A Linear Transportation $\mathrm{L}^p$ Distance for Pattern Recognition
This work addresses computational inefficiency for researchers and practitioners in pattern recognition, signal processing, and image analysis, though it is incremental as it builds on existing transportation distance frameworks.
The paper tackled the high computational cost of transportation L^p distances in pattern recognition by proposing linear versions, resulting in a method that is several orders of magnitude faster while improving performance over linear Wasserstein distances on signal processing tasks.
The transportation $\mathrm{L}^p$ distance, denoted $\mathrm{TL}^p$, has been proposed as a generalisation of Wasserstein $\mathrm{W}^p$ distances motivated by the property that it can be applied directly to colour or multi-channelled images, as well as multivariate time-series without normalisation or mass constraints. These distances, as with $\mathrm{W}^p$, are powerful tools in modelling data with spatial or temporal perturbations. However, their computational cost can make them infeasible to apply to even moderate pattern recognition tasks. We propose linear versions of these distances and show that the linear $\mathrm{TL}^p$ distance significantly improves over the linear $\mathrm{W}^p$ distance on signal processing tasks, whilst being several orders of magnitude faster to compute than the $\mathrm{TL}^p$ distance.