# Tensor-Based Classifiers for Hyperspectral Data Analysis

arXiv: https://arxiv.org/abs/1709.08164 · HTML: https://mlsanity.com/paper/1709.08164/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Sep 2017.

## Built on by (most cited first, 10 of 10)

- [Tensor Methods in Computer Vision and Deep Learning](https://mlsanity.com/paper/2107.03436/) (2021)
- [Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification](https://mlsanity.com/paper/2104.05048/) (2021)
- [Patch Tracking-based Streaming Tensor Ring Completion for Visual Data Recovery](https://mlsanity.com/paper/2105.14620/) (2021)
- [2D Self-Organized ONN Model For Handwritten Text Recognition](https://mlsanity.com/paper/2207.08139/) (2022)
- [Lower and Upper Bounds on the VC-Dimension of Tensor Network Models](https://mlsanity.com/paper/2106.11827/) (2021)
- [DTR: A Unified Deep Tensor Representation Framework for Multimedia Data Recovery](https://mlsanity.com/paper/2407.05267/) (2024)
- [Virtual-mask Informed Prior for Sparse-view Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2504.07753/) (2025)
- [Automatic inspection of cultural monuments using deep and tensor-based learning on hyperspectral imagery](https://mlsanity.com/paper/2207.02163/) (2022)
- [Marine Debris Detection in Satellite Surveillance using Attention Mechanisms](https://mlsanity.com/paper/2307.04128/) (2023)
- [Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcity](https://mlsanity.com/paper/2609.40131/) (2026)

## Abstract (arXiv)

In this work, 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 satisfies the it rank-1 canonical decomposition property. Then, we introduce learning algorithms to train both the linear and the non-linear classifier in a way to i) to minimize the error over the training samples and ii) the weight coefficients satisfies the it rank-1 canonical decomposition property. The advantages of the proposed classification model is that i) it reduces the number of parameters required and thus reduces the respective number of training samples required to properly train the model, ii) it provides a physical interpretation regarding the model coefficients on the classification output and iii) it retains the spatial and spectral coherency of the input samples. To address issues related with linear classification, characterizing by low capacity, since it can produce rules that are linear in the input space, we introduce non-linear classification models based on a modification of a feedforward neural network. We call the proposed architecture it rank-1 Feedfoward Neural Network (FNN), since their weights satisfy the it rank-1 caconical decomposition property. Appropriate learning algorithms are also proposed to train the network. Experimental results and comparisons with state of the art classification methods, either linear (e.g., SVM) and non-linear (e.g., deep learning) indicates the outperformance of the proposed scheme, especially in cases where a small number of training samples are available. Furthermore, the proposed tensor-based classfiers are evaluated against their capabilities in dimensionality reduction.