Deep clustering has achieved remarkable success in handling various types of real-world data, but often suffers from overconfidence, forcing ambiguous samples into specific clusters even when the evidence is insufficient. To address this limitation, we propose trustworthy deep credal clustering, a novel framework for uncertainty that integrates deep neural networks with the Dempster-Shafer Theory of evidence (DST). This method leverages credal cluster structures to enhance the model's robustness against uncertain data. Our model can refrain from assigning uncertain samples to a specific cluster, thereby reducing errors and enhancing the model's trustworthiness. Theoretically, we derive closed-form solutions for updating cluster memberships and prototypes, employing a coordinate descent strategy to rigorously optimize the objective function. Experiments on various datasets confirm that our proposed trustworthy clustering method leads to enhanced overall clustering effectiveness. Code is available at https://github.com/H1nkik/Trustworthy-Clustering.

In reliability analysis, mixed Weibull distributions have gained considerable attention due to its exceptional flexibility in modeling complex failure mechanisms. In the practical analysis of mixed distribution life data, obtaining complete failure information presents significant challenges, leading to various forms of uncertainty. In this paper, we propose a novel framework based on evidence theory to address uncertainty in the reliability analysis of progressively censored data following a mixed Weibull distribution. This approach can simultaneously handle the uncertainty arising from unobserved censored data and prior knowledge in the dataset. The maximum likelihood estimation is derived by optimizing the introduced evidential likelihood. Moreover, we prove the asymptotic normality and invariance property of the estimators. Furthermore, leveraging these properties, we provide both point and interval estimates for the reliability function. Numerical experiments are conducted to demonstrate the effectiveness of the proposed method.

Identifying key nodes in a graph is critical for the analysis and management of networked systems. Traditional centrality-based methods primarily focus on the intrinsic characteristics of nodes and the topological properties of graphs. However, these approaches depend heavily on handcrafted feature selection, resulting in poor generalization across networks with diverse structures. Graph Convolutional Networks (GCNs), as a classical deep learning model for graph-structured data, have demonstrated promising performance in key node identification. By aggregating features from a node and its neighbors, GCNs construct expressive node representations and enhance the model’s generalization ability. Nevertheless, existing GCN-based methods often fail to adequately capture the relative importance of neighboring nodes. To address this limitation, this paper introduces a novel key node identification model based on Graph Attention Networks (GAT), termed KeyGAT. By leveraging an attention mechanism, the proposed model enables adaptive and reliable fusion of node and neighbor features, thereby improving identification accuracy. Experimental results on different graph datasets validate the effectiveness of the proposed approach.

Traditional machine-learning approaches face limitations when confronted with insufficient data. Transfer learning addresses this by leveraging knowledge from closely related domains. The key in transfer learning is to find a transferable feature representation to enhance cross-domain classification models. However, in some scenarios, some features correlated with samples in the source domain may not be relevant to those in the target. Causal inference enables us to uncover the underlying patterns and mechanisms within the data, mitigating the impact of confounding factors. Nevertheless, most existing causal inference algorithms have limitations when applied to high-dimensional datasets with nonlinear causal relationships. In this work, a new causal representation method based on a Graph autoencoder embedded AutoEncoder, named GeAE, is introduced to learn invariant representations across domains. The proposed approach employs a causal structure learning module, similar to a graph autoencoder, to account for nonlinear causal relationships present in the data. Moreover, the cross-entropy loss as well as the causal structure learning loss and the reconstruction loss are incorporated in the objective function designed in a united autoencoder. This method allows for the handling of high-dimensional data and can provide effective representations for cross-domain classification tasks. Experimental results on generated and real-world datasets demonstrate the effectiveness of GeAE compared with the state-of-the-art methods.

In this work, we study the unsupervised robust domain adaptation problem where only a single well labeled source domain data is available during the learning process. A new causal representation method based on a Graph autoen-coder embedded AutoEncoder, named GeAE, is introduced to learn invariant representations across domains for robust domain adaption. The proposed method can handle nonlinear causal relations included in the data by a causal structure learning process similar to a graph autoencoder. Moreover, the cross-entropy loss as well as the causal structure loss and the reconstruction loss are incorporated in the objective function designed in a united autoencoder to improve the quality of predictions using causal representations. Experimental results on one generated dataset and three real-world datasets demonstrate the effectiveness of GeAE in comparison with the state-of-the-art methods.

With the increasing prominence of smart mobile devices, an innovative distributed computing paradigm, namely Mobile Crowdsourcing (MCS), has emerged. By directly recruiting skilled workers, MCS exploits the power of the crowd to complete location-dependent tasks. Currently, based on online social networks, a new and complementary worker recruitment mode, i.e., socially aware MCS, has been proposed to effectively enlarge worker pool and enhance task execution quality, by harnessing underlying social relationships. In this paper, we propose and develop a novel worker recruitment game in socially aware MCS, i.e.,Acceptance-awareWorkerRecruitment (AWR). To accommodate MCS task invitation diffusion over social networks, we design a Random Diffusion model, where workers randomly propagate task invitations to social neighbors, and receivers independently make a decision whether to accept or not. Based on the diffusion model, we formulate the AWR game as a combinatorial optimization problem, which strives to search a subset of seed workers to maximize overall task acceptance under a pre-given incentive budget. We prove its NP hardness, and devise a meta-heuristic-based evolutionary approach namedMA-RAWRto balance exploration and exploitation during the search process. Comprehensive experiments using two real-world data sets clearly validate the effectiveness and efficiency of our proposed approach.

