In multimodal learning, multimodal coordinated representation is an important yet challenging issue, which establishes the interaction between different modalities to describe multimodal data more effectively. Existing coordinated representation methods are implemented in the deep feature space (or encoding space) of each modality. In this paper, based on the framework of evidence theory, we propose a novel coordinated representation method, where multimodal data is described as the basic belief assignment (BBA), and coordinated learning is implemented in the evidential space (i.e., the BBA-based space). That is, the information interaction between different modalities is implemented at the level of evidence modeling (or uncertainty modeling). To use the intra-class and inter-class difference information of multimodal data, we design an evidential coordinated constraint. Furthermore, to represent each modality clearly, we introduce an ambiguity constraint. Experimental results of multimodal classification show that our proposed method is rational and effective.

Dempster-Shafer evidence theory (DST) is a theoretical framework for uncertainty modeling and reasoning, with modeling the basic belief assignment (BBA) as one of its most crucial and challenging tasks. The prevailing BBA determination methods have their own pros and cons, and the joint use of them is expected to provide a better BBA. To realize an end-to-end BBA modeling without explicitly using various prevailing BBA modeling methods, a learning-based BBA modeling approach with multi-method fusion (LBMMF) is proposed in this paper. Deep learning is used to train a deep network which learns the mapping from the training samples to the comprehensive BBAs obtained by jointly using the prevailing BBA modeling methods as the generalized training labels. Given a test sample, the corresponding BBA can be obtained in an end-to-end manner, which is the output of the trained deep neural network. Experimental results show that to use the BBA obtained by our method can achieve better classification performance.

Background Aware Correlation Filter (BACF) tracker achieves accurate tracking result in visual object tracking by mitigating boundary effects, yet is limited in challenging scenarios especially in viewpoint change and illumination variation, which are frequently encountered in Unmanned Aerial Vehicle (UAV) tracking tasks. To address the shortcomings, we propose a Foreground Aware Correlation Filter with adaptive feature response fusion (FACF). In this paper, we use saliency detection to generate foreground prior knowledge in training phase for suppressing potential noise. Furthermore, recognizing the limitation of BACF, which relies on a single feature, a novel adaptive fusion strategy is designed to fuse multiple feature responses during the detection phase. This strategy aims to enhance the robustness of the tracker. Extensive experiments have been conducted on three challenging benchmarks. The tracking results show that the proposed tracker performs accurate and robust tracking result and satisfies real-time requirement with 48.28fps.

Traditional pattern recognition systems, tasked with categorizing inputs into known classes, often struggle when they encounter samples they haven’t been trained to recognize. This introduces the need for the open set recognition—enhancing models to reject unidentified samples effectively. The Openmax method represents a significant breakthrough in this field by leveraging deep learning to spot and handle these new, unseen classes, broadening the traditional Softmax layer to accommodate an “unknown” class and employing a single threshold to separate the known from the unknown. However, the reliance of the original Openmax method on a single threshold may result in incorrect classifications if the parameters are not selected appropriately. To address this, we introduce a dual-threshold fusion mechanism based on Dempster-Shafer evidence theory in this paper. This approach releases the difficulty of finding a precise threshold in the complex and dynamic real-world environments. By integrating deep networks with a novel evidence-based system, the refined approach can bolster the robustness of rejecting undefined classes.

In this paper, we propose a new fusion approach to combine basic belief assignments (BBAs) defined on a dichotomous frame of discernment based on their canonical decomposition. In a companion paper, we have already proved that the canonical decomposition of this type of BBA (called dichotomous BBA) is always possible and unique thanks to the proportional conflict redistribution rule No 5 (PCR5). More precisely, any dichotomous BBA is always the PCR5 combination of two simpler basic belief assignments named respectively the pro-evidence, and the contra-evidence. From this interesting canonical decomposition, we present a new way of combining many dichotomous BBAs and we show that the computational time for fusing these dichotomous BBAs based on their canonical decomposition is quasi-linear with the number of sources to combine, contrary to the direct fusion of the dichotomous BBAs altogether.

In this paper, we propose a new Multi-Criteria Decision-Making method (MCDM) which is rank reversal free. We call it the SPOTIS method standing for Stable Preference Ordering Towards Ideal Solution method. Our method is exempt of rank reversal because the preference ordering established from the score matrix of the MCDM problem under consideration does not require the relative comparisons between alternatives, but only comparisons with respect to the ideal solution chosen by the MCDM system designer after transforming the incomplete original MCDM problem into a well-defined one thanks to the specification of the min and max bounds of each criterion involved in the problem.

