Visualizing long vectors of measurements by use of the Hilbert curve

TL;DR

This paper revisits the use of Hilbert curves for visualizing large data vectors, introducing Hilbert plots combined with Fourier transforms to reveal patterns, periodicity, and structure in diverse datasets including biological signals.

Contribution

It demonstrates how Hilbert plots and their Fourier transforms can effectively visualize and analyze complex data sequences, enhancing pattern detection and periodicity identification.

Findings

Hilbert plots preserve data locality and reveal patterns.

Fourier transforms of Hilbert plots identify underlying periodicities.

Application to diverse data sources demonstrates versatility.

Abstract

The use of Hilbert curves to visualize massive vector of data is revisited following previous authors. The Hilbert curve mapping preserves locality and makes meaningful representation of the data. We call such visualization as Hilbert plots. The combination of a Hilbert plot with its Fourier transform allows to identify patterns in the underlying data sequence. The use of different granularity representation also allows to identify periodic intervals within the data. Data from different sources are presented: periodic, aperiodic, logistic map and 1/2-Ising model. A real data example from the study of heartbeat data is also discussed.