Linear and Order Statistics Combiners for Pattern Classification

Several researchers have experimentally shown that substantial improvements can be obtained in difficult pattern recognition problems by combining or integrating the outputs of multiple classifiers. This chapter provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and order statistics combiners. We first show that to a first order approximation, the error rate obtained over and above the Bayes error rate, is directly proportional to the variance of the actual decision boundaries around the Bayes optimum boundary. Combining classifiers in output space reduces this variance, and hence reduces the "added" error. If N unbiased classifiers are combined by simple averaging, the added error rate can be reduced by a factor of N if the individual errors in approximating the decision boundaries are uncorrelated. Expressions are then derived for linear combiners which are biased or correlated, and the effect of output correlations on ensemble performance is quantified. For order statistics based non-linear combiners, we derive expressions that indicate how much the median, the maximum and in general the ith order statistic can improve classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions, and combining in output space. Experimental results on several public domain data sets are provided to illustrate the benefits of combining and to support the analytical results.Comment: 31 page

Popular Ensemble Methods: An Empirical Study

An ensemble consists of a set of individually trained classifiers (such as neural networks or decision trees) whose predictions are combined when classifying novel instances. Previous research has shown that an ensemble is often more accurate than any of the single classifiers in the ensemble. Bagging (Breiman, 1996c) and Boosting (Freund and Shapire, 1996; Shapire, 1990) are two relatively new but popular methods for producing ensembles. In this paper we evaluate these methods on 23 data sets using both neural networks and decision trees as our classification algorithm. Our results clearly indicate a number of conclusions. First, while Bagging is almost always more accurate than a single classifier, it is sometimes much less accurate than Boosting. On the other hand, Boosting can create ensembles that are less accurate than a single classifier -- especially when using neural networks. Analysis indicates that the performance of the Boosting methods is dependent on the characteristics of the data set being examined. In fact, further results show that Boosting ensembles may overfit noisy data sets, thus decreasing its performance. Finally, consistent with previous studies, our work suggests that most of the gain in an ensemble's performance comes in the first few classifiers combined; however, relatively large gains can be seen up to 25 classifiers when Boosting decision trees

One-Class Classification: Taxonomy of Study and Review of Techniques

One-class classification (OCC) algorithms aim to build classification models when the negative class is either absent, poorly sampled or not well defined. This unique situation constrains the learning of efficient classifiers by defining class boundary just with the knowledge of positive class. The OCC problem has been considered and applied under many research themes, such as outlier/novelty detection and concept learning. In this paper we present a unified view of the general problem of OCC by presenting a taxonomy of study for OCC problems, which is based on the availability of training data, algorithms used and the application domains applied. We further delve into each of the categories of the proposed taxonomy and present a comprehensive literature review of the OCC algorithms, techniques and methodologies with a focus on their significance, limitations and applications. We conclude our paper by discussing some open research problems in the field of OCC and present our vision for future research.Comment: 24 pages + 11 pages of references, 8 figure

Analysis of the Correlation Between Majority Voting Error and the Diversity Measures in Multiple Classifier Systems

Combining classifiers by majority voting (MV) has recently emerged as an effective way of improving performance of individual classifiers. However, the usefulness of applying MV is not always observed and is subject to distribution of classification outputs in a multiple classifier system (MCS). Evaluation of MV errors (MVE) for all combinations of classifiers in MCS is a complex process of exponential complexity. Reduction of this complexity can be achieved provided the explicit relationship between MVE and any other less complex function operating on classifier outputs is found. Diversity measures operating on binary classification outputs (correct/incorrect) are studied in this paper as potential candidates for such functions. Their correlation with MVE, interpreted as the quality of a measure, is thoroughly investigated using artificial and real-world datasets. Moreover, we propose new diversity measure efficiently exploiting information coming from the whole MCS, rather than its part, for which it is applied

Combining Parametric and Non-parametric Algorithms for a Partially Unsupervised Classification of Multitemporal Remote-Sensing Images

In this paper, we propose a classification system based on a multiple-classifier architecture, which is aimed at updating land-cover maps by using multisensor and/or multisource remote-sensing images. The proposed system is composed of an ensemble of classifiers that, once trained in a supervised way on a specific image of a given area, can be retrained in an unsupervised way to classify a new image of the considered site. In this context, two techniques are presented for the unsupervised updating of the parameters of a maximum-likelihood (ML) classifier and a radial basis function (RBF) neural-network classifier, on the basis of the distribution of the new image to be classified. Experimental results carried out on a multitemporal and multisource remote-sensing data set confirm the effectiveness of the proposed system

A Multiple Cascade-Classifier System for a Robust and Partially Unsupervised Updating of Land-Cover Maps

A system for a regular updating of land-cover maps is proposed that is based on the use of multitemporal remote-sensing images. Such a system is able to face the updating problem under the realistic but critical constraint that, for the image to be classified (i.e., the most recent of the considered multitemporal data set), no ground truth information is available. The system is composed of an ensemble of partially unsupervised classifiers integrated in a multiple classifier architecture. Each classifier of the ensemble exhibits the following novel peculiarities: i) it is developed in the framework of the cascade-classification approach to exploit the temporal correlation existing between images acquired at different times in the considered area; ii) it is based on a partially unsupervised methodology capable to accomplish the classification process under the aforementioned critical constraint. Both a parametric maximum-likelihood classification approach and a non-parametric radial basis function (RBF) neural-network classification approach are used as basic methods for the development of partially unsupervised cascade classifiers. In addition, in order to generate an effective ensemble of classification algorithms, hybrid maximum-likelihood and RBF neural network cascade classifiers are defined by exploiting the peculiarities of the cascade-classification methodology. The results yielded by the different classifiers are combined by using standard unsupervised combination strategies. This allows the definition of a robust and accurate partially unsupervised classification system capable of analyzing a wide typology of remote-sensing data (e.g., images acquired by passive sensors, SAR images, multisensor and multisource data). Experimental results obtained on a real multitemporal and multisource data set confirm the effectiveness of the proposed system