This paper presents two new theoretical contributions for reasoning under uncertainty: 1) the Total Belief Theorem (TBT) which is a direct generalization of the Total Probability Theorem, and 2) the Generalized Bayes' Theorem drawn from TBT. A constructive justification of Fagin-Halpern belief conditioning formulas proposed in the nineties is also given. We also show how our new approach and formulas work through simple illustrative examples.

In this paper the notion of (probabilistic) independence of two events defined classically in the theory of probability is extended in the theory of belief functions as the credibilistic independence of two propositions. This new notion of independence which is compatible with the probabilistic independence as soon as the belief function is Bayesian, is defined from Fagin-Halpern belief conditioning formulas drawn from Total Belief Theorem (TBT) when working in the framework of belief functions to model epistemic uncertainties. We give some illustrative examples of this notion at the end of the paper.

Evidence combination is typical uncertainty reasoning or information fusion in the theory of belief functions, which combines bodies of evidence stemming from different information sources. In traditional applications of evidence combination (e.g., pattern classification), given a sample, the basic belief assignments (BBAs) of different information sources are generated first, and then they are combined by a rule, e.g., Dempster's rule. In this paper, we propose a new modelized method for evidence combination. By just inputting the sample into the learned model of combination, a “combined” BBA is obtained. That is, it does not need to generate multiple BBAs for each sample for the combination. In our proposed modelized combination, we can generate different combination models with different combination rules. Experimental results and related analyses validate the rationality and efficiency of our proposed method.

Image segmentation is one of the most important tasks in image processing and recognition. Image segmentation based on two-dimensional histogram considers not only the target pixel information but also its neighborhood information. It segments the image according to the calculated threshold, which is a hard decision method actually. However, there is uncertainty when labeling the pixels around the threshold. In this paper, we propose a new binary segmentation method for color image based on information fusion. We use two thresholds to model the uncertainty and use Cautious OWA with evidential reasoning (COWA-ER) to implement the fusion-based color image segmentation. Experimental results show that the proposed method achieves better performance compared with the traditional two-dimensional histogram method.

In this paper, new theoretical results for reasoning with belief functions are obtained and discussed. After a judicious decomposition of the set of focal elements of a belief function, we establish the total belief theorem (TBT). which is the direct generalization of the total probability theorem when working in the framework of belief functions. The TBT is also generalized for dealing with different frames of discernments thanks to Cartesian product space. From TBT, we can derive and define formally the expressions of conditional belief functions, which are consistent with the bounds of imprecise conditional probability. This work provides a direct establishment and solid justification of Fagin–Halpern belief conditioning formulas. The well-known Bayes' theorem of probability theory is then generalized in the framework of belief functions, and we illustrate it with an example at the end of this paper.

In 2016 we developed a new approach for Multi-Criteria Decision-Making (MCDM) inspired by the technique for order preference by similarity to ideal solution (TOPSIS) and based on belief functions (BF). Our BF-TOPSIS (Belief Function based TOPSIS) approach assumes that the input score of each hypothesis for each criterion was a real precise number which is a quite restrictive assumption. In this paper we extend our BF-TOPSIS to deal with imprecise score values (intervals of real numbers) and we call it Imp-BF-TOPSIS. This new approach follows main ideas of BF-TOPSIS but extends its applicability for more realistic MCDM problems where the scores are given with a finite precision. Imp-BF-TOPSIS is based on Interval Arithmetic (IA), new probabilistic order relations between intervals and belief functions. We also present results of Imp-BF-TOPSIS for simple examples for illustrating its effectiveness.

Dempster-Shafer theory (DST) is an important theory for information fusion. However, in DST how to determinate the basic belief assignment (BBA) is still an open issue. The interval number based BBA determination method is simple and effective, where the features of different classes' samples are modeled using the interval numbers, i.e., an interval number model is constructed for each focal element. Then, the distances of interval numbers are used for measuring the similarity degrees between the testing sample and each focal element, and the similarity degrees are used for determinating the BBA. The definition of interval numbers' distance is crucial for the effectiveness of the interval number based BBA determination methods. In this paper, we use different interval numbers' distances for determinating BBAs. By using the artificial data set and the Iris date set of open UCI data base, respectively, we compare and analyze the determination of BBAs with different distances.

