提出可解释的用电量周期建模方法,让低维表示直接对应日/周/年周期。
Calendar-SPCA: Interpretable Representation Learning for Multi-Periodic Electricity Consumption Profiles

- 基于日历坐标网格,用稀疏与图总变差约束提取周期模式
- 在两个数据集上保留96.92%和82.90%方差,稀疏度达61.95%和81.50%
- 结果可读性强,适合电力系统、能源管理等需解释性的场景
长期用电量呈现日、周、年多重周期结构。本文提出Calendar-SPCA,一种将已知多周期几何嵌入低维表示学习的时序稀疏主成分分析方法。特征空间表示为循环日历坐标的笛卡尔积,通过L1加载惩罚与日历图上的图总变差进行低秩分解,生成稀疏且局部连贯的加载模式,保持原始时间坐标的可读性。在两个独立智能电表数据集GoiEner和Low Carbon London上评估,样本量与时间分辨率不同。因子实验分析稀疏性与日历一致性互补效应,并检验样本量、潜在维度及重复拟合下的鲁棒性。在秩15下,分别保留了与匹配秩PCA相当的96.92%和82.90%解释方差,平均加载稀疏度为61.95%和81.50%。相比经典稀疏PCA与SPCA-TV,Calendar-SPCA在原始日历坐标中系统组织潜变量,同时保留大量低秩信息。所得成分呈现一致且互补的日、周、季节及联合定位的日历模式,两个数据集表现出特定几何结构。
原文摘要 · Abstract (English)
Long-term electricity-consumption profiles exhibit several simultaneous periodic structures, including daily, weekly, and annual cycles. This work introduces Calendar-SPCA, a calendar-structured sparse principal component method that incorporates this known multi-periodic geometry directly into low-dimensional representation learning. The feature domain is represented as the Cartesian product of cyclic calendar axes, and a low-rank factorization is estimated using an L1 loading penalty together with graph total variation over the resulting calendar graph. The method therefore produces sparse and locally coherent loading patterns that remain directly readable in their original temporal coordinates. Calendar-SPCA is evaluated on two independent smart-meter datasets with different sample sizes and temporal resolutions: GoiEner and Low Carbon London. A factorial experiment characterizes the complementary 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 PCA in GoiEner and Low Carbon London, respectively, while producing mean loading sparsities of 61.95% and 81.50%. Comparisons with classical sparse PCA and SPCA-TV further show that Calendar-SPCA adds a systematic organization of the latent factors in the original calendar coordinates while preserving substantial low-rank information. The resulting components form coherent and complementary daily, weekly, seasonal, and jointly localized calendar patterns, with dataset-specific geometries across the two datasets.
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。