Tensor-based Nonlinear Classifier for High-Order Data Analysis
This work addresses classification challenges in domains like hyperspectral imaging, offering a more efficient solution for small sample sizes, though it appears incremental as it modifies existing neural network architectures.
The authors tackled the problem of high-order data classification by proposing a tensor-based nonlinear model that reduces weight parameters and retains spatial structure, achieving state-of-the-art performance with fewer training samples.
In this paper we propose a tensor-based nonlinear model for high-order data classification. The advantages of the proposed scheme are that (i) it significantly reduces the number of weight parameters, and hence of required training samples, and (ii) it retains the spatial structure of the input samples. The proposed model, called \textit{Rank}-1 FNN, is based on a modification of a feedforward neural network (FNN), such that its weights satisfy the {\it rank}-1 canonical decomposition. We also introduce a new learning algorithm to train the model, and we evaluate the \textit{Rank}-1 FNN on third-order hyperspectral data. Experimental results and comparisons indicate that the proposed model outperforms state of the art classification methods, including deep learning based ones, especially in cases with small numbers of available training samples.