Improving image classification of one-dimensional convolutional neural networks using Hilbert space-filling curves

Convolutional neural networks (CNNs) have significantly contributed to recent advances in machine learning and computer vision. Although initially designed for image classification, the application of CNNs has stretched far beyond the context of images alone. Some exciting applications, e.g., in natural language processing and image segmentation, implement one-dimensional CNNs, often after a pre-processing step that transforms higher-dimensional input into a suitable data format for the networks. However, local correlations within data can diminish or vanish when one converts higher-dimensional data into a one-dimensional string. The Hilbert space-filling curve can minimize this loss of locality. Here, we study this claim rigorously by comparing an analytical model that quantifies locality preservation with the performance of several neural networks trained with and without Hilbert mappings. We find that Hilbert mappings offer a consistent advantage over the traditional flatten transformation in test accuracy and training speed. The results also depend on the chosen kernel size, agreeing with our analytical model. Our findings quantify the importance of locality preservation when transforming data before training a one-dimensional CNN and show that the Hilbert space-filling curve is a preferential transformation to achieve this goal.