2025/03/14 by Martin Výboh, Výboh, Martin, Zuzana Chladná +5
Computer Science · Engineering · #Energy Load and Power Forecasting #FOS: Computer and information sciences #I.2.6 #I.5.1 #I.6.3 #J.2 #J.4 #Machine Learning (cs.LG) #Smart Grid Energy Management #Time Series Analysis and Forecasting
paper · pdf · doi:10.48550/arxiv.2503.11294
openalex publication_date 2025/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02
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.