Preface * Introduction * The Bayes Error * Inequalities and alternatedistance measures * Linear discrimination * Nearest neighbor rules *Consistency * Slow rates of convergence Error estimation * The regularhistogram rule * Kernel rules Consistency of the k-nearest neighborrule * Vapnik-Chervonenkis theory * Combinatorial aspects of Vapnik-Chervonenkis theory * Lower bounds for empirical classifier selection* The maximum likelihood principle * Parametric classification *Generalized linear discrimination * Complexity regularization *Condensed and edited nearest neighbor rules * Tree classifiers * Data-dependent partitioning * Splitting the data * The resubstitutionestimate * Deleted estimates of the error probability * Automatickernel rules * Automatic nearest neighbor rules * Hypercubes anddiscrete spaces * Epsilon entropy and totally bounded sets * Uniformlaws of large numbers * Neural networks * Other error estimates *Feature extraction * Appendix * Notation * References * Index

/pdf/a-probabilistic-theory-of-pattern-recognition-1p19dg485x.pdf

A Probabilistic Theory of Pattern Recognition

The nearest neighbor classifier is one of the most used and well-known techniques for performing recognition tasks. It has also demonstrated itself to be one of the most useful algorithms in data mining in spite of its simplicity. However, the nearest neighbor classifier suffers from several drawbacks such as high storage requirements, low efficiency in classification response, and low noise tolerance. These weaknesses have been the subject of study for many researchers and many solutions have been proposed. Among them, one of the most promising solutions consists of reducing the data used for establishing a classification rule (training data) by means of selecting relevant prototypes. Many prototype selection methods exist in the literature and the research in this area is still advancing. Different properties could be observed in the definition of them, but no formal categorization has been established yet. This paper provides a survey of the prototype selection methods proposed in the literature from a theoretical and empirical point of view. Considering a theoretical point of view, we propose a taxonomy based on the main characteristics presented in prototype selection and we analyze their advantages and drawbacks. Empirically, we conduct an experimental study involving different sizes of data sets for measuring their performance in terms of accuracy, reduction capabilities, and runtime. The results obtained by all the methods studied have been verified by nonparametric statistical tests. Several remarks, guidelines, and recommendations are made for the use of prototype selection for nearest neighbor classification.

/pdf/prototype-selection-for-nearest-neighbor-classification-3c75s4xkiz.pdf

Prototype Selection for Nearest Neighbor Classification: Taxonomy and Empirical Study

The nearest neighbor (NN) technique is very simple, highly efficient and effective in the field of pattern recognition, text categorization, object recognition etc. Its simplicity is its main advantage, but the disadvantages can't be ignored even. The memory requirement and computation complexity also matter. Many techniques are developed to overcome these limitations. NN techniques are broadly classified into structure less and structure based techniques. In this paper, we present the survey of such techniques. Weighted kNN, Model based kNN, Condensed NN, Reduced NN, Generalized NN are structure less techniques whereas k-d tree, ball tree, Principal Axis Tree, Nearest Feature Line, Tunable NN, Orthogonal Search Tree are structure based algorithms developed on the basis of kNN. The structure less method overcome memory limitation and structure based techniques reduce the computational complexity.

pdf/survey-of-nearest-neighbor-techniques-2wgp3sbkgf.pdf

Survey of Nearest Neighbor Techniques

Combination (ensembles) of classifiers is now a well established research line. It has been observed that the predictive accuracy of a combination of independent classifiers excels that of the single best classifier. While ensembles of classifiers have been mostly employed to achieve higher recognition accuracy, this paper focuses on the use of combinations of individual classifiers for handling several problems from the practice in the machine learning, pattern recognition and data mining domains. In particular, the study presented concentrates on managing the imbalanced training sample problem, scaling up some preprocessing algorithms and filtering the training set. Here, all these situations are examined mainly in connection with the nearest neighbour classifier. Experimental results show the potential of multiple classifier systems when applied to those situations.

New Applications of Ensembles of Classifiers

Proportions of the classes for each ensemble member are chosen randomly.Member training data: sub-sample and over-sample through SMOTE.RB-Boost combines Random Balance with AdaBoost.M2.Experiments with 86 data sets demonstrate the advantage of Random Balance. In Machine Learning, a data set is imbalanced when the class proportions are highly skewed. Imbalanced data sets arise routinely in many application domains and pose a challenge to traditional classifiers. We propose a new approach to building ensembles of classifiers for two-class imbalanced data sets, called Random Balance. Each member of the Random Balance ensemble is trained with data sampled from the training set and augmented by artificial instances obtained using SMOTE. The novelty in the approach is that the proportions of the classes for each ensemble member are chosen randomly. The intuition behind the method is that the proposed diversity heuristic will ensure that the ensemble contains classifiers that are specialized for different operating points on the ROC space, thereby leading to larger AUC compared to other ensembles of classifiers. Experiments have been carried out to test the Random Balance approach by itself, and also in combination with standard ensemble methods. As a result, we propose a new ensemble creation method called RB-Boost which combines Random Balance with AdaBoost.M2. This combination involves enforcing random class proportions in addition to instance re-weighting. Experiments with 86 imbalanced data sets from two well known repositories demonstrate the advantage of the Random Balance approach.

Random Balance

A two-stage iterative algorithm for selecting a subset of a training set of samples for use in a condensed nearest neighbor (CNN) decision rule is introduced. The proposed method uses the concept of mutual nearest neighborhood for selecting samples close to the decision line. The efficacy of the algorithm is brought out by means of an example.

/pdf/the-condensed-nearest-neighbor-rule-using-the-concept-of-3g0x0uy3ml.pdf

The condensed nearest neighbor rule using the concept of mutual nearest neighborhood (Corresp.)

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The condensed nearest neighbor rule using the concept of mutual nearest neighborhood (Corresp.)