[Paper Review] Water Disaggregation via Shape Features based Bayesian Discriminative Sparse Coding

Bingsheng Wang, Xuchao Zhang+2 more|arXiv (Cornell University)|Aug 26, 2018

Water Systems and Optimization35 references3 citations

TL;DR

This paper proposes a Bayesian discriminative sparse coding model with Laplace prior (BDSC-LP) enhanced by shape features to improve low-sampling-rate water disaggregation. By extracting discriminative shape features from device consumption patterns and using Gibbs sampling for inference, the method achieves superior performance over baselines in disaggregating residential water usage at both device and whole-home levels.

ABSTRACT

As the issue of freshwater shortage is increasing daily, it is critical to take effective measures for water conservation. According to previous studies, device level consumption could lead to significant freshwater conservation. Existing water disaggregation methods focus on learning the signatures for appliances; however, they are lack of the mechanism to accurately discriminate parallel appliances' consumption. In this paper, we propose a Bayesian Discriminative Sparse Coding model using Laplace Prior (BDSC-LP) to extensively enhance the disaggregation performance. To derive discriminative basis functions, shape features are presented to describe the low-sampling-rate water consumption patterns. A Gibbs sampling based inference method is designed to extend the discriminative capability of the disaggregation dictionaries. Extensive experiments were performed to validate the effectiveness of the proposed model using both real-world and synthetic datasets.

Motivation & Objective

• Address the challenge of water disaggregation using low-sampling-rate smart meter data, which lacks the temporal resolution to capture high-frequency device signatures.
• Improve disaggregation accuracy by incorporating domain-specific knowledge about device usage patterns, particularly in terms of consumption duration and trends.
• Develop a Bayesian discriminative sparse coding model that enhances dictionary discriminability through adaptive basis learning on aggregated data.
• Design an effective inference mechanism using Gibbs sampling to handle the intractable posterior distributions arising from Laplace and Gamma priors in the model.
• Validate the model’s effectiveness across both synthetic and real-world residential water consumption datasets, demonstrating robust performance at device and whole-home levels.

Proposed method

• Define shape features based on prior knowledge of device consumption patterns, such as duration, rise/fall times, and trend profiles, to capture low-sampling-rate dynamics.
• Construct a Bayesian sparse coding model with Laplace prior on coefficients and Gamma prior on noise precision to promote sparsity and robustness.
• Initialize basis functions using invariant shape features and apply smoothing to adapt to label data variance, improving model generalization.
• Combine individual device models into a joint disaggregation dictionary and minimize the objective function with respect to aggregated data to enhance discriminative power.
• Implement a Gibbs sampling-based inference algorithm to estimate posterior distributions over latent variables and hyperparameters, enabling scalable learning.
• Use shape features as input to the model to guide basis function learning, ensuring that the learned representations are sensitive to distinct device behaviors.

Experimental results

Research questions

• RQ1 Can shape features derived from domain knowledge effectively capture the distinguishing patterns of low-sampling-rate water consumption across different household fixtures?
• RQ2 Does integrating shape features into a Bayesian discriminative sparse coding framework significantly improve disaggregation accuracy compared to baseline models?
• RQ3 How does the Bayesian treatment of sparse coding with Laplace priors compare to conventional discriminative models in terms of robustness and performance?
• RQ4 To what extent does Gibbs sampling inference enable effective learning in the presence of intractable posteriors due to complex priors?
• RQ5 Can the proposed model generalize well across diverse real-world and synthetic datasets while maintaining high precision, recall, and F-measure?

Key findings

• BDSC-LP+SF achieved the highest F-measure of 0.6646 ± 0.0711 on real data, significantly outperforming BDSC-LP and other baselines.
• The inclusion of shape features (SF) improved F-measure by up to 15% compared to models without them, confirming their critical role in performance enhancement.
• BDSC-LP outperformed DDSC in all metrics, demonstrating the advantage of Bayesian treatment in sparse coding for disaggregation.
• The model achieved an average F-measure of 0.6646 ± 0.0711 and accuracy of 0.8521 ± 0.0513 on real data, with NDE of 0.2828 ± 0.0593, indicating strong whole-home performance.
• CDF and PDF analyses of event start times revealed distinct usage patterns—e.g., showers in morning and evening, dishwashers in evenings—validating the utility of shape features.
• FHMM and DDSC+SF showed comparable performance to DDSC+SF, but BDSC-LP+SF consistently outperformed all others across all evaluation metrics.