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  • https://doi.org/10.1109/tgrs.2018.2845450Copy DOI Icon

Tensor-Based Classification Models for Hyperspectral Data Analysis

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Abstract

In this work, we present tensor-based linear and nonlinear models for\nhyperspectral data classification and analysis. By exploiting principles of\ntensor algebra, we introduce new classification architectures, the weight\nparameters of which satisfies the {\\it rank}-1 canonical decomposition\nproperty. Then, we introduce learning algorithms to train both the linear and\nthe non-linear classifier in a way to i) to minimize the error over the\ntraining samples and ii) the weight coefficients satisfies the {\\it rank}-1\ncanonical decomposition property. The advantages of the proposed classification\nmodel is that i) it reduces the number of parameters required and thus reduces\nthe respective number of training samples required to properly train the model,\nii) it provides a physical interpretation regarding the model coefficients on\nthe classification output and iii) it retains the spatial and spectral\ncoherency of the input samples. To address issues related with linear\nclassification, characterizing by low capacity, since it can produce rules that\nare linear in the input space, we introduce non-linear classification models\nbased on a modification of a feedforward neural network. We call the proposed\narchitecture {\\it rank}-1 Feedfoward Neural Network (FNN), since their weights\nsatisfy the {\\it rank}-1 caconical decomposition property. Appropriate learning\nalgorithms are also proposed to train the network. Experimental results and\ncomparisons with state of the art classification methods, either linear (e.g.,\nSVM) and non-linear (e.g., deep learning) indicates the outperformance of the\nproposed scheme, especially in cases where a small number of training samples\nare available. Furthermore, the proposed tensor-based classfiers are evaluated\nagainst their capabilities in dimensionality reduction.\n

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