Adjusting the outputs of a classifier to new a priori probabilities may significantly improve classification accuracy: Evidence from a multi-class problem in remote sensing

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Any reasonable cost function can be used for a posteriori probability approximation.

In this paper, we provide a straightforward proof of an important, but nevertheless little known, result obtained by Lindley in the framework of subjective probability theory. This result, once interpreted in the machine learning/pattern recognition context, puts new light on the probabilistic interpretation of the output of a trained classifier. A learning machine, or more generally a model, is usually trained by minimizing a criterion-the expectation of the cost function-measuring the discrepancy between the model output and the desired output. In this letter, we first show that, for the binary classification case, training the model with any "reasonable cost function" can lead to Bayesian a posteriori probability estimation. Indeed, after having trained the model by minimizing the criterion, there always exists a computable transformation that maps the output of the model to the Bayesian a posteriori probability of the class membership given the input. Then, necessary conditions allowing the computation of the transformation mapping the outputs of the model to the a posteriori probabilities are derived for the multioutput case. Finally, these theoretical results are illustrated through some simulation examples involving various cost functions.Journal Articleinfo:eu-repo/semantics/publishe

Mixing Bagging and Multiple Feature Subsets to Improve Classification Accuracy of Decision Tree Combination

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Different ways of weakening decision trees and their impact on classification accuracy of DT combination

Recent classifier combination frameworks have proposed several ways of weakening a learning set and have shown that these weakening methods improve prediction accuracy. In the present paper we focus on learning set sampling (Breiman's bagging) and random feature subset selections (Bay's Multiple Feature Subsets). We present a combination scheme labeled 'Bagfs', in which new learning sets are generated on the basis of both bootstrap replicates and selected feature subsets. The performances of the three methods (Bagging, MFS and Bagfs) are assessed by means of a decision-tree inducer (C4.5) and a majority voting rule. In addition, we also study whether the way in which weak classifiers are created has a significant influence on the performance of their combination. To answer this question, we undertook the strict application of the Cochran Q test. This test enabled us to compare the three weakening methods together on a given database, and to conclude whether or not these methods differ significantly. We also used the McNemar test to compare algorithms pair by pair. The first results, obtained on 14 conventional databases, show that on average, Bagfs exhibits the best agreement between prediction and supervision. The Cochran Q test indicated that the weak classifiers so created significantly influenced combination performance in the case of at least 4 of the 14 databases analyzed. © Springer-Verlag Berlin Heidelberg 2000.SCOPUS: cp.kinfo:eu-repo/semantics/publishe

Combining Different Methods and Numbers of Weak Decision Trees

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Limiting the Number of Trees in Random Forests

Abstract. The aim of this paper is to propose a simple procedure that aprioridetermines a minimum number of classifiers to combine in order to obtain a prediction accuracy level similar to the one obtained with the combination of larger ensembles. The procedure is based on the McNemar non-parametric test of significance. Knowing a priori the minimum size of the classifier ensemble giving the best prediction accuracy, constitutes a gain for time and memory costs especially for huge data bases and real-time applications. Here we applied this procedure to four multiple classifier systems with C4.5 decision tree (Breiman’s Bagging, Ho’s Random subspaces, their combination we labeled ‘Bagfs’, and Breiman’s Random forests) and five large benchmark data bases. It is worth noticing that the proposed procedure may easily be extended to other base learning algorithms than a decision tree as well. The experimental results showed that it is possible to limit significantly the number of trees. We also showed that the minimum number of trees required for obtaining the best prediction accuracy may vary from one classifier combination method to another. 2 Patrice Latinne et al

Remote Sensing Classification of Spectral, Spatial and Contextual Data Using Multiple Classifier Systems

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Assembly planning with an ordering genetic algorithm

The goal of assembly planning consists in generating feasible sequences to assemble a product and selecting an efficient assembly sequence from amongst these. This paper describes an original ordering genetic algorithm (OGA) developed to solve this problem. The developed approach permits the generation of assembly trees for a mechanical product. The algorithm is based on three main ideas. First, a mapping transforms any studied assembly plan into a valid one using 'precedence values' changing through the sequence, so that an invalid sequence will never be proposed. Secondly, to identify subsets, trace is kept all along the sequence of the components membership to a set of parts. Finally, the individuals of the OGA are compared with each other using a multi-criteria decision aided method called PROMETHEE II. The use of this method avoids aggregating several technical criteria into a unique fitness value. The proposed algorithm, illustrated through the simple example of a mouse device, has been applied on an industrial signalling relay made of 34 parts.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

An ordering genetic algorithm for assembly planning

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