Quantification and reduction of uncertainty in deep-learning techniques have received much attention but ignored how to characterize the imprecision caused by such uncertainty. In some tasks, we prefer to obtain an imprecise result rather than being willing or unable to bear the cost of an error. For this purpose, we investigate the representation of imprecision in deep-learning (RIDL) techniques based on the theory of belief functions (TBF). First, the labels of some training images are reconstructed using the learning mechanism of neural networks to characterize the imprecision in the training set. In the process, a label assignment rule is proposed to reassign one or more labels to each training image. Once an image is assigned with multiple labels, it indicates that the image may be in an overlapping region of different categories from the feature perspective or the original label is wrong. Second, those images with multiple labels are rechecked. As a result, the imprecision (multiple labels) caused by the original labeling errors will be corrected, while the imprecision caused by insufficient knowledge is retained. Images with multiple labels are called imprecise ones, and they are considered to belong to meta-categories, the union of some specific categories. Third, the deep network model is retrained based on the reconstructed training set, and the test images are then classified. Finally, some test images that specific categories cannot distinguish will be assigned to meta-categories to characterize the imprecision in the results. Experiments based on some remarkable networks have shown that RIDL can improve accuracy (AC) and reasonably represent imprecision both in the training and testing sets.

Classification of missing data based on estimation is still challenging since existing methods relying on one imputation strategy fail to consider the diversity of different attribute distributions. In this case, there are inevitably some “bad” estimations at the attribute level, reducing the performance of classification. This article proposes a mixed-type imputation method (MTI) to classify missing data under the theory of belief functions (TBF) via two quality matrices to address this problem. The proposed MTI method has the advantages of making estimations as close to the truth as possible at the attribute level while reducing the negative impact of possible bad estimations on the classification. Specifically, the first matrix used to impute missing values can characterize the different supports of multiple imputation methods for estimating various attributes. The other matrix used to perform the classification task can extract the reliabilities of estimations on the different classes. The validity has been demonstrated in the final decision support based on the TBF, famous for characterizing uncertainty and imprecision, for example, caused by missing values.

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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.

Nowadays, we are interconnected with people whether professionally or personally using different social networks. However, we sometimes receive messages or advertisements that are not correlated to the nature of the relation established between the persons. Therefore, it became important to be able to sort out our relationships. Thus, based on the type of links that connect us, we can decide if this last is spammed and should be deleted. Thereby, we propose in this paper a belief approach in order to detect the spammed links. Our method consists on modelling the belief that a link is perceived as spammed by taking into account the prior information of the nodes, the links and the messages that pass through them. To evaluate our method, we first add some noise to the messages, then to both links and messages in order to distinguish the spammed links in the network. Second, we select randomly spammed links of the network and observe if our model is able to detect them. The results of the proposed approach are compared with those of the baseline and to the k-nn algorithm. The experiments indicate the efficiency of the proposed model.

Crowdsourcing is characterized by the externalization of tasks to a crowd of workers. In some platforms the tasks are easy, open access and remunerated by micropayment. The crowd is very diversified due to the simplicity of the tasks, but the payment can attract malicious workers. It is essential to identify these malicious workers in order not to consider their answers. In addition, not all workers have the same qualification for a task, so it might be interesting to give more weight to those with more qualifications. In this paper we propose a new method for characterizing the profile of contributors and aggregating answers using the theory of belief functions to estimate uncertain and imprecise answers. In order to evaluate the contributor profile we consider both his qualification for the task and his behaviour during its achievement thanks to his reflection.

In pattern classification problem, different classifiers learnt using different training data can provide more or less complementary knowledge, and the combination of classifiers is expected to improve the classification accuracy. Evidential reasoning (ER) provides an efficient framework to represent and combine the imprecise and uncertain informations. In this paper, we want to focus on the weighted combination of classifiers based on ER. Because each classifier may have different performance on the given dataset, the classifiers to combine are considered with different weights. A new weighted classifier combination method is proposed based on ER to enhance the classification accuracy. The optimal weighting factors of classifiers are obtained by minimizing the distances between fusion results obtained by Dempster's rule and the target output in training data space to fully take advantage of the complementarity of the classifiers. A confusion matrix is additionally introduced to characterize the probability of the object belonging to one class but classified to another class by the fusion result. This matrix is also optimized using training data jointly with classifier weight, and it is used to modify the fusion result to make it as close as possible to truth. Moreover, the training patterns are considered with different weights for the parameter optimization in classifier fusion, and the patterns hard to classify are committed with bigger weight than the ones easy to deal with. The pattern weight and the other parameters (i.e., classifier weight and confusion matrix) are iteratively optimized for obtaining the highest classification accuracy. A cautious decision making strategy is introduced to reduce the errors, and the pattern hard to classify will be cautiously committed to a set of classes, because the partial imprecision of decision is considered better than error in certain case. The effectiveness of the proposed method is demonstrated with various real datasets from UCI repository, and its performances are compared with those of other classical 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.

