用UMAP+等单调回归，让电力市场曲线降维不失经济逻辑。
Latent Space Representation of Electricity Market Curves: Maintaining Structural Integrity
- 采用UMAP降维并结合等单调回归修复，确保重构曲线单调性。
- 在三年每小时的MIBEL数据上，UMAP误差最低，性能最佳。
- 适合电力市场建模、预测与分类任务，保障物理合理性。
高效表示供需曲线对能源市场分析和下游建模至关重要，但降维常导致重构违反基本经济原则（如单调性）。本文评估了PCA、核PCA、UMAP及自编码器在二维和三维潜在空间中的表现。预处理阶段通过数据转换实现结构统一，削弱异常值影响，并聚焦关键曲线片段。为确保理论有效性，引入等单调回归作为可选后处理步骤，强制重构输出满足单调约束。基于三年每小时的MIBEL数据集结果表明，非线性方法UMAP在多个误差指标上持续领先，位居第一。此外，等单调回归作为关键修正层，显著降低误差并恢复多种方法的物理合理性。我们认为，UMAP对局部结构的保持能力与智能后处理相结合，为预测、分类与聚类等下游任务提供了稳健基础。
原文摘要 · Abstract (English)
Efficiently representing supply and demand curves is vital for energy market analysis and downstream modelling; however, dimensionality reduction often produces reconstructions that violate fundamental economic principles such as monotonicity. This paper evaluates the performance of PCA, Kernel PCA, UMAP, and AutoEncoder across 2d and 3d latent spaces. During preprocessing, we transform the original data to achieve a unified structure, mitigate outlier effects, and focus on critical curve segments. To ensure theoretical validity, we integrate Isotonic Regression as an optional post-processing step to enforce monotonic constraints on reconstructed outputs. Results from a three-year hourly MIBEL dataset demonstrate that the non-linear technique UMAP consistently outperforms other methods, securing the top rank across multiple error metrics. Furthermore, Isotonic Regression serves as a crucial corrective layer, significantly reducing error and restoring physical validity for several methods. We argue that UMAP`s local structure preservation, combined with intelligent post-processing, provides a robust foundation for downstream tasks such as forecasting, classification, and clustering.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。