Benjamin Quost

Classifier fusion in the Dempster--Shafer framework using optimized t-norm based combination rules

When combining classifiers in the Dempster-Shafer framework, Dempsters rule is generally used. However, this rule assumes the classifiers to be independent. This paper investigates the use of other operators for combining non independent classifiers, including the cautious rule and, more generally, t-norm based rules with behavior ranging between Dempsters rule and the cautious rule. Two strategies are investigated for learning an optimal combination scheme, based on a parameterized family of t-norms. The first one learns a single rule by minimizing an error criterion. The second strategy is a two-step procedure, in which groups of classifiers with similar outputs are first identified using a clustering algorithm. Then, within- and between-cluster rules are determined by minimizing an error criterion. Experiments with various synthetic and real data sets demonstrate the effectiveness of both the single rule and two-step strategies. Overall, optimizing a single t-norm based rule yields better results than using a fixed rule, including Dempsters rule, and the two-step strategy brings further improvements.

Pairwise classifier combination using belief functions

In the so-called pairwise approach to polychotomous classification, a multiclass problem is solved by combining classifiers trained to discriminate between each pair of classes. In this paper, this approach is revisited in the framework of the Dempster-Shafer theory of belief functions, a non-probabilistic framework for quantifying and manipulating partial knowledge. It is proposed to interpret the output of each pairwise classifiers by a conditional belief function. The problem of classifier combination then amounts to computing the non-conditional belief function which is the most consistent, according to some criterion, with the conditional belief functions provided by the classifiers. Experiments with various datasets demonstrate the good performances of this method as compared to previous approaches to the same problem.

CECM: Constrained evidential C-means algorithm

In clustering applications, prior knowledge about cluster membership is sometimes available. To integrate such auxiliary information, constraint-based (or semi-supervised) methods have been proposed in the hard or fuzzy clustering frameworks. This approach is extended to evidential clustering, in which the membership of objects to clusters is described by belief functions. A variant of the Evidential C-means (ECM) algorithm taking into account pairwise constraints is proposed. These constraints are translated into the belief function framework and integrated in the cost function. Experiments with synthetic and real data sets demonstrate the interest of the method. In particular, an application to medical image segmentation is presented.

Contextual discounting of belief functions

The Transferable Belief Model is a general framework for managing imprecise and uncertain information using belief functions. In this framework, the discounting operation allows to combine information provided by a source (in the form of a belief function) with metaknowledge regarding the reliability of that source, to compute a “weakened”, less informative belief function. In this article, an extension of the discounting operation is proposed, allowing to make use of more detailed information regarding the reliability of the source in different contexts, a context being defined as a subset of the frame of discernment. Some properties of this contextual discounting operation are studied, and its relationship with classical discounted is explained.

CEVCLUS: evidential clustering with instance-level constraints for relational data

Recent advances in clustering consider incorporating background knowledge in the partitioning algorithm, using, e.g., pairwise constraints between objects. As a matter of fact, prior information, when available, often makes it possible to better retrieve meaningful clusters in data. Here, this approach is investigated in the framework of belief functions, which allows us to handle the imprecision and the uncertainty of the clustering process. In this context, the EVCLUS algorithm was proposed for partitioning objects described by a dissimilarity matrix. It is extended here so as to take pairwise constraints into account, by adding a term to its objective function. This term corresponds to a penalty term that expresses pairwise constraints in the belief function framework. Various synthetic and real datasets are considered to demonstrate the interest of the proposed method, called CEVCLUS, and two applications are presented. The performances of CEVCLUS are also compared to those of other constrained clustering algorithms.

Learning from data with uncertain labels by boosting credal classifiers

In this article, we investigate supervised learning when training data are associated with uncertain labels. We tackle this problem within the theory of belief functions. Each training pattern xi is thus associated with a basic belief assignment, representing partial knowledge of its actual class. Here, we propose to use the approach known as boosting to solve the classification problem. We propose a variant of the AdaBoost algorithm where the outputs of the classifiers are interpreted as belief functions. During training, our algorithm estimates the reliability of each classifier to identify patterns from the various classes. During test phase, the outputs of the classifiers are first discounted according to these reliabilities, and then combined using a suitable rule. Experiments conducted on classical datasets show that our algorithm is comparable to AdaBoost in accuracy. Processing EEG data with imperfect labels clearly demonstrates the interest of taking into account the reliability of the labelling, and thus the relevance of our approach.

Clustering fuzzy data using the fuzzy EM algorithm

In this article, we address the problem of clustering imprecise data using finite mixtures of Gaussians. We propose to estimate the parameters of the mixture model using the fuzzy EM algorithm. This extension of the EM algorithm allows us to handle imprecise data represented by fuzzy numbers. First, we briefly recall the principle of the fuzzy EM algorithm. Then, we provide the update equations for the parameters of a Gaussian mixture model for fuzzy data. Experiments carried out on synthetic and real data demonstrate the interest of our approach for clustering data that are only imprecisely known.

Clustering and classification of fuzzy data using the fuzzy EM algorithm

In this article, we address the problem of clustering imprecise data using a finite mixture of Gaussians. We propose to estimate the parameters of the model using the fuzzy EM algorithm. This extension of the EM algorithm allows us to handle imprecise data represented by fuzzy numbers. First, we briefly recall the principle of the fuzzy EM algorithm. Then, we provide closed-forms for the parameter estimates in the case of Gaussian fuzzy data. We also describe a Monte-Carlo procedure for estimating the parameter updates in the general case. Experiments carried out on synthetic and real data demonstrate the interest of our approach for taking into account attribute and label uncertainty.

On modeling ego-motion uncertainty for moving object detection from a mobile platform

In this paper, we propose an effective approach for moving object detection based on modeling the ego-motion uncertainty and using a graph-cut based motion segmentation. First, the relative camera pose is estimated by minimizing the sum of reprojection errors and its covariance matrix is calculated using a first-order errors propagation method. Next, a motion likelihood for each pixel is obtained by propagating the uncertainty of the ego-motion to the Residual Image Motion Flow (RIMF). Finally, the motion likelihood and the depth gradient are used in a graph-cut based approach as region and boundary terms respectively, in order to obtain the moving objects segmentation. Experimental results on real-world data show that our approach can detect dynamic objects which move on the epipolar plane or that are partially occluded in complex urban traffic scenes.

Combining binary classifiers with imprecise probabilities

This paper proposes a simple framework to combine binary classifiers whose outputs are imprecise probabilities (or are transformed into some imprecise probabilities, e.g., by using confidence intervals). This combination comes down to solve linear programs describing constraints over events (here, subsets of classes). The number of constraints grows linearly with the number of classifiers, making the proposed framework tractable for problems involving a relatively large number of classes. After detailing the method, we provide some first experimental results illustrating the method interests.