Calendar-Structured Sparse Principal Component Analysis for Interpretable Multi-Periodic Electricity Consumption Profiles
Carlos Quesada-Granja, Tony Castillo-Calzadilla, Carlos Rizo-Maestre
cs.LG · cs.AI
Quick verdict
Calendar-SPCA adds cyclic calendar graph-TV to sparse PCA; retains most PCA variance with interpretable factors on GoiEner/LCL, but baseline tuning asymmetric.
Summary
The paper introduces Calendar-SPCA, a structured sparse PCA variant for long-term electricity-consumption profiles. The feature space (hour-of-day × day-of-week × week-of-year) is modeled as the Cartesian product of cyclic graphs, and loadings are estimated jointly under an ℓ1 sparsity penalty plus graph total-variation regularization, solved by alternating score updates and a Condat–Vũ primal–dual loading solve. Evaluation uses two public smart-meter datasets: GoiEner (87,187 hourly Spanish annual profiles, 24×7×52 domain) and Low Carbon London (5,359 half-hourly UK profiles, 48×7×52). A factorial experiment (5,880 fits over both penalties, rank K, and sample size N) shows complementary roles — λ1 controls support size, λTV controls local coherence — with repeat stability reaching 0.996 at N=20,000, K=15. Operating points are chosen by maximum L-curve curvature (λ*=2.0 GoiEner, 1.5 LCL). At rank 15, Calendar-SPCA retains 96.92% (GoiEner) and 82.90% (LCL) of rank-matched PCA explained variance with 61.95%/81.50% loading sparsity and the lowest relative total variation among compared methods. Main limitations: rank-15 PCA itself explains only 41.95% (GoiEner) and 27.63% (LCL) of variance; baseline regularization paths were partly tuned on a 5,000-profile subsample (GoiEner) under fixed penalty ratios; interpretability rests on qualitative component maps without downstream-task validation; and 40.5% of factorial fits hit the iteration budget instead of fully converging.
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Assessment at a glance
5
risk flags identified
● high 0
● medium 3
● low 2
5 strengths · 5 weaknesses · 5 author questions
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Key claims under review
- Representing the feature domain as the Cartesian product of cyclic calendar graphs allows graph-TV-regularized sparse PCA to recover loadings directly interpretable on daily, weekly, and annual axes (§3, Fig. 6).
- At rank 15, Calendar-SPCA retains 96.92% (GoiEner) and 82.90% (LCL) of rank-matched PCA explained variance while attaining the highest sparsity (61.95%/81.50%) and lowest relative TV (0.615/0.450) among the compared structured methods (Tables 3 and 8).
- The two penalties have separable, complementary roles: λ1 controls loading support size while λTV controls local coherence and support organization (Table 6 matched ablation).
- Joint K-factor estimation over the calendar graph yields more coherent and complete temporal decompositions than sequential-deflation SPCA-TV or unstructured sparse PCA (§5.5, Fig. 7).
Strengths
Principled structural prior with clean positioning
The calendar domain is formalized as the cycle-product graph G = Ch□Cd□Cw (Eq. 3) with anisotropic graph TV (Eqs. 4-5); Table 1 contrasts the design against PCA/SPCA/fused-SPCA/SPCA-TV/tensor families, and joint K-factor estimation (Eq. 8) is a genuine improvement over SPCA-TV's sequential deflation.
Large-scale, well-controlled factorial characterization
5,880 fits spanning a 7×7 (λ1, λTV) grid, K∈{5..30}, N∈{5k..20k}, 5 repetitions with paired seeds and nested subsamples (§4.2) yield the regularization landscape (Fig. 2), robustness curves (Fig. 3), and repeat stability rising to 0.996 at N=20,000, K=15.
Clean penalty-separation ablation
Transparent convergence reporting
Strong reproducibility posture
Weaknesses
Modest absolute reconstruction ceiling
Asymmetric baseline tuning
Interpretability never quantified
Sample-size confound in regularization
Convergence burden undermines grid completeness
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Calendar-SPCA: Structured Review
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Frequently asked questions
What is Calendar-SPCA?
It is a sparse PCA variant for periodic time series. The feature space (hour of day, day of week, week of year) is treated as a graph built from joined cycles, and the loading vectors are penalized to be sparse (ℓ1) and locally smooth (graph total variation). Each resulting component reads as a mask over the calendar, e.g. 'weekend afternoons in summer', rather than as a diffuse global pattern.
How much accuracy does Calendar-SPCA lose compared with plain PCA?
At rank 15 it keeps 96.92% of PCA's explained variance on the GoiEner dataset (Spain, hourly) and 82.90% on Low Carbon London (UK, half-hourly), in exchange for loadings that are 61.95% and 81.50% sparse and the most locally coherent among the compared methods. Note that rank-15 PCA itself captures only 41.95% (GoiEner) and 27.63% (LCL) of total variance.
Which datasets and code does the paper use, and can I reproduce it?
Two public smart-meter datasets: GoiEner (87,187 annual profiles, Zenodo version 7.1) and Low Carbon London (5,359 annual profiles, London Datastore). The implementation and main experiment code are on GitHub (quesadagranja/calendar-spca), and the paper discloses all numerical settings, so independent reproduction is feasible at CPU scale.
Does Calendar-SPCA work on data other than electricity consumption?
The authors argue the construction extends to any domain with known periodic coordinates — telecom traffic, road traffic, building occupancy, ecological cycles — via a product of cycle graphs (Eq. 32). However, the paper only evaluates electricity consumption; other applications are proposed as future directions, not tested.
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This is an AI-generated preliminary review by Evolve.Pub, produced from the openly available text of the paper. It is not peer review and does not represent the authors' views. The canonical record of the paper is at the publisher link above.
- Figures 2-7 are heatmap panels; their underlying per-cell values could only be assessed from printed axis annotations, component contribution percentages, and numbers quoted in the text, not from the rendered images themselves.
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