank-1 canonical decomposition property. Then, we propose learning algorithms to train both linear and non-linear classifiers. The advantages of the proposed classification approach are that i) it significantly reduces the number of weight parameters required to train the model (and thus the respective number of training samples), ii) it provides a physical interpretation of model coefficients on the classification output and iii) it retains the spatial and spectral coherency of the input samples. The linear tensor-based model exploits principles of logistic regression assuming the rank-1 canonical decomposition property among its weights. For the non-linear classifier, we propose a modification of a feedforward neural network (FNN), called rank-1 FNN, since its weights satisfy again the rank-1 canonical decomposition property. An appropriate learning algorithm is also proposed to train the network. Experimental results and comparisons with state of the art classification methods, either linear (e.g., Linear SVM) or non-linear (e.g., deep learning) indicates the outperformance of the proposed scheme, especially in cases where a small number of training samples is available.

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“…The aforementioned concept can be extended in case of tensor inputs, X ∈ R p1×···×p D , [21]. In this way, we have that…”

Section: Tensor-based Logistic Regressionmentioning

confidence: 99%

Section: A Our Contributionmentioning

confidence: 99%

Section: A Our Contributionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Tensor-based machine learning models are promising alternatives for hyperspectral data classification [21], [22]. In particular, Zhou et al [21] and Tan et.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Tensor-Based Classification Models for Hyperspectral Data Analysis

Makantasis

Doulamis

Nikitakis

2018

IEEE Trans. Geosci. Remote Sensing

116

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A Survey of Statistics in the Neurological Sciences with a Focus on Human Neuroimaging

Caffo

Zhao

Eloyan

et al. 2018

Wiley StatsRef: Statistics Reference Online

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Neuroscience is a vast subject; understanding the brain is one of the most complex, deep, and challenging tasks in all of science. In this article, we survey statistical contributions to the field of neuroscience, though focus heavily on human brain imaging. Statistics has made fundamental contributions in the processing and analysis of neuroscience and neuroimaging data. Contributions range from processing the measurements of new technologies to analyzing large groups of subjects and inference on the impact of behavior or disease. Developments in statistical algorithms and signal processing help in the pipeline that takes raw images and converts them to those used for diagnosis or research. Statistics has provided key protections from type I errors for the high‐dimensional spatially correlated and complex data arising in this domain. In addition, novel modeling and testing approaches have allowed researchers to perform inference for this challenging data. We end the article with recommendations for statisticians and other quantitative scientists to get involved in this exciting and rapidly evolving field.

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Bayesian Methods for Tensor Regression

Guhaniyogi¹

2020

Wiley StatsRef: Statistics Reference Online

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For many applications pertaining to neuroimaging, social science, international relations, chemometrics, genomics, and molecular omics, datasets often involve variables which are best represented in the form of a multidimensional array or tensor , which extends the familiar two‐way data matrix into higher dimensions. Rather than vectorizing tensor‐valued variables prior to analysis which results in loss of inference, new methods have emerged developing regression relationships between variables with either tensor‐valued response(s) or predictor(s). Bayesian approaches, in particular, have shown great promise in applications pertaining to tensor regressions. A remarkable feature of fully Bayesian approaches is that they allow flexible modeling of tensor‐valued parameters in the regressions involving tensor variables and naturally offer characterization of uncertainty in the parametric and predictive inferences. This article provides a review of some relevant Bayesian models on tensor regressions developed in recent years. We divide methods according to the objective of the analysis. We begin with tensor regression approaches with a scalar response and a tensor‐valued covariate and discuss both parametric and nonparametric modeling options and applications in this framework. We then address the problem of making inference with a tensor response and a vector of covariates, with applications including task‐related brain activation and connectivity studies. Finally, we offer discussion on Bayesian models involving a tensor response and a tensor covariate. Discussion of each model is accompanied by available results on its posterior contraction properties, laying out restrictions on key model parameters (such as the tensor dimensions) to draw accurate posterior inference.

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Tensor Regression with Applications in Neuroimaging Data Analysis

Cited by 444 publications

References 41 publications

Tensor-Based Classification Models for Hyperspectral Data Analysis

Tensor-Based Classification Models for Hyperspectral Data Analysis

A Survey of Statistics in the Neurological Sciences with a Focus on Human Neuroimaging

Bayesian Methods for Tensor Regression

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