SepNet: A neural network for directionally correlated data

Abstract

Multi-dimensional tensor data appear in diverse settings, including multichannel signals, spectrograms, and hyperspectral data from remote sensing. In many cases, these data are directionally correlated, i.e. the correlation between variables from different dimensions is significantly weaker than the correlation between variables from the same dimension. Convolutional neural networks are readily applicable to directionally correlated data but are often inefficient, as they impose many unnecessary connections between neurons. Here we propose a novel architecture, SepNet, specifically for directionally correlated datasets. SepNet uses directional operators to extract directional features from each dimension separately, followed by a linear operator along the depth to generate higher-level features from the directional features. Experiments on two representative directionally correlated datasets showed that SepNet improved network efficiency up to 100-fold while maintaining high accuracy comparable with state-of-the-art convolutional neural network models. Furthermore, SepNet can be flexibly constructed with minimal restriction on the output shape of each layer. These results reveal the potential of data-specific architecting of neural networks.

Keywords: Correlation matrix; Directional convolutional operator; Directional linear operator; Multichannel signal; Neural network; Spectrogram.