It is still a challenging problem to characterize uncertainty and imprecision between specific (singleton) clusters with arbitrary shapes and sizes. In order to solve such a problem, we propose a belief shift clustering (BSC) method for dealing with object data. The BSC method is considered as the evidential version of mean shift or mode seeking under the theory of belief functions. First, a new notion, called belief shift, is provided to preliminarily assign each query object as the noise, precise, or imprecise one. Second, a new evidential clustering rule is designed to partial credal redistribution for each imprecise object. To avoid the “uniform effect” and useless calculations, a specific dynamic framework with simulated cluster centers is established to reassign each imprecise object to a singleton cluster or related meta-cluster. Once an object is assigned to a meta-cluster, this object may be in the overlapping or intermediate areas of different singleton clusters. Consequently, the BSC can reasonably characterize the uncertainty and imprecision between singleton clusters. The effectiveness has been verified on several artificial, natural, and image segmentation/classification datasets by comparison with other related methods.

The classification analysis of missing data is still a challenging task since the training patterns may be insufficient and incomplete in many fields. To train a high-performance classifier and pursue high accuracy, we learn a credal classifier based on an optimized and adaptive multiestimation (OAME) method for missing data imputation on training and test sets. In OAME, some incomplete training patterns are estimated as multiple versions by a global optimization method thereby expanding the training set. On the other hand, the test pattern is adaptively estimated as one or multiple versions depending on the neighbors. For the test pattern with multiple versions, the corresponding outputs with different discounting factors (weights), represented by the basic belief assignments (BBAs), are fused for final credal classification based on evidence theory. The discounting factor contains two aspects: the importance and reliability factors that are used, respectively, to quantify the importance of the edited version itself and to represent the reliability of the classification result of the version. The effectiveness of OAME is widely validated on several real datasets and critically compared to other related methods.

In applications of domain adaptation, there may exist multiple source domains, which can provide more or less complementary knowledge for pattern classification in the target domain. In order to improve the classification accuracy, a decision-level combination method is proposed for the multisource domain adaptation based on evidential reasoning. The classification results obtained from different source domains usually have different reliabilities/weights, which are calculated according to domain consistency. Therefore, the multiple classification results are discounted by the corresponding weights under belief functions framework, and then, Dempster's rule is employed to combine these discounted results. In order to reduce errors, a neighborhood-based cautious decision-making rule is developed to make the class decision depending on the combination result. The object is assigned to a singleton class if its neighborhoods can be (almost) correctly classified. Otherwise, it is cautiously committed to the disjunction of several possible classes. By doing this, we can well characterize the partial imprecision of classification and reduce the error risk as well. A unified utility value is defined here to reflect the benefit of such classification. This cautious decision-making rule can achieve the maximum unified utility value because partial imprecision is considered better than an error. Several real data sets are used to test the performance of the proposed method, and the experimental results show that our new method can efficiently improve the classification accuracy with respect to other related combination methods.

It is a challenging problem for pattern classification with few labeled instances. Transfer learning provides an efficient solution to improve the classification accuracy using some training knowledge in the related domain (called source domain). Nevertheless, the single transformation in one direction may be uncertain in some cases, and this is harmful for classification. So we propose a new classification method based on the fusion of data transformations in different directions between source domain and target domain. At first, the mapping of target in the source domain is estimated by K-nearest neighbor technique using some one-to-one instance pairs, and the estimated mapping instance (pattern) can be classified in the source domain according to the available training data. Then, the credibility of classification result is evaluated. If the credibility achieves the expected threshold, the classification result is directly output. Otherwise, it indicates that the transformation may be not very reliable, and the labeled instances in source domain will be transferred to target domain for the classification of target. The two versions of classification results will be fused with different weights based on evidential reasoning, and the weighting factors are optimized using the available training instances. By doing this, we can efficiently reduce the uncertainty of transformation and improve the classification accuracy. Some real data sets from UCI have been employed to validate the effectiveness of the proposed by comparing with other related methods.

Currently, there are many approaches designed for the task of detecting communities in social networks. Among them, some methods only consider the topological graph structure, while others can take use of both the graph structure and the node attributes. In real-world networks, there are many uncertain and noisy attributes in the graph. In this paper, we will present how we can detect communities for graphs with uncertain attributes in the first step. The numerical, probabilistic as well as evidential attributes are generated according to the graph structure. In the second step, some noise will be added to the attributes. We perform experiments on graphs with different types of attributes and compare the detection results in terms of the Normalized Mutual Information (NMI) values. The experimental results show that the clustering with evidential attributes give better results comparing to those with probabilistic and numerical attributes. This illustrates the advantages of evidential attributes.

