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.

翻译：高效表示供需曲线对于能源市场分析和下游建模至关重要；然而，降维过程产生的重构结果常常违反单调性等基本经济学原理。本文评估了PCA、Kernel PCA、UMAP和AutoEncoder在二维与三维隐空间中的性能表现。在预处理阶段，我们对原始数据进行变换以实现统一结构、减弱异常值影响，并聚焦于关键曲线段。为确保理论有效性，我们引入保序回归作为可选后处理步骤，对重构输出施加单调性约束。基于三年期MIBEL小时数据集的实验结果表明，非线性方法UMAP在多项误差指标上持续优于其他方法，始终位列第一。此外，保序回归作为关键校正层，显著降低了多种方法的误差并恢复了物理有效性。我们认为，UMAP的局部结构保持特性与智能后处理相结合，为预测、分类和聚类等下游任务提供了稳健基础。