How to Simplify a Line Chart: A Taxonomy and Feature-Based Evaluation

Simplifying large or noisy time-series is often a prerequisite for producing interpretable line charts, yet existing methods vary widely in how they alter visual features such as trends, extrema, periodicity, curvature, roughness, and overall complexity. We introduce a feature-based taxonomy of line chart simplification that evaluates 19 commonly used algorithms across three families: Transformers, Reducers, and Aggregators. We also formalize 12 perceptually motivated, computationally defined visual features commonly used when analyzing time-series in line charts. We assess preservation using multiple similarity metrics per feature to capture different aspects of fidelity, yielding 21 distinct feature-preservation measurements. To capture the trade-off between fidelity and simplicity, we introduce a Feature-Complexity (FC) score that combines feature preservation with complexity. Our systematic evaluation on 80 datasets reveals distinct family-level patterns: Transformers such as ${\sf Gaussian}$, ${\sf Mean}$, and ${\sf Median}$ filters achieve A-mode grades on nearly all metrics but retain full temporal resolution; Reducers such as ${\sf Douglas-Peucker}$ and ${\sf M4}$ receive predominantly D-F mode grades trading fidelity for a reduction in the number of rendered points; and Aggregators ${\sf ASAP}$ and ${\sf PAA}$ occupy a middle ground with primarily B-C mode grades. We further characterize the predictability of algorithm behavior across datasets: some methods produce consistent grades regardless of dataset type (${\sf Gaussian}$, ${\sf Mean}$, ${\sf Douglas-Peucker}$), while others exhibit high data-dependency, with performance varying substantially based on dataset characteristics (${\sf FPCS}$, ${\sf ASAP}$). An interactive website supporting exploration of all evaluated techniques, datasets, and results is available at https://feature-taxonomy.vercel.app/.