Detection of surface water in natural environment via multi-spectral imagery has been widely utilized in many fields, such land cover identification. However, due to the similarity of the spectra of water bodies, built-up areas, approaches based on high-resolution satellites sometimes confuse these features. A popular direction to detect water is spectral index, often requiring the ground truth to find appropriate thresholds manually. As for traditional machine learning methods, they identify water merely via differences of spectra of various land covers, without taking specific properties of spectral reflection into account. In this paper, we propose an automatic approach to detect water bodies based on Dempster-Shafer theory, combining supervised learning with specific property of water in spectral band in a fully unsupervised context. The benefits of our approach are twofold. On the one hand, it performs well in mapping principle water bodies, including little streams and branches. On the other hand, it labels all objects usually confused with water as `ignorance', including half-dry watery areas, built-up areas and semi-transparent clouds and shadows. `Ignorance' indicates not only limitations of the spectral properties of water and supervised learning itself but insufficiency of information from multi-spectral bands as well, providing valuable information for further land cover classification.

Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences over certain alternatives under uncertainty, to get a collective representative opinion of the whole community, a preference fusion process is required. The aim of this work is to propose a preference fusion method that copes with uncertainty and escape from the Condorcet paradox. To model preferences under uncertainty, we propose to develop a model of preferences based on belief function theory that accurately describes and captures the uncertainty associated with individual or collective preferences. This work improves and extends the previous results. This work improves and extends the contribution presented in a previous work. The benefits of our contribution are twofold. On the one hand, we propose a qualitative and expressive preference modeling strategy based on belief-function theory which scales better with the number of sources. On the other hand, we propose an incremental distance-based algorithm (using Jousselme distance) for the construction of the collective preference order to avoid the Condorcet Paradox.

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.

Online Question Answering Communities (Q& A C) provide a valuable amount of information in several topics. The major challenge with Q& A C is the detection of the authoritative users. When manipulating real world data, we have to deal with imperfections and uncertainty that can occur. In this paper, we propose a belief measure of expertise allowing us to detect users with the highest degree of expertise based on their attributes. Experiments on a dataset from a large online Q&A Community prove that the proposed model can be used to improve the identification of most expert users.

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.

The web plays an important role in people's social lives since the emergence of Web 2.0. It facilitates the interaction between users, gives them the possibility to freely interact, share and collaborate through social networks, online community forums, blogs, wikis and other online collaborative media. However, an other side of the web is negatively taken such as posting inflammatory messages. Thus, when dealing with the online community forums, the managers seek to always enhance the performance of such platforms. In fact, to keep the serenity and prohibit the disturbance of the normal atmosphere, managers always try to novice users against these malicious persons by posting such message (DO NOT FEED TROLLS). But, this kind of warning is not enough to reduce this phenomenon. In this context we propose a new approach for detecting malicious people also called 'Trolls' in order to allow community managers to take their ability to post online. To be more realistic, our proposal is defined within an uncertain framework. Based on the assumption consisting on the trolls' integration in the successful discussion threads, we try to detect the presence of such malicious users. Indeed, this method is based on a conflict measure of the belief function theory applied between the different messages of the thread. In order to show the feasibility and the result of our approach, we test it in different simulated data.

In this contribution, an accurate description of the ocean backscatter from a probability density function is proposed. The Elfouhaily spectrum has been used to generate a realistic sea surface. The scattering field will be computed by using the Physical Optics (PO). The K distribution has been already used to characterize the Radar Cross Section (RCS) of the sea surface. However, the probability density function of the RCS can have heavy tails. Consequently, we use the α-stable distributions which can take care the property of heavy tails. The probability density function is estimated with a least squared method. We finally compare the results obtained with each model by using the Kolmogorov-Smirnov test from several random surfaces and a statistical study is made by giving a boxplot of the estimated parameters of the α-stable distribution.

We present and discuss a mixed conjunctive and disjunctive rule, a generalization of conflict repartition rules, and a combination of these two rules. In the belief functions theory one of the major problem is the conflict repartition enlightened by the famous Zadeh's example. To date, many combination rules have been proposed in order to solve a solution to this problem. Moreover, it can be important to consider the specificity of the responses of the experts. Since few year some unification rules are proposed. We have shown in our previous works the interest of the proportional conflict redistribution rule. We propose here a mixed combination rule following the proportional conflict redistribution rule modified by a discounting procedure. This rule generalizes many combination rules.

The Kelvin wake of a ship is directly linked to the ship's speed, heading and hull shape. This wake can be visible in high resolution synthetic aperture radar images or optical images. Whenever it is possible, analyzing it can provide elements to identify the ship and track its course. We propose a strategy based on the generalized Radon Transform and the Stochastic Matched Filtering where the locus of the wake signature in the 2D spectrum of the image is to be detected.

