So far few theoretical works investigated the conditions under which specific fusion rules can work well, and a unifying framework for comparing rules of different complexity is clearly beyond the state of the art. A clear theoretical comparison is lacking even if one focuses on specific classes of combiners (e.g., linear combiners). In this paper, we theoretically compare simple and weighted averaging rules for fusion of imbalanced classifiers.

Abstract—Classifier combination holds the potential of improving performance by combining the results of multiple classifers. For domains with very large numbers of classes, such as biometrics, we present an axiomatic framework of desirable mathematical properties for combination functions of rank-based classifiers. This framework represents a continuum of combination rules, including the Borda Count, Logistic Regression, and Highest Rank combination methods as extreme cases [11], [23], [4], [13]. Intuitively, this framework captures how the two complementary concepts of general preference for specific classifiers and the confidence it has in any specific result (as indicated by ranks) can be balanced while maintaining consistent rank interpretation. Mixed Group Ranks (MGR) is a new combination function that balances preference and confidence by generalizing these other functions. We demonstrate that MGR is an effective combination approach by performing multiple experiments on data sets with large numbers of classes and classifiers from the FERET face recognition study. Index Terms—Classification, classifier combination, ensemble methods, sensor fusion, biometrics, face recognition, mixed group ranks, logistic regression, Borda count, highest rank, voting methods. 1

In this paper, we report a theoretical and experimental comparison between two widely used combination rules for classifier fusion: simple average and weighted average of classifiers outputs. We analyse the conditions which affect the difference between the performance of simple and weighted averaging and discuss the relation between these conditions and the concept of classifiers' "imbalance". Experiments aimed at assessing some of the theoretical results for cases where the theoretical assumptions could not be hold are reported.

Abstract — Inner product measures how closely two feature vectors are related. It is an important primitive for many popular data mining tasks, e.g., clustering, classification, correlation computation, and decision tree construction. If the entire data set is available at a single site, then computing the inner product matrix and identifying the top (in terms of magnitude) entries is trivial. However, in many real-world scenarios, data is distributed across many locations and transmitting the data to a central server would be quite communication-intensive and not scalable. This paper presents an approximate local algorithm for identifying top-l inner products among pairs of feature vectors in a large asynchronous distributed environment such as a peer-to-peer (P2P) network. We develop a probabilistic algorithm for this purpose using order statistics and Hoeffding bound. We present experimental results to show the effectiveness and scalability of the algorithm. Finally, we demonstrate an application of this technique for interest-based community formation in a P2P environment. Index Terms — distributed data mining, inner product, peer-topeer network I.

Broad classes of statistical classification algorithms have been developed and applied successfully to a wide range of real world domains. In general, ensuring that the particular classification algorithm matches the properties of the data is crucial in providing results that meet the needs of the particular application domain. One way in which the impact of this algorithm/application match can be alleviated is by using ensembles of classifiers, where a variety of classifiers (either different types of classifiers or different instantiations of the same classifier) are pooled before a final classification decision is made. Intuitively, classifier ensembles allow the different needs of a difficult problem to be handled by classifiers suited to those particular needs. Mathematically, classifier ensembles provide an extra degree of freedom in the classical bias/variance tradeoff, allowing solutions that would be difficult (if not impossible) to reach with only a single classifier. Because of these advantages, classifier ensembles have been applied to many difficult real world problems. In this paper, we survey select applications of ensemble methods to problems that have historically been most representative of the difficulties in classification. In particular, we survey applications of ensemble methods to remote sensing, person recognition, one vs. all recognition, and medicine.

Abstract. Biometric authentication is a process of verifying an identity claim using a person’s behavioural and physiological characteristics. Due to the vulnerability of the system to environmental noise and variation caused by the user, fusion of several biometric-enabled systems is identified as a promising solution. In the literature, various fixed rules (e.g. min, max, median, mean) and trainable classifiers (e.g. linear combination of scores or weighted sum) are used to combine the scores of several base-systems. How exactly do correlation and imbalance nature of base-system performance affect the fixed rules and trainable classifiers? We study these joint aspects using the commonly used error measurement in biometric authentication, namely Equal Error Rate (EER). Similar to several previous studies in the literature, the central assumption used here is that the class-dependent scores of a biometric system are approximately normally distributed. However, different from them, the novelty of this study is to make a direct link between the EER measure and the fusion schemes mentioned. Both synthetic and real experiments (with as many as 256 fusion experiments carried out on the XM2VTS benchmark score-level fusion data sets) verify our proposed theoretical modeling of EER of the two families of combination scheme. In particular, it is found that weighted sum can provide the best generalisation performance when its weights are estimated correctly. It also has the additional advantage that score normalisation prior to fusion is not needed, contrary to the rest of fixed fusion rules. 1

Prediction of landcover types from airborne/spaceborne sensors is an important classification problem in remote sensing. Due to recent advances in sensor technology, it is now possible to acquire hyperspectral data simultaneously in #200 bands, each of which measures the integrated response of a target over a narrow window of the electromagnetic spectrum. This unprecedented spectral resolution can provide vastly improved mapping of several types of landcover and monitoring of ecological changes. However, the increased dimensionality also constitutes a challenge in terms of storage and analysis. This paper presents a Polyline Feature Extraction (PFE) technique that exploits the spectral correlations between certain adjacent bands in hyperspectral data, to reduce dimensionality without sacrificing discrimination power. It uses an interpretable piecewise linear representation of the data that is somewhat robust to environmental changes. Using the Binary Hierarchical Classifier Framework for multi-class problems, PFE's e#ectiveness is demonstrated on two large hyperspectral datasets obtained over the Texas and Florida coasts respectively.

We introduce a multi-stage ensemble framework, Error-Driven Generalist+Expert or Edge, for improved classification on large-scale text categorization problems. Edge first trains a generalist, capable of classifying under all classes, to deliver a reasonably accurate initial category ranking given an instance. Edge then computes a confusion graph for the generalist and allocates the learning resources to train experts on relatively small groups of classes that tend to be systematically confused with one another by the generalist. The experts ’ votes, when invoked on a given instance, yield a reranking of the classes, thereby correcting the errors of the generalist. Our evaluations showcase the improved classification and ranking performance on several large-scale text categorization datasets. Edge is in particular efficient when the underlying learners are efficient. Our study of confusion graphs is also of independent interest.