Rank-R FNN: A Tensor-Based Learning Model for High-Order Data Classification
This addresses inefficiencies in standard ML for high-order tensor data, offering a computationally efficient solution for applications like hyperspectral imaging, though it is incremental as it builds on existing tensor decomposition methods.
The authors tackled the problem of high-dimensional data classification by proposing Rank-R FNN, a tensor-based neural network that avoids vectorization and reduces parameters, achieving state-of-the-art performance on hyperspectral datasets.
An increasing number of emerging applications in data science and engineering are based on multidimensional and structurally rich data. The irregularities, however, of high-dimensional data often compromise the effectiveness of standard machine learning algorithms. We hereby propose the Rank-R Feedforward Neural Network (FNN), a tensor-based nonlinear learning model that imposes Canonical/Polyadic decomposition on its parameters, thereby offering two core advantages compared to typical machine learning methods. First, it handles inputs as multilinear arrays, bypassing the need for vectorization, and can thus fully exploit the structural information along every data dimension. Moreover, the number of the model's trainable parameters is substantially reduced, making it very efficient for small sample setting problems. We establish the universal approximation and learnability properties of Rank-R FNN, and we validate its performance on real-world hyperspectral datasets. Experimental evaluations show that Rank-R FNN is a computationally inexpensive alternative of ordinary FNN that achieves state-of-the-art performance on higher-order tensor data.