We describe in detail the theoretical and practical implementation aspects of a simulation for marine radars which can, in particular, be used in multistatic configurations. Since the simulator is intended to deliver pseudoraw signals, it can be used later as a tool to benchmark and improve postprocessing algorithms such as bistatic synthetic aperture radar focusing algorithms and ship wake detection algorithms. The work is divided into two parts. This paper reviews and recalls theoretical prerequisites necessary in implementing such a simulator. Included are the full derivation of the bistatic radar equation from the transmitter to the receiver, accounting also for the transmit-receive time, a description of the sea state phenomenology, a review of the theory of electromagnetic scattering from the sea surface, and the presentation and validation of the method used in the simulation. A companion paper discusses the practical implementation aspects of the simulator as well as an analysis of our results.

We present a bistatic, polarimetric, and real aperture marine radar simulator (MaRS) producing pseudoraw radar signals. The simulation takes the main elements of the environment into account (sea temperature, salinity, and wind speed). Realistic sea surfaces are generated using a two-scale model on a semideterministic basis to incorporate the presence of ship wakes. Then, the radar acquisition chain (antennas, modulation, and polarization) is modeled, as well as the movements of the sensors, on which uncertainties can be introduced, and ship wakes. The pseudoraw temporal signals delivered by MaRS are further processed using, for instance, bistatic synthetic aperture beamforming. The scene itself represents the sea surface as well as ship wakes. The main points covered here are the scene discretization, the ship wake modeling, and the computational cost aspects. We also present images simulated in various monostatic and bistatic configurations and discuss the results. This paper follows its companion paper, where much of the theory used here is recalled and developed in detail. a bistatic, polarimetric, and real aperture marine radar simulator (MaRS) producing pseudoraw radar signals. The simulation takes the main elements of the environment into account (sea temperature, salinity, and wind speed). Realistic sea surfaces are generated using a two-scale model on a semideterministic basis to incorporate the presence of ship wakes. Then, the radar acquisition chain (antennas, modulation, and polarization) is modeled, as well as the movements of the sensors, on which uncertainties can be introduced, and ship wakes. The pseudoraw temporal signals delivered by MaRS are further processed using, for instance, bistatic synthetic aperture beamforming. The scene itself represents the sea surface as well as ship wakes. The main points covered here are the scene discretization, the ship wake modeling, and the computational cost aspects. We also present images simulated in various monostatic and bistatic configurations and discuss the results. This paper follows its companion paper, where much of the theory used here is recalled and developed in detail.

We present in this article a new evaluation method for classification and segmentation of textured images in uncertain environments. In uncertain environments, real classes and boundaries are known with only a partial certainty given by the experts. Most of the time, in many presented papers, only classification or only segmentation are considered and evaluated. Here, we propose to take into account both the classification and segmentation results according to the certainty given by the experts. We present the results of this method on a fusion of classifiers of sonar images for a seabed characterization

Distances between fusion operators are measured using a class of random belief functions. With similarity analysis, the structure of this family is extracted, for two and three information sources. The conjunctive operator, quick and associative but very isolated on a large discernment space, and the arithmetic mean are identified as outliers, while the hybrid method and six proportional conflict-redistributing rules (PCR) form a continuum. The hybrid method is showed as being central for the family of fusion methods. All the fusion operators tested with random belief functions are validated on the fusion of radar data classifiers, and show the interest of some new PCR methods

In adverse conditions, the speech recognition performances decrease in part due to imperfect speech/non-speech detection. In this paper, a new combination of voicing parameter and energy for speech/non-speech detection is described. This combination avoids especially the noise detections in real life very noisy environments and provides better performances for continuous speech recognition. This new speech/non-speech detection approach outperforms both noise statistical based [1] and Linear Discriminate Analysis (LDA) based [2] criteria in noisy environments and for continuous speech recognition applications.

In speech recognition, speech/non-speech detection must be robust to,noise. In the paper, a method for speech/non-speech detection using a linear discriminant analysis (LDA) applied to mel frequency cepstrum coefficients (MFCC) is presented. The energy is the most discriminant parameter between noise and speech. But with this single parameter, the speech/non-speech detection system detects too many noise segments. The LDA applied to MFCC and the associated test reduces the detection of noise segments. This new algorithm is compared to the one based on signal to noise ratio (Mauuary and Monne, 1993).

Continuous speech recognition applications need precise detection because the number of words to recognize is unknown and vocabulary words can be short. The speech/non-speech detection must be robust to the boundary precision. In this work, a new approach to evaluate detection algorithm for continuous speech recognition is presented. The speech/non-speech detection using energy parameter combined with a Linear Discriminant Analysis (LDA) applied to Mel Frequency Cepstrum Coefficients (MFCC) is compared to the algorithm based on signal to noise ratio (SNR). The LDA applied to MFCC for speech/non-speech detection improves recognition performance in noisy environment and for continuous speech recognition applications.