Tensor-Based Classification Models for Hyperspectral Data Analysis

In this paper, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting the 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 nonlinear classifiers. The advantages of the proposed classification approach are that: 1) it significantly reduces the number of weight parameters required to train the model (and thus the respective number of training samples); 2) it provides a physical interpretation of model coefficients on the classification output; and 3) it retains the spatial and spectral coherency of the input samples. The linear tensor-based model exploits the principles of logistic regression, assuming the rank-1 canonical decomposition property among its weights. For the nonlinear 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 support vector machine) or nonlinear (e.g., deep learning), indicate the outperformance of the proposed scheme, especially in the cases where a small number of training samples is available.