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67
Bagging Predictors
 Machine Learning
, 1996
"... Bagging predictors is a method for generating multiple versions of a predictor and using these to get an aggregated predictor. The aggregation averages over the versions when predicting a numerical outcome and does a plurality vote when predicting a class. The multiple versions are formed by making ..."
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Cited by 2492 (1 self)
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Bagging predictors is a method for generating multiple versions of a predictor and using these to get an aggregated predictor. The aggregation averages over the versions when predicting a numerical outcome and does a plurality vote when predicting a class. The multiple versions are formed by making bootstrap replicates of the learning set and using these as new learning sets. Tests on real and simulated data sets using classification and regression trees and subset selection in linear regression show that bagging can give substantial gains in accuracy. The vital element is the instability of the prediction method. If perturbing the learning set can cause significant changes in the predictor constructed, then bagging can improve accuracy. 1. Introduction A learning set of L consists of data f(y n ; x n ), n = 1; : : : ; Ng where the y's are either class labels or a numerical response. We have a procedure for using this learning set to form a predictor '(x; L)  if the input is x we ...
The use of the area under the ROC curve in the evaluation of machine learning algorithms
 Pattern Recognition
, 1997
"... AbstractIn this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multilayer Percept ..."
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Cited by 435 (0 self)
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AbstractIn this paper we investigate the use of the area under the receiver operating characteristic (ROC) curve (AUC) as a performance measure for machine learning algorithms. As a case study we evaluate six machine learning algorithms (C4.5, Multiscale Classifier, Perceptron, Multilayer Perceptron, kNearest Neighbours, and a Quadratic Discriminant Function) on six "real world " medical diagnostics data sets. We compare and discuss the use of AUC to the more conventional overall accuracy and find that AUC exhibits a number of desirable properties when compared to overall accuracy: increased sensitivity in Analysis of Variance (ANOVA) tests; a standard error that decreased as both AUC and the number of test samples increased; decision threshold independent; and it is invariant to a priori class probabilities. The paper concludes with the recommendation that AUC be used in preference to overall accuracy for "single number " evaluation of machine
A System for Induction of Oblique Decision Trees
 Journal of Artificial Intelligence Research
, 1994
"... This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hillclimbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a decision tree. Oblique decision tree methods are tuned espe ..."
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Cited by 250 (13 self)
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This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hillclimbing with two forms of randomization to find a good oblique split (in the form of a hyperplane) at each node of a decision tree. Oblique decision tree methods are tuned especially for domains in which the attributes are numeric, although they can be adapted to symbolic or mixed symbolic/numeric attributes. We present extensive empirical studies, using both real and artificial data, that analyze OC1's ability to construct oblique trees that are smaller and more accurate than their axisparallel counterparts. We also examine the benefits of randomization for the construction of oblique decision trees. 1. Introduction Current data collection technology provides a unique challenge and opportunity for automated machine learning techniques. The advent of major scientific projects such as the Human Genome Project, the Hubble Space Telescope, and the human brain mappi...
Linear and Order Statistics Combiners for Pattern Classification
 Combining Artificial Neural Nets
, 1999
"... 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 resul ..."
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Cited by 65 (7 self)
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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 nonlinear 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.
NeuralNetwork Feature Selector
 IEEE Transactions on Neural Networks
, 1997
"... Feature selection is an integral part of most learning algorithms. Due to the existence of irrelevant and redundant attributes, by selecting only the relevant attributes of the data, higher predictive accuracy can be expected from a machine learning method. In this paper, we propose the use of a ..."
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Cited by 56 (3 self)
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Feature selection is an integral part of most learning algorithms. Due to the existence of irrelevant and redundant attributes, by selecting only the relevant attributes of the data, higher predictive accuracy can be expected from a machine learning method. In this paper, we propose the use of a threelayer feedforward neural network to select those input attributes that are most useful for discriminating classes in a given set of input patterns. A network pruning algorithm is the foundation of the proposed algorithm. By adding a penalty term to the error function of the network, redundant network connections can be distinguished from those relevant ones by their small weights when the network training process has been completed. A simple criterion to remove an attribute based on the accuracy rate of the network is developed. The network is retrained after removal of an attribute, and the selection process is repeated until no attribute meets the criterion for removal. Our ...
StatLog: Comparison of Classification Algorithms on Large RealWorld Problems
, 1995
"... This paper describes work in the StatLog project comparing classification algorithms on large realworld problems. The algorithms compared were from: symbolic learning (CART, C4.5, NewID, AC 2 , ITrule, Cal5, CN2), statistics (Naive Bayes, knearest neighbor, kernel density, linear discriminant, qua ..."
