In this paper, we address an anomaly detection problem in smart power grids using Multimodal Subspace Support Vector Data Description (MS-SVDD). This approach aims to leverage better feature relations by considering the data as coming from different modalities. These data are projected into a shared lower-dimensionality subspace which aims to preserve their inner characteristics. To supplement the previous work on this subject, we introduce novel multimodal graph-embedded regularizers that leverage graph information for every modality to enhance the training process, and we consider an improved training equation that allows us to maximize or minimize each modality according to the specified criteria. We apply this regularized graph-embedded model on a 3-modalities dataset after having generalized MS-SVDD algorithms to any number of modalities. To set up our application, we propose a whole preprocessing procedure to extract One-Class Classification training instances from time-bounded event time series that are used to evaluate both the reliability and earliness of our model for Event Detection.

Network reliability analysis remains a challenge due to the increasing size and complexity of networks. This paper presents a novel sampling method and an active learning method for efficient and accurate network reliability estimation under node failure and edge failure scenarios. The proposed sampling method adopts Monte Carlo technique to sample component lifetimes and the K-terminal spanning tree algorithm to accelerate structure function computation. Unlike existing methods that compute only one structure function value per sample, our method generates multiple component state vectors and corresponding structure function values from each sample. Network reliability is estimated based on survival signatures derived from these values. A transformation technique extends this method to handle both node failure and edge failure. To enhance efficiency of proposed sampling method and achieve adaptability to network topology changes, we introduce an active learning method utilizing a random forest (RF) classifier. This classifier directly predicts structure function values, integrates network behaviors across diverse topologies, and undergoes iterative refinement to enhance predictive accuracy. Importantly, the trained RF classifier can directly predict reliability for variant networks, a capability beyond the sampling method alone. Through investigating several network examples and two practical applications, the effectiveness of both proposed methods is demonstrated.