Tensor-Based Classifiers for Hyperspectral Data Analysis

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.