This paper advances the theory of reproducing kernel Banach spaces (RKBSs) by investigating the general $\ell^p$ regularization framework, with a particular focus on the non-convex regime $0<p<1$. While our preceding work established the foundation for RKBSs with the $\ell^1$ norm, the pursuit of stronger sparsity---closer to the $\ell^0$ pseudo-norm---naturally motivates this exploration into $\ell^p$ quasi-norms. For $0<p<1$, we construct reproducing kernel quasi-Banach spaces (RKQBSs) with $\ell^p$ quasi-norms and establish existence and sparsity results for interpolation and regularized learning under appropriate assumptions. We characterize the linear and relaxed representer theorems in terms of a generalized Lebesgue constant and derive bounds under kernel decay, sample spacing, and stability assumptions. For $p>1$, we construct RKBSs using a fixed countable dictionary, establish minimizer existence, and identify the optimal relaxed representer factor through an off-sample coefficient operator. These results reveal fundamental differences between the regimes $0<p<1$, $p=1$, and $p>1$. Numerical experiments compare the accuracy and sparsity of solutions for these three cases.
Multivariate time series are ubiquitous in monitoring smart systems such as power plants, smart houses, and servers. These systems use multiple sensors to collect the system's status over time. Those sensors represent the status of the whole system as one entity. Anomaly detection in such smart systems is of critical importance to prevent system failure and maintain functionality. But anomaly detection in such multivariate time series data is very challenging since this type of data includes both temporal and spatial information. Capturing both of these pieces of information is important to detect anomalies. In this paper, we propose a hybrid deep learning-based anomaly detection method, which captures both temporal and spatial information. We propose to take advantage of the feature extraction capabilities of 2d convolutional network in a variational autoencoder, alongside a prediction-based deep neural network of 2d convolutional networks and a gated recurrent unit network to capture both spatial and temporal information. Experiments on public data against state-of-the-art show the potential of our method.
Ali Babalhavaeji, Hui Song, Mohammadreza Radmanesh, Mahdi Jalili
原文摘要
In recent years, electric vehicles (EVs) have attracted much attention due to their potential to decarbonize the transport system. EV charging imposes challenges on power grids, such as load imbalance and voltage instability. Therefore, electricity distributors need to identify which users have an EV. Smart meter recordings can be effectively used for this purpose. The major issue associated with such data is the imbalance problem, where the majority of the data belongs to users without EVs. The existing methods for EV identification from smart meter recordings have framed it as a classification task. In this paper, we frame the problem as an unsupervised problem and propose a hybrid anomaly detection method that combines the power of prediction-based and reconstruction-based anomaly detection methods. The proposed model considers temporal and stochastic representation information of smart meter time series via prediction-based and reconstruction-based components, respectively. The performance of the proposed model is compared with state-of-the-art supervised and unsupervised methods. Its superiority is verified on real-world data.