Latent Space Representation of Electricity Market Curves: Maintaining Structural Integrity

Abstract

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.