Thierry Denœux

An evidential classifier based on feature selection and two-step classification strategy

In this paper, we investigate ways to learn efficiently from uncertain data using belief functions. In order to extract more knowledge from imperfect and insufficient information and to improve classification accuracy, we propose a supervised learning method composed of a feature selection procedure and a two-step classification strategy. Using training information, the proposed feature selection procedure automatically determines the most informative feature subset by minimizing an objective function. The proposed two-step classification strategy further improves the decision-making accuracy by using complementary information obtained during the classification process. The performance of the proposed method was evaluated on various synthetic and real datasets. A comparison with other classification methods is also presented. HighlightsA classifier is based on Belief Functions to tackle uncertain data.The classifier composed by feature selection and a two-step classification.A new combination rule to better represent data uncertainty.A new feature selection is based on minimizing uncertainty with sparse constraint.Two-step classification improving accuracy of decision making.

Resample and combine: an approach to improving uncertainty representation in evidential pattern classification

Abstract Uncertainty representation is a major issue in pattern recognition. In many applications, the outputs of a classifier do not lead directly to a final decision, but are used in combination with other systems, or as input to an interactive decision process. In such contexts, it may be advantageous to resort to rich and flexible formalisms for representing and manipulating uncertain information. This paper addresses the issue of uncertainty representation in pattern classification, in the framework of the Dempster–Shafer theory of evidence. It is shown that the quality and reliability of the outputs of a classifier may be improved using a variant of bagging, a resample-and-combine approach introduced by Breiman in a conventional statistical context. This technique is explained and studied experimentally on simulated data and on a character recognition application. In particular, results show that bagging improves classification accuracy and limits the influence of outliers and ambiguous training patterns.

Selecting radiomic features from FDG-PET images for cancer treatment outcome prediction

As a vital task in cancer therapy, accurately predicting the treatment outcome is valuable for tailoring and adapting a treatment planning. To this end, multi-sources of information (radiomics, clinical characteristics, genomic expressions, etc) gathered before and during treatment are potentially profitable. In this paper, we propose such a prediction system primarily using radiomic features (e.g., texture features) extracted from FDG-PET images. The proposed system includes a feature selection method based on Dempster-Shafer theory, a powerful tool to deal with uncertain and imprecise information. It aims to improve the prediction accuracy, and reduce the imprecision and overlaps between different classes (treatment outcomes) in a selected feature subspace. Considering that training samples are often small-sized and imbalanced in our applications, a data balancing procedure and specified prior knowledge are taken into account to improve the reliability of the selected feature subsets. Finally, the Evidential K-NN (EK-NN) classifier is used with selected features to output prediction results. Our prediction system has been evaluated by synthetic and clinical datasets, consistently showing good performance.

Belief Function Correction Mechanisms

Different operations can be used in the theory of belief functions to correct the information provided by a source, given metaknowledge about that source. Examples of such operations are discounting, de-discounting, extended discounting and contextual discounting. In this article, the links between these operations are explored. New interpretations of these schemes, as well as two families of belief function correction mechanisms are introduced and justified. The first family generalizes previous non-contextual discounting operations, whereas the second generalizes the contextual discounting.

Clustering of proximity data using belief functions

Publisher Summary This chapter presents the novel approach of clustering proximity data, based on Dempster-Shafer (DS) theory of belief functions, which is also referred as the “evidence theory”. Cluster analysis is concerned with methods for finding groups in data, groups (or classes) being defined as subsets of more or less “similar objects.” In this approach, the allocation of objects to classes is performed using the concept of basic belief assignment (bba), whereby a “mass of belief” is assigned to each possible subset of classes.. The classification task is performed in a very natural way, by only imposing that, the more two objects are similar, the more likely they belong to the same cluster. The two most frequent data types are object data, in which each object is described explicitly by a list of attributes, and proximity (or relational) data, in which only pairwise similarities, or dissimilarities are given. The methods of relational clustering model can be classified into three broad categories—hierarchical methods, methods based on the decomposition of fuzzy relations, and methods based on the optimization of an objective function. Experiments on various datasets also have shown the efficiency of this approach.

Classification Trees Based on Belief Functions

Decision tree classifiers are popular classification methods. In this paper, we extend to multi-class problems a decision tree method based on belief functions previously described for two-class problems only. We propose three possible extensions: combining multiple two-class trees together and directly extending the estimation of belief functions within the tree to the multi-class setting. We provide experiment results and compare them to usual decision trees.

Allowing Imprecision in Belief Representation using Fuzzy-Valued Belief Structures

This paper extends the theory of Evidence, by allowing subjective degrees of belief in crisp or fuzzy propositions to be represented in the form of intervals or fuzzy numbers. The usual concepts of credibility, plausibility and combination rules are generalized in this framework.

Evidential Clustering: A Review

In evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibility and rough partitions, which are recovered as special cases. Three algorithms to generate a credal partition are reviewed. Each of these algorithms is shown to implement a decision-directed clustering strategy. Their relative merits are discussed.

Dempster-Shafer Reasoning in Large Partially Ordered Sets: Applications in Machine Learning

The Dempster-Shafer theory of belief functions has proved to be a powerful formalism for uncertain reasoning. However, belief functions on a finite frame of discernment \({\it \Omega}\) are usually defined in the power set 2Ω , resulting in exponential complexity of the operations involved in this framework, such as combination rules. When \({\it \Omega}\) is linearly ordered, a usual trick is to work only with intervals, which drastically reduces the complexity of calculations. In this paper, we show that this trick can be extrapolated to frames endowed with an arbitrary lattice structure, not necessarily a linear order. This principle makes it possible to apply the Dempster-Shafer framework to very large frames such as, for instance, the power set of a finite set \({\it \Omega}\), or the set of partitions of a finite set. Applications to multi-label classification and ensemble clustering are demonstrated.

Beyond Fuzzy, Possibilistic and Rough: An Investigation of Belief Functions in Clustering

In evidential clustering, uncertainty about the assignment of objects to clusters is represented by Dempster-Shafer mass functions. The resulting clustering structure, called a credal partition, is shown to be more general than hard, fuzzy, possibility and rough partitions, which are recovered as special cases. Different algorithms to generate a credal partition are reviewed. We also describe different ways in which a credal partition, such as produced by the EVCLUS or ECM algorithms, can be summarized into any of the simpler clustering structures.