A fuzzy consensus aggregation operator

Abstract An aggregation operator of quantitative opinions about the acceptance or rejection of a certain alternative is proposed. The main idea is to include a degree of consensus between the experts in computing the final value. We aim at strengthening the acceptance or rejection rate if the experts agree in their assessments. The proposed operator is directly applicable to the two-level classification paradigm where a pool of classifiers is used to infer the decision. The operator allows us to form a complex classification boundary in the space of experts' (classifiers') decisions expressed in terms of degrees of membership. The connective can easily be extended to define a classifier with a "refuse-to-decide" option

Context-dependent fusion with application to landmine detection.

Traditional machine learning and pattern recognition systems use a feature descriptor to describe the sensor data and a particular classifier (also called expert or learner ) to determine the true class of a given pattern. However, for complex detection and classification problems, involving data with large intra-class variations and noisy inputs, no single source of information can provide a satisfactory solution. As a result, combination of multiple classifiers is playing an increasing role in solving these complex pattern recognition problems, and has proven to be viable alternative to using a single classifier. In this thesis we introduce a new Context-Dependent Fusion (CDF) approach, We use this method to fuse multiple algorithms which use different types of features and different classification methods on multiple sensor data. The proposed approach is motivated by the observation that there is no single algorithm that can consistently outperform all other algorithms. In fact, the relative performance of different algorithms can vary significantly depending on several factions such as extracted features, and characteristics of the target class. The CDF method is a local approach that adapts the fusion method to different regions of the feature space. The goal is to take advantages of the strengths of few algorithms in different regions of the feature space without being affected by the weaknesses of the other algorithms and also avoiding the loss of potentially valuable information provided by few weak classifiers by considering their output as well. The proposed fusion has three main interacting components. The first component, called Context Extraction, partitions the composite feature space into groups of similar signatures, or contexts. Then, the second component assigns an aggregation weight to each detector\u27s decision in each context based on its relative performance within the context. The third component combines the multiple decisions, using the learned weights, to make a final decision. For Context Extraction component, a novel algorithm that performs clustering and feature discrimination is used to cluster the composite feature space and identify the relevant features for each cluster. For the fusion component, six different methods were proposed and investigated. The proposed approached were applied to the problem of landmine detection. Detection and removal of landmines is a serious problem affecting civilians and soldiers worldwide. Several detection algorithms on landmine have been proposed. Extensive testing of these methods has shown that the relative performance of different detectors can vary significantly depending on the mine type, geographical site, soil and weather conditions, and burial depth, etc. Therefore, multi-algorithm, and multi-sensor fusion is a critical component in land mine detection. Results on large and diverse real data collections show that the proposed method can identify meaningful and coherent clusters and that different expert algorithms can be identified for the different contexts. Our experiments have also indicated that the context-dependent fusion outperforms all individual detectors and several global fusion methods

A generic framework for context-dependent fusion with application to landmine detection.

For complex detection and classification problems, involving data with large intra-class variations and noisy inputs, no single source of information can provide a satisfactory solution. As a result, combination of multiple classifiers is playing an increasing role in solving these complex pattern recognition problems, and has proven to be a viable alternative to using a single classifier. Over the past few years, a variety of schemes have been proposed for combining multiple classifiers. Most of these were global as they assign a degree of worthiness to each classifier, that is averaged over the entire training data. This may not be the optimal way to combine the different experts since the behavior of each one may not be uniform over the different regions of the feature space. To overcome this issue, few local methods have been proposed in the last few years. Local fusion methods aim to adapt the classifiers\u27 worthiness to different regions of the feature space. First, they partition the input samples. Then, they identify the best classifier for each partition and designate it as the expert for that partition. Unfortunately, current local methods are either computationally expensive and/or perform these two tasks independently of each other. However, feature space partition and algorithm selection are not independent and their optimization should be simultaneous. In this dissertation, we introduce a new local fusion approach, called Context Extraction for Local Fusion (CELF). CELF was designed to adapt the fusion to different regions of the feature space. It takes advantage of the strength of the different experts and overcome their limitations. First, we describe the baseline CELF algorithm. We formulate a novel objective function that combines context identification and multi-algorithm fusion criteria into a joint objective function. The context identification component thrives to partition the input feature space into different clusters (called contexts), while the fusion component thrives to learn the optimal fusion parameters within each cluster. Second, we propose several variations of CELF to deal with different applications scenario. In particular, we propose an extension that includes a feature discrimination component (CELF-FD). This version is advantageous when dealing with high dimensional feature spaces and/or when the number of features extracted by the individual algorithms varies significantly. CELF-CA is another extension of CELF that adds a regularization term to the objective function to introduce competition among the clusters and to find the optimal number of clusters in an unsupervised way. CELF-CA starts by partitioning the data into a large number of small clusters. As the algorithm progresses, adjacent clusters compete for data points, and clusters that lose the competition gradually become depleted and vanish. Third, we propose CELF-M that generalizes CELF to support multiple classes data sets. The baseline CELF and its extensions were formulated to use linear aggregation to combine the output of the different algorithms within each context. For some applications, this can be too restrictive and non-linear fusion may be needed. To address this potential drawback, we propose two other variations of CELF that use non-linear aggregation. The first one is based on Neural Networks (CELF-NN) and the second one is based on Fuzzy Integrals (CELF-FI). The latter one has the desirable property of assigning weights to subsets of classifiers to take into account the interaction between them. To test a new signature using CELF (or its variants), each algorithm would extract its set of features and assigns a confidence value. Then, the features are used to identify the best context, and the fusion parameters of this context are used to fuse the individual confidence values. For each variation of CELF, we formulate an objective function, derive the necessary conditions to optimize it, and construct an iterative algorithm. Then we use examples to illustrate the behavior of the algorithm, compare it to global fusion, and highlight its advantages. We apply our proposed fusion methods to the problem of landmine detection. We use data collected using Ground Penetration Radar (GPR) and Wideband Electro -Magnetic Induction (WEMI) sensors. We show that CELF (and its variants) can identify meaningful and coherent contexts (e.g. mines of same type, mines buried at the same site, etc.) and that different expert algorithms can be identified for the different contexts. In addition to the land mine detection application, we apply our approaches to semantic video indexing, image database categorization, and phoneme recognition. In all applications, we compare the performance of CELF with standard fusion methods, and show that our approach outperforms all these methods