Video anomaly detection (VAD) is important in many fields because of its theoretical and practical values. One of the challenges in VAD is the difficulty in obtaining segment-level labels due to the high annotation cost. In recent years, researchers have adopted video-level labels as a form of weak supervision, leading to the development of weakly supervised video anomaly detection (WS-VAD). Among different WS-VAD approaches, graph convolutional networks (GCNs) have attracted much attention, since they have the ability to model relationship information in video data. Typically, the relationship, represented by the graph edges, is the class label similarity, and this similarity is built based on the feature similarity and temporal consistency among video segments. Undoubtedly, the more information about class label similarity is provided, the higher the performance of GCN tends to be. In real-world scenarios of VAD, anomalies exhibit several unique properties such as diversity and rarity. These properties may lead to the following situation. Given two video segments, although their feature similarity is low and their time separation is large, both of them are anomalies, that is, they have the same class label. Likewise, normal samples also encounter such situation. However, the existing graph structures in GCN methods do not adequately account for this situation. To address this issue, this paper proposes an extended graph learning (EGL) method that incorporates additional class label similarity among video segments. The proposed EGL includes two extended graph convolutional networks (EGCNs): a spatial EGCN and a temporal EGCN. To capture more accurate information about class label similarity, EGL incorporates a feedback module to update the graph structures of EGCNs. EGL can effectively extract more information about class label similarity, thereby ensuring good performance when training data is scarce. Experimental results highlight the advantages of the proposed EGL method, particularly with limited training samples. In particular, when only 30% of the training data is used, EGL achieves the best performance of 95.55% AUC on ShanghaiTech, 81.29% AUC on UCF-Crime, and 75.31% AP on XD-Violence, outperforming the existing VAD methods by up to 6.86%, 3.23%, and 4.40%, respectively.

In artificial intelligence, it is crucial for pattern recognition systems to process data with uncertain information, necessitating uncertainty reasoning approaches such as evidence theory. As an orderable extension of evidence theory, random permutation set (RPS) theory has received increasing attention. However, RPS theory lacks a suitable generation method for the element order of permutation mass function (PMF) and an efficient determination method for the fusion order of permutation orthogonal sum (POS). To solve these two issues, this paper proposes a reasoning model for RPS theory, called random permutation set reasoning (RPSR). RPSR consists of three techniques, including RPS generation method (RPSGM), RPSR rule of combination, and ordered probability transformation (OPT). Specifically, RPSGM can construct RPS based on Gaussian discriminant model and weight analysis; RPSR rule incorporates POS with reliability vector, which can combine RPS sources with reliability in fusion order; OPT is used to convert RPS into a probability distribution for the final decision. Besides, numerical examples are provided to illustrate the proposed RPSR. Moreover, the proposed RPSR is applied to classification problems. An RPSR-based classification algorithm (RPSRCA) and its hyperparameter tuning method are presented. The results demonstrate the efficiency and stability of RPSRCA compared to existing classifiers.

Belief entropy is an effective uncertainty measurement in Dempster–Shafer evidence theory. However, the weight ratio between discord and non-specificity in the belief entropy is static and cannot be further modified according to different environments. To overcome this issue, this paper proposes dynamic belief entropy (DBE), which is a generalization of belief entropy by introducing a dynamic parameter. Compared with belief entropy, DBE can be flexibly modified based on the dynamic parameter, so as to improve the performance of measuring uncertainty in different environments. Besides, some properties of DBE are presented and illustrated with examples. Also, we design a dynamic data fusion method based on DBE. Compared with the existing methods, the proposed method utilizes DBE-based dynamic techniques, thereby enhancing the classification performance. Moreover, to illustrate the general applicability, the proposed method is verified on classification problems. The experimental results show that the proposed method outperforms the existing methods with a classification accuracy of 95.93% and an F1 score of 96.08%, demonstrating the effectiveness of our method.

Dempster–Shafer evidence theory (evidence theory) has been widely used as an efficient method for dealing with uncertainty. In evidence theory, Dempster's rule is the most well-known evidence combination method but it does not work well when the evidence is in high conflict. To improve the performance of combining conflicting evidence, an original and novel evidence combination method is presented based on the Pearson correlation coefficient and weighted graph. The proposed method can correctly recognize the alternative situation with a high accuracy. Besides, the convergence performance of this method is better when compared with other combination rules. In addition, the weighted graph generated by the proposed method can directly represent the relationship between different evidence, which can help researchers estimate the reliability of different body of evidence. Our experimental results indicate the advantages of our proposed evidence combination rule over existing methods, and the results are analyzed and discussed.