Edge detection is one of the most important tasks in image processing and pattern recognition. Edge detector with multiple color channels can provide more edge information. However, the uncertainty occurring with the edge detection in each single channel and the discordance existing in the fusion of multiple channels edge detectors make the detection difficult. In this paper, we propose a new edge detection method in color images based on information fusion. We show that obtaining final edge through fusing the edge information in each channel is a challenging problem to make decision in the framework of Multi-Criteria decision making (MCDM). In this work, we propose to detect edges in color images using Cautious OWA with evidential reasoning (COWA-ER) and Fuzzy-Cautious OWA with evidential reasoning (FCOWA-ER) to handle the uncertainty and discordance. Experimental results show that the proposed approaches achieve better edge detection performance compared with the original edge detector.

Topics on clustering ensemble have attracted much attention in recent years. In many clustering ensemble frameworks, the simple partitional clustering methods, e.g., the most famous κ-means, are used as the ensemble's member “clusterers”, due to their low computational complexity. These ensemble approaches extend the scope of application of individual clustering algorithms, and improve the robustness of the final clustering results. However, by applying the ensemble approaches, many problems of clustering algorithms still cannot be settled. For example, the clustering ensemble based on κ-means might still not able to effectively deal with the clustering tasks with arbitrary clusters' shapes or imbalanced clusters's sizes. This problem is caused by the geometric-distance-based closeness measures (e.g. the Euclidean distance) used in the member clusterers. In this paper, we propose a multi-layer clustering ensemble framework where different kinds of closeness measures are used for different data points in one clustering task. In this framework, the data points which are hard to deal with (called the “bad data points”, e.g., the data points in the “overlapping” region of two non-spherical shaped clusters) are identified based on the outputs of a group of member clusterers, and the closeness between these bad data points will be calculated with a non-geometric-distance-based closeness measure called C M NC. In this way, the new framework can counter-act the drawbacks of the traditional ensemble approaches based on partitional clustering algorithms, and at the same time, it partially retains their merits of low computational cost.

Support vector machine (SVM) is a popular machine learning method and has been widely applied in many real-world applications. Since SVM is sensitive to noises, fuzzy SVM (FSVM) has been proposed to relieve the over-fitting problem caused by noises through assigning a fuzzy membership to each sample. Then, different samples make different contributions to the learning of classification hyperplane. However, standard fuzzy SVM only concerns on the information within the classes. It can't make full use of the prior information of the samples. Therefore, we propose a new method called weighted SVM based on the theory of belief functions (BFW-SVM). The main idea is to associate the samples with corresponding weights before training according to the theory of belief functions, which can describe the information more detailed. Experiments on benchmark datasets show that our proposed BFW-SVM can handle the classification problems with noises and outliers more effectively.

Ensemble clustering consists in combining multiple clustering solutions into a single one, called the consensus, which can produce a more accurate and robust clustering of the data. In this paper, we attempt to implement ensemble clustering using Dempster-Shafer evidence theory. Individual clustering solutions are obtained using evidence theory and a novel diversity measure is proposed using the distance of evidence for selecting complementary individual solutions. After establishing the correspondence among different clustering solutions' labels, the consensus clustering solution can be obtained using evidence combination. Experimental results and related analyses show that our proposed approach can effectively implement the ensemble clustering.

A practical method for full-dimension attitude determination based on the combination of two-antenna global positioning system (GPS) and strapdown inertial navigation system (SINS) is presented. In view of the fact that two-antenna GPS can only provide two attitude angles using carrier phase difference measurements, not all of the SINS attitude errors can be directly corrected by the integrated navigation system. The proposed method makes use of the coordinate transformation about the attitude and the related measurements provided by two-antenna GPS and SINS to solve the full-dimension attitude determination problem through information fusion. The simulation results indicate that the proposed method can effectively determine the required attitude in real time.

Dempster-Shafer evidence theory (DST) is a theoretical framework for uncertainty modeling and reasoning. The determination of basic belief assignment (BBA) is crucial in DST, however, there is no general theoretical method for BBA determination. In this paper, a method of generating BBA using fuzzy numbers is proposed. First, the training data are modeled as fuzzy numbers. Then, the dissimilarities between each test sample and the training data are measured by the distance between fuzzy numbers. In the final, the BBAs are generated from the normalized dissimilarities. The effectiveness of this method is demonstrated by an application of classification problem. Experimental results show that the proposed method is robust to outliers.