# Preference-Optimal Multi-Metric Weighting for Parallel Coordinate Plots

arXiv: https://arxiv.org/abs/2507.02905 · HTML: https://mlsanity.com/paper/2507.02905/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 21 references that are in the map.
- First posted on arXiv 24 Jun 2025.

## Builds on (most cited first, 12 of 12)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Tree-Structured Parzen Estimator: Understanding Its Algorithm Components and Their Roles for Better Empirical Performance](https://mlsanity.com/paper/2304.11127/) (2023)
- [Towards Assessing the Impact of Bayesian Optimization's Own Hyperparameters](https://mlsanity.com/paper/1908.06674/) (2019)
- [PED-ANOVA: Efficiently Quantifying Hyperparameter Importance in Arbitrary Subspaces](https://mlsanity.com/paper/2304.10255/) (2023)
- [DeepCAVE: An Interactive Analysis Tool for Automated Machine Learning](https://mlsanity.com/paper/2206.03493/) (2022)
- [Hyperparameter Importance Analysis for Multi-Objective AutoML](https://mlsanity.com/paper/2405.07640/) (2024)
- [Speeding Up Multi-Objective Hyperparameter Optimization by Task Similarity-Based Meta-Learning for the Tree-Structured Parzen Estimator](https://mlsanity.com/paper/2212.06751/) (2022)
- [Weighted Random Search for Hyperparameter Optimization](https://mlsanity.com/paper/2004.01628/) (2020)
- [How to Read Many-Objective Solution Sets in Parallel Coordinates](https://mlsanity.com/paper/1705.00368/) (2017)
- [Python Tool for Visualizing Variability of Pareto Fronts over Multiple Runs](https://mlsanity.com/paper/2305.08852/) (2023)

## Abstract (arXiv)

Parallel coordinate plots (PCPs) are a prevalent method to interpret the relationship between the control parameters and metrics. PCPs deliver such an interpretation by color gradation based on a single metric. However, it is challenging to provide such a gradation when multiple metrics are present. Although a naive approach involves calculating a single metric by linearly weighting each metric, such weighting is unclear for users. To address this problem, we first propose a principled formulation for calculating the optimal weight based on a specific preferred metric combination. Although users can simply select their preference from a two-dimensional (2D) plane for bi-metric problems, multi-metric problems require intuitive visualization to allow them to select their preference. We achieved this using various radar charts to visualize the metric trade-offs on the 2D plane reduced by UMAP. In the analysis using pedestrian flow guidance planning, our method identified unique patterns of control parameter importance for each user preference, highlighting the effectiveness of our method.