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Cited by 50 (0 self)
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This paper describes work in the StatLog project comparing classification algorithms on large realworld problems. The algorithms compared were from: symbolic learning (CART, C4.5, NewID, AC 2 , ITrule, Cal5, CN2), statistics (Naive Bayes, knearest neighbor, kernel density, linear discriminant, quadratic discriminant, logistic regression, projection pursuit, Bayesian networks), and neural networks (backpropagation, radial basis functions). Twelve datasets were used: five from image analysis, three from medicine, and two each from engineering and finance. We found that which algorithm performed best depended critically on the dataset investigated. We therefore developed a set of dataset descriptors to help decide which algorithms are suited to particular datasets. For example, datasets with extreme distributions (skew ? 1 and kurtosis ? 7) and with many binary/categorical attributes (? 38%) tend to favor symbolic learning algorithms. We suggest how classification algorith...
An Implementation of Logical Analysis of Data
 IEEE Transactions on Knowledge and Data Engineering
, 2000
"... The paper describes a new, logicbased methodology for analyzing observations. The key features of the Logical Analysis of Data (LAD) are the discovery of minimal sets of features necessary for explaining all observations and the detection of hidden patterns in the data capable of distinguishing o ..."
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Cited by 47 (25 self)
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The paper describes a new, logicbased methodology for analyzing observations. The key features of the Logical Analysis of Data (LAD) are the discovery of minimal sets of features necessary for explaining all observations and the detection of hidden patterns in the data capable of distinguishing observations describing positive outcome events from negative outcome events. Combinations of such patterns are used for developing general classification procedures. An implementation of this methodology is described in the paper along with the results of numerical experiments demonstrating the classification performance of LAD in comparison with the reported results of other procedures. In the final section, we describe three pilot studies on applications of LAD to oil exploration, psychometric testing, and the analysis of developments in the Chinese transitional economy. These pilot studies demonstrate not only the classification power of LAD, but also its flexibility and capability t...
A Novel Evolutionary Data Mining Algorithm With Applications to Churn Prediction
, 2003
"... Classification is an important topic in data mining research. Given a set of data records, each of which belongs to one of a number of predefined classes, the classification problem is concerned with the discovery of classification rules that can allow records with unknown class membership to be cor ..."
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Cited by 40 (4 self)
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Classification is an important topic in data mining research. Given a set of data records, each of which belongs to one of a number of predefined classes, the classification problem is concerned with the discovery of classification rules that can allow records with unknown class membership to be correctly classified. Many algorithms have been developed to mine large data sets for classification models and they have been shown to be very effective. However, when it comes to determining the likelihood of each classification made, many of them are not designed with such purpose in mind. For this, they are not readily applicable to such problem as churn prediction. For such an application, the goal is not only to predict whether or not a subscriber would switch from one carrier to another, it is also important that the likelihood of the subscriber's doing so be predicted. The reason for this is that a carrier can then choose to provide special personalized offer and services to those subscribers who are predicted with higher likelihood to churn. Given its importance, we propose a new data mining algorithm, called data mining by evolutionary learning (DMEL), to handle classification problems of which the accuracy of each predictions made has to be estimated. In performing its tasks, DMEL searches through the possible rule space using an evolutionary approach that has the following characteristics: 1) the evolutionary process begins with the generation of an initial set of firstorder rules (i.e., rules with one conjunct/condition) using a probabilistic induction technique and based on these rules, rules of higher order (two or more conjuncts) are obtained iteratively; 2) when identifying interesting rules, an objective interestingness measure is used; 3) the fitness of a ch...
Theoretical Foundations Of Linear And Order Statistics Combiners For Neural Pattern Classifiers
 IEEE Transactions on neural networks
, 1996
"... : 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 paper provides an analytical framework to quantify the improvements in classification results ..."
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Cited by 29 (5 self)
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: 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 paper provides an analytical framework to quantify the improvements in classification results due to combining. The results apply to both linear combiners and the order statistics combiners introduced in this paper. We show that combining networks in output space reduces the variance of the actual decision region boundaries around the optimum boundary. For linear combiners, we show that in the absence of classifier bias, the added classification error is proportional to the boundary variance. For nonlinear combiners, we show analytically that the selection of the median, the maximum and in general the ith order statistic improves classifier performance. The analysis presented here facilitates the understanding of the relationships among error rates, classifier boundary distributions...
Learning from sparse data by exploiting monotonicity constraints
 Conf. Uncertainty in Artificial Intelligence
, 2005
"... When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into le ..."
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Cited by 18 (3 self)
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When training data is sparse, more domain knowledge must be incorporated into the learning algorithm in order to reduce the effective size of the hypothesis space. This paper builds on previous work in which knowledge about qualitative monotonicities was formally represented and incorporated into learning algorithms (e.g., Clark & Matwinâ€™s work with the CN2 rule learning algorithm). We show how to interpret knowledge of qualitative influences, and in particular of monotonicities, as constraints on probability distributions, and to incorporate this knowledge into Bayesian network learning algorithms. We show that this yields improved accuracy, particularly with very small training sets. 1