Calendar-SPCA：多周期电力消费曲线的可解释表示学习
Calendar-Structured Sparse Principal Component Analysis for Interpretable Multi-Periodic Electricity Consumption Profiles
- University of Alicante（阿利坎特大学）
- University of La Laguna（拉古纳大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出Calendar-SPCA，一种将日历多周期结构融入稀疏主成分分析的表示学习方法，在智能电表数据上以高方差保留率和稀疏性生成可解释的周期模式。
中文摘要 AI 辅助
长期电力消费曲线表现出多种同时存在的周期结构，包括日周期、周周期和年周期。本文提出了Calendar-SPCA，一种日历结构稀疏主成分方法，将已知的多周期几何结构直接融入低维表示学习中。特征域被表示为循环日历轴的笛卡尔积，并通过L1载荷惩罚以及对所得日历图上的图全变差来估计低秩分解。因此，该方法产生稀疏且局部连贯的载荷模式，这些模式在其原始时间坐标中保持直接可读。Calendar-SPCA在两个独立的智能电表数据集上进行了评估，这两个数据集具有不同的样本大小和时间分辨率：GoiEner和Low Carbon London。一个析因实验刻画了稀疏性和日历一致性的互补效应，并检验了在不同样本量、潜在维度和重复拟合下的鲁棒性。在秩为15时，Calendar-SPCA在GoiEner和Low Carbon London中分别保留了秩匹配PCA解释方差的96.92%和82.90%，同时产生61.95%和81.50%的平均载荷稀疏度。与经典稀疏PCA和SPCA-TV的比较进一步表明，Calendar-SPCA在原始日历坐标中增加了潜在因子的系统组织，同时保留了大量的低秩信息。所得分量形成连贯且互补的日、周、季节以及联合局部的日历模式，在两个数据集中具有数据集特定的几何结构。
英文摘要
Long-term electricity-consumption profiles exhibit several simultaneous periodic structures, including daily, weekly, and annual cycles. This work introduces Calendar-Structured Sparse Principal Component Analysis (Calendar-SPCA), a structured representation-learning method that incorporates this known multi-periodic geometry directly into a low-dimensional factorization. The method represents the feature domain as the Cartesian product of cyclic calendar axes and combines an L1 loading penalty with graph total variation, producing sparse, locally coherent, and directly interpretable latent factors. In this study, Calendar-SPCA is applied to the interpretable analysis of long-term electricity-consumption profiles and evaluated on two independent public smart-meter datasets, GoiEner and Low Carbon London, with different population sizes and temporal resolutions. A factorial experiment characterizes the effects of sparsity and calendar coherence and examines robustness across sample size, latent dimensionality, and repeated fits. At rank 15, Calendar-SPCA retains 96.92% and 82.90% of the explained variance of rank-matched principal component analysis (PCA) in GoiEner and Low Carbon London, respectively, with mean loading sparsities of 61.95% and 81.50%. Comparisons with classical sparse PCA and sparse PCA with total variation (SPCA-TV) show that Calendar-SPCA organizes latent factors into interpretable structures over the daily, weekly, and annual calendar axes while preserving substantial low-rank information.