In the complex pattern classification problem, the fusion of multiple classification results produced by different attributes is able to efficiently improve the accuracy. Evidence theory is good at representing and combining the uncertain information, and it is employed here. Each attribute (set) can be considered as one source of evidence (information). In some applications, the observation of target attributes can be costly, and some unreliable information sources may harm the fusion result. Therefore, we want to use as few as possible sources of information with high quality to achieve the admissible classification accuracy. So we propose a new fusion method based on the adaptive selection of the information sources for pattern classification. For each pattern, the attribute (set) producing the highest accuracy among the various ones will be chosen to classify the pattern at first. If the reliability of classification result, which is evaluated by the K-nearest neighbors (K-NN) technique using training data, cannot satisfy the request, the next attribute source will be chosen according to its classification performance on the selected neighborhoods of the object. In the fusion, the classification results corresponding to different attributes are assigned different weights because of their different classification abilities, and the weighted evidence combination method is adopted to produce the best possible classification performance. Several real data sets from UCI have been used for the evaluation of the proposed method by comparison with other related fusion methods, and it shows that our new method can produce higher accuracy with smaller number of information sources than the other fusion methods which are directly used to combine all the sources of information.

The theory of belief functions is an effective tool to deal with the multiple uncertain information. In recent years, many evidence combination rules have been proposed in this framework, such as the conjunctive rule, the cautious rule, the PCR (Proportional Conflict Redistribution) rules and so on. These rules can be adopted for different types of sources. However, most of these rules are not applicable when the number of sources is large. This is due to either the complexity or the existence of an absorbing element (such as the total conflict mass function for the conjunctive-based rules when applied on unreliable evidence). In this paper, based on the assumption that the majority of sources are reliable, a combination rule for a large number of sources, named LNS (stands for Large Number of Sources), is proposed on the basis of a simple idea: the more common ideas one source shares with others, the more reliable the source is. This rule is adaptable for aggregating a large number of sources among which some are unreliable. It will keep the spirit of the conjunctive rule to reinforce the belief on the focal elements with which the sources are in agreement. The mass on the empty set will be kept as an indicator of the conflict. Moreover, it can be used to elicit the major opinion among the experts. The experimental results on synthetic mass functions verify that the rule can be effectively used to combine a large number of mass functions and to elicit the major opinion.

Doze mode, which was introduced from Android 6.0 aiming at reducing battery consumption when the device is unused for a long time. This work firstly reveals the internal details of the battery-saving feature, especially about the state transitions. Furthermore, we discover several defects in Android's device drivers associated with doze mode. By exploiting the defects, we implement various proof-of-concept attacks that could drain battery without acquiring any permissions by subverting doze mode. The proposed attacks are silent (hardly discerned by normal users), because they keep hidden when the smartphone is in use, while letting benign applications do battery-intensive work when the smartphone is unused rather than consuming excessive power by the attacks themselves. Google has confirmed that our attacks can reduce battery life. Finally, we discuss how to defend against the proposed attacks.

One difficulty faced in knowledge engineering for Bayesian Network (BN) is the quantification step where the Conditional Probability Tables (CPTs) are determined. The number of parameters included in CPTs increases exponentially with the number of parent variables. The most common solution is the application of the so-called canonical gates. The Noisy-OR (NOR) gate, which takes advantage of the independence of causal interactions, provides a logarithmic reduction of the number of parameters required to specify a CPT. In this paper, an extension of NOR model based on the theory of belief functions, named Belief Noisy-OR (BNOR), is proposed. BNOR is capable of dealing with both aleatory and epistemic uncertainty of the network. Compared with NOR, more rich information which is of great value for making decisions can be got when the available knowledge is uncertain. Specially, when there is no epistemic uncertainty, BNOR degrades into NOR. Additionally, different structures of BNOR are presented in this paper in order to meet various needs of engineers. The application of BNOR model on the reliability evaluation problem of networked systems demonstrates its effectiveness.

In this work, a new prototype-based clustering method named Evidential C -Medoids (ECMdd), which belongs to the family of medoid-based clustering for proximity data , is proposed as an extension of Fuzzy C -Medoids (FCMdd) on the theoretical framework of belief functions . In the application of FCMdd and original ECMdd, a single medoid (prototype), which is supposed to belong to the object set, is utilized to represent one class. For the sake of clarity, this kind of ECMdd using a single medoid is denoted by sECMdd. In real clustering applications, using only one pattern to capture or interpret a class may not adequately model different types of group structure and hence limits the clustering performance. In order to address this problem, a variation of ECMdd using multiple weighted medoids, denoted by wECMdd, is presented. Unlike sECMdd, in wECMdd objects in each cluster carry various weights describing their degree of representativeness for that class. This mechanism enables each class to be represented by more than one object. Experimental results in synthetic and real data sets clearly demonstrate the superiority of sECMdd and wECMdd. Moreover, the clustering results by wECMdd can provide richer information for the inner structure of the detected classes with the help of prototype weights.