Multi-scale analysis of linear data in a two-dimensional space

Many disciplines are faced with the problem of handling time-series data. This study introduces an innovative visual representation for time series, namely the continuous triangular model. In the continuous triangular model, all subintervals of a time series can be represented in a two-dimensional continuous field, where every point represents a subinterval of the time series, and the value at the point is derived through a certain function (e. g. average or summation) of the time series within the subinterval. The continuous triangular model thus provides an explicit overview of time series at all different scales. In addition to time series, the continuous triangular model can be applied to a broader sense of linear data, such as traffic along a road. This study shows how the continuous triangular model can facilitate the visual analysis of different types of linear data. We also show how the coordinate interval space in the continuous triangular model can support the analysis of multiple time series through spatial analysis methods, including map algebra and cartographic modelling. Real-world datasets and scenarios are employed to demonstrate the usefulness of this approach.