Variational Autoencoder-Based Approach to Latent Feature Analysis on Efficient Representation of Power Load Monitoring Data

Abstract: With the development of smart grids, High-Dimensional and Incomplete (HDI) Power Load Monitoring (PLM) data challenges the performance of Power Load Forecasting (PLF) models. In this paper, we propose a potential characterization model VAE-LF based on Variational Autoencoder (VAE) for efficiently representing and complementing PLM missing data. VAE-LF learns a low-dimensional latent representation of the data using an Encoder-Decoder structure by splitting the HDI PLM data into vectors and feeding them sequentially into the VAE-LF model, and generates the complementary data. Experiments on the UK-DALE dataset show that VAE-LF outperforms other benchmark models in both 5% and 10% sparsity test cases, with significantly lower RMSE and MAE, and especially outperforms on low sparsity ratio data. The method provides an efficient data-completion solution for electric load management in smart grids.

• The paper presents VAE-LF, a variational autoencoder model that robustly extracts nonlinear latent features and imputes missing entries in high-dimensional power load data.
• The paper demonstrates notable improvements with an MAE of 0.0820 and an RMSE of 0.1384 on the UK-DALE dataset, outperforming conventional methods.
• The paper highlights practical implications for smart grid analytics by enhancing power load forecasting accuracy and operational resilience in incomplete data scenarios.

Variational Autoencoder-Based Latent Feature Analysis for Efficient Power Load Monitoring Data Representation

Introduction

The paper "Variational Autoencoder-Based Approach to Latent Feature Analysis on Efficient Representation of Power Load Monitoring Data" (2506.08698) addresses the challenge of data incompleteness and high dimensionality in Power Load Monitoring (PLM) datasets, which are foundational for downstream Power Load Forecasting (PLF) and intelligent grid operation. The authors present VAE-LF, a Variational Autoencoder-based model, specifically tailored for extracting nonlinear latent representations and effective imputation of missing entries in high-dimensional and incomplete (HDI) PLM data.

Context and Motivation

Smart grid architectures increasingly depend on accurate, high-frequency PLM data encompassing parameters such as voltage, current, and power, typically organized as high-dimensional matrices indexed by time and day. However, practical deployment is impeded by incomplete data resulting from sensor failures, transmission bottlenecks, or operational anomalies. Traditional latent feature models—particularly linear Matrix Factorization (MF)—offer limited representational power for nonlinear dependencies intrinsic to real-world PLM signals. Recent work leveraging Neural Networks (NNs), Autoencoders (AEs), and more advanced architectures such as Graph Neural Networks (GNNs) has demonstrated advantages, but the explicit modeling of underlying data distributions and robust generative capability remain under-explored in the context of PLM.

Model Architecture and Methodological Contributions

VAE-LF operates by decomposing the k-parameter $\times$ |N| days $\times$ |M| times matrix into sequential vectors, which are individually processed by a VAE framework. The encoder approximates the posterior distribution of the latent variable $z$ conditioned on the observed vector $x$, learning $\mu(x)$ and $\sigma(x)$ via fully connected feedforward layers. This parameterization enables the use of the reparameterization trick for backpropagation-compatible stochastic sampling. The decoder reconstructs the input vector from $z$, yielding imputations of missing values.

The main innovations are:

• Sequential Vectorization: Instead of inputting a monolithic HDI matrix, VAE-LF splits the temporal matrix into vectors, leveraging VAE's generative capacity over sequential time slices which matches the temporal and sparsity patterns common in PLM datasets.
• Explicit Variational Bayesian Inference: By maximizing the Evidence Lower Bound (ELBO), VAE-LF regularizes the learned latent space according to a Gaussian prior, optimizing both reconstruction fidelity (via mean squared error) and distributional alignment (via KL divergence).
• Scalability to Sparsity: The architecture is evaluated for low-ratio (5%) and higher-ratio (10%) observed entries, simulating the severe sparsity encountered in real-world PLM scenarios.

Empirical Results

Extensive experimentation on the UK-DALE dataset validates the proposed approach. Under 5% observed data (D1), VAE-LF (M1) achieves an MAE of 0.0820 and an RMSE of 0.1384—an improvement of 8.16%, 20.18%, and 24.58% in RMSE over HMLET (M2), GTN (M3), and LightGCN (M4), respectively. Under the 10% observed data case (D2), similar trends persist with VAE-LF outperforming the baseline models across both error metrics.

The performance gap is even more pronounced for lower sparsity settings, indicating superior latent feature recovery and more reliable imputation by VAE-LF especially when data is extremely sparse. This is attributed to the nonlinearity and generative regularization embedded in the VAE architecture.

Theoretical and Practical Implications

The results substantiate the claim that VAEs, when properly adapted with vectorized sequential input, are well-suited for learning nonlinear manifold structure in high-dimensional PLM data and for robustly imputing missing entries. The superiority over not just traditional MF paradigms but also contemporary GNN-based models (including LightGCN) positions VAE-LF as a strong candidate for real-world smart grid analytics pipelines.

For practical deployment, the model's capability to generate plausible imputations can directly enhance PLF accuracy, facilitate equipment diagnostics, and ensure more resilient smart grid operation even in the face of pervasive data incompleteness. The approach is also generalizable to other domains characterized by HDI sensory data with temporal dependencies.

On the theoretical front, the success of VAE-LF reaffirms the utility of variational Bayesian NNs in unsupervised and semi-supervised representation learning for industrial time-series, suggesting promising directions in further coupling deep generative models with structured priors and real-time streaming architectures.

Future Directions

The paper identifies avenues for advancing VAE-LF, including incorporating more expressive VAE variants (e.g., hierarchical or disentangled VAEs), investigating model robustness at even higher sparsity ratios, and scaling the architecture to online (real-time) streaming data settings. Integration with adversarial or self-supervised objectives, and joint optimization with downstream PLF modules, could further amplify representational power and operational utility.

Conclusion

This work makes a compelling case for deep variational generative models in the efficient representation and completion of high-dimensional, incomplete PLM datasets. The demonstrated empirical advantages of VAE-LF over linear and graph-based alternatives underline the necessity of nonlinear latent models for the next generation of smart grid data analytics. The methodology and outcomes provide a blueprint for extending generative NN frameworks to broader time-series and sensor network scenarios in complex cyber-physical systems.