Instance-based learning techniques typically handle continuous and linear input values well, but often do not handle nominal input attributes appropriately. The Value Difference Metric (VDM) was designed to find reasonable distance values between nominal attribute values, but it largely ignores continuous attributes, requiring discretization to map continuous values into nominal values. This paper proposes three new heterogeneous distance functions, called the Heterogeneous Value Difference Metric (HVDM), the Interpolated Value Difference Metric (IVDM), and the Windowed Value Difference Metric (WVDM). These new distance functions are designed to handle applications with nominal attributes, continuous attributes, or both. In experiments on 48 applications the new distance metrics achieve higher classification accuracy on average than three previous distance functions on those datasets that have both nominal and continuous attributes. 1. Introduction Instance-Based Learning (IBL) (Aha, ...

. Instance-based learning algorithms are often faced with the problem of deciding which instances to store for use during generalization. Storing too many instances can result in large memory requirements and slow execution speed, and can cause an oversensitivity to noise. This paper has two main purposes. First, it provides a survey of existing algorithms used to reduce storage requirements in instance-based learning algorithms and other exemplar-based algorithms. Second, it proposes six additional reduction algorithms called DROP1--DROP5 and DEL (three of which were first described in Wilson & Martinez, 1997c, as RT1--RT3) that can be used to remove instances from the concept description. These algorithms and 10 algorithms from the survey are compared on 31 classification tasks. Of those algorithms that provide substantial storage reduction, the DROP algorithms have the highest average generalization accuracy in these experiments, especially in the presence of uniform class noise. ...

The nearest neighbor algorithm and its derivatives are often quite successful at learning a concept from a training set and providing good generalization on subsequent input vectors. However, these techniques often retain the entire training set in memory, resulting in large memory requirements and slow execution speed, as well as a sensitivity to noise. This paper provides a discussion of issues related to reducing the number of instances retained in memory while maintaining (and sometimes improving) generalization accuracy, and mentions algorithms other researchers have used to address this problem. It presents three intuitive noise-tolerant algorithms that can be used to prune instances from the training set. In experiments on 29 applications, the algorithm that achieves the highest reduction in storage also results in the highest generalization accuracy of the three methods.

The basic nearest neighbour classifier suffers from the indiscriminate storage of all presented training instances. With a large database of instances classification response time can be slow. When noisy instances are present classification accuracy can suffer. Drawing on the large body of relevant work carried out in the past 30 years, we review the principle approaches to solving these problems. By deleting instances, both problems can be alleviated, but the criterion used is typically assumed to be all encompassing and effective over many domains. We argue against this position and introduce an algorithm that rivals the most successful existing algorithm. When evaluated on 30 different problems, neither algorithm consistently outperforms the other: consistency is very hard. To achieve the best results, we need to develop mechanisms that provide insights into the structure of class definitions. We discuss the possibility of these mechanisms and propose some initial measures that could be useful for the data miner.

. Case-based reasoning systems solve problems by reusing a corpus of previous problem solving experience stored as a case-base of individual problem solving cases. In this paper we describe a new technique for constructing compact competent case-bases. The technique is novel in its use of an explicit model of case competence. This allows cases to be selected on the basis of their individual competence contributions. An experimental study shows how this technique compares favorably to more traditional strategies across a range of standard data-sets. 1 Introduction Case-based reasoning (CBR) solves problems by reusing the solutions to similar problems stored as cases in a case-base [9]. Two important factors contribute to the performance of a CBR system. First there is competence, that is the range of target problems that can be successfully solved. Second, there is efficiency, the computational cost of solving a set of target problems. Competence and efficiency both depend cri...

Combining the predictions of a set of classifiers has been shown to be an effective way to create composite classifiers that are more accurate than any of the component classifiers. Increased accuracy has been shown in a variety of real-world applications, ranging from protein sequence identification to determining the fat content of ground meat. Despite such individual successes, the answers are not known to fundamental questions about classifier combination, such as "Can classifiers from any given model class be combined to create a composite classifier with higher accuracy?" or "Is it possible to increase the accuracy of a given classifier by combining its predictions with those of only a small number o...

Exemplar-based learning algorithms are often faced with the problem of deciding which instances or other exemplars to store for use during generalization. Storing too many exemplars can result in large memory requirements and slow execution speed, and can cause an oversensitivity to noise. This paper has two main purposes. First, it provides a survey of existing algorithms used to reduce the number of exemplars retained in exemplar-based learning models. Second, it proposes six new reduction algorithms called DROP1-5 and DEL that can be used to prune instances from the concept description. These algorithms and 10 algorithms from the survey are compared on 31 datasets. Of those algorithms that provide substantial storage reduction, the DROP algorithms have the highest generalization accuracy in these experiments, especially in the presence of noise.

The basic nearest-neighbor rule generalizes well in many domains but has several shortcomings, including inappropriate distance functions, large storage requirements, slow execution time, sensitivity to noise, and an inability to adjust its decision boundaries after storing the training data. This paper proposes methods for overcoming each of these weaknesses and combines these methods into a comprehensive learning system called the Integrated Decremental Instance-Based Learning Algorithm (IDIBL) that seeks to reduce storage, improve execution speed, and increase generalization accuracy, when compared to the basic nearest neighbor algorithm and other learning models. IDIBL tunes its own parameters using a new measure of fitness that combines confidence and cross-validation (CVC) accuracy in order to avoid discretization problems with more traditional leave-one-out cross-validation (LCV). In our experiments IDIBL achieves higher generalization accuracy than other less comprehensive instance-based learning algorithms, while requiring less than onefourth the storage of the nearest neighbor algorithm and improving execution speed by a corresponding factor. In experiments on 21 datasets, IDIBL also achieves higher generalization accuracy than those reported for 16 major machine learning and neural network models.

In the typical nonparametric approach to pattern classification, random data (the training set of patterns) are collected and used to design a decision rule (classifier). One of the most well known such rules is the k-nearest-neighbor decision rule (also known as instance-based learning, and lazy learning) in which an unknown pattern is classified into the majority class among its k nearest neighbors in the training set. Several questions related to this rule have received considerable attention over the years. Such questions include the following. How can the storage of the training set be reduced without degrading the performance of the decision rule? How should the reduced training set be selected to represent the different classes? How large should k be? How should the value of k be chosen? Should all k neighbors be equally weighted when used to decide the class of an unknown pattern? If not, how should the weights be chosen? Should all the features (attributes) we weighted equally and if not how should the feature weights be chosen? What distance metric should be used? How can the rule be made robust to overlapping classes or noise present in the training data? How can the rule be made invariant to scaling of the measurements? Geometric proximity graphs such as Voronoi diagrams and their many relatives provide elegant solutions to most of these problems. After a brief and non-exhaustive review of some of the classical canonical approaches to solving these problems, the methods that use proximity graphs are discussed, some new observations are made, and avenues for further research are proposed.

This paper is an continuation of the accompanying paper with the same main title. The first paper reviewed instance selection algorithms, here results of empirical comparison and comments are presented. Several test