This article describes a new system for induction of oblique decision trees. This system, OC1, combines deterministic hill-climbing 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 axis-parallel 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...

Neural networks, despite their empirically-proven abilities, have been little used for the refinement of existing knowledge because this task requires a three-step process. First, knowledge in some form must be inserted into a neural network. Second, the network must be refined. Third, knowledge must be extracted from the network. We have previously described a method for the first step of this process. Standard neural learning techniques can accomplish the second step. In this paper, we propose and empirically evaluate a method for the final, and possibly most difficult, step. This method efficiently extracts symbolic rules from trained neural networks. The four major results of empirical tests of this method are that the extracted rules: (1) closely reproduce (and can even exceed) the accuracy of the network from which they are extracted; (2) are superior to the rules produced by methods that directly refine symbolic rules; (3) are superior to those produced by previous techniques fo...

Decision trees have proved to be valuable tools for the description, classification and generalization of data. Work on constructing decision trees from data exists in multiple disciplines such as statistics, pattern recognition, decision theory, signal processing, machine learning and artificial neural networks. Researchers in these disciplines, sometimes working on quite different problems, identified similar issues and heuristics for decision tree construction. This paper surveys existing work on decision tree construction, attempting to identify the important issues involved, directions the work has taken and the current state of the art. Keywords: classification, tree-structured classifiers, data compaction 1. Introduction Advances in data collection methods, storage and processing technology are providing a unique challenge and opportunity for automated data exploration techniques. Enormous amounts of data are being collected daily from major scientific projects e.g., Human Genome...

This paper describes an experimental comparison of seven different learning algorithms on the problem of learning to disambiguate the meaning of a word from context. The algorithms tested include statistical, neural-network, decision-tree, rule-based, and case-based classification techniques. The specific problem tested involves disambiguating six senses of the word "line" using the words in the current and proceeding sentence as context. The statistical and neural-network methods perform the best on this particular problem and we discuss a potential reason for this ob- served difference. We also discuss the role of bias in machine ]earning and its importance in explaining performance differences observed on specific problems.

Abstract Despite the fact that many symbolic and neural network (connectionist) learning algorithms address the same problem of learning from classified examples, very little is known regarding their comparative strengths and weaknesses. Experiments comparing the ID3 symbolic learning algorithm with the perception and backpropagation neural learning algorithms have been performed using five large, real-world data sets. Overall, backpropagation performs slightly better than the other two algorithms in terms of classification accuracy on new examples, but takes much longer to train. Experimental results suggest that backpropagation can work significantly better on data sets containing numerical data. Also analyzed empirically are the effects of (1) the amount of training data, (2) imperfect training examples, and (3) the encoding of the desired outputs. Backpropagation occasionally outperforms the other two systems when given relatively small amounts of training data. It is slightly more accurate than ID3 when examples are noisy or incompletely specified. Finally, backpropagation more effectively utilizes a "distributed " output encoding.

Many lazy learning algorithms are derivatives of the k-nearest neighbor (k-NN) classifier, which uses a distance function to generate predictions from stored instances. Several studies have shown that k-NN's performance is highly sensitive to the definition of its distance function. Many k-NN variants have been proposed to reduce this sensitivity by parameterizing the distance function with feature weights. However, these variants have not been categorized nor empirically compared. This paper reviews a class of weight-setting methods for lazy learning algorithms. We introduce a framework for distinguishing these methods and empirically compare them. We observed four trends from our experiments and conducted further studies to highlight them. Our results suggest that methods which use performance feedback to assign weight settings demonstrated three advantages over other methods: they require less pre-processing, perform better in the presence of interacting features, and generally require less training data to learn good settings. We also found that continuous weighting methods tend to outperform feature selection algorithms for tasks where some features are useful but less important than others.

This paper introduces a randomized technique for partitioning examples using oblique hyperplanes. Standard decision tree techniques, such as ID3 and its descendants, partition a set of points with axis-parallel hyperplanes. Our method, by contrast, attempts to find hyperplanes at any orientation. The purpose of this more general technique is to find smaller but equally accurate decision trees than those created by other methods. We have tested our algorithm on both real and simulated data, and found that in some cases it produces surprisingly small trees without losing predictive accuracy. Small trees allow us, in turn, to obtain simple qualitative descriptions of each problem domain. 1 Introduction Decision trees have been used successfully for many different decision making and classification tasks. A number of standard techniques have been developed in the machine learning community, most notably Quinlan's ID3 (1986) and Breiman et al.'s CART (1984). Since the introduction of thes...

The main contributions of this thesis are a Bayesian theory of learning classification rules, the unification and comparison of this theory with some previous theories of learning, and two extensive applications of the theory to the problems of learning class probability trees and bounding error when learning logical rules. The thesis is motivated by considering some current research issues in machine learning such as bias, overfitting and search, and considering the requirements placed on a learning system when it is used for knowledge acquisition. Basic Bayesian decision theory relevant to the problem of learning classification rules is reviewed, then a Bayesian framework for such learning is presented. The framework has three components: the hypothesis space, the learning protocol, and criteria for successful learning. Several learning protocols are analysed in detail: queries, logical, noisy, uncertain and positive-only examples. The analysis is done by interpreting a protocol as a...

Abstract. Supervised learning in attribute-based spaces is one of the most popular machine learning problems studied and, consequently, has attracted considerable attention of the genetic algorithm community. The fullmemory approach developed here uses the same nigh-level descriptive language that is used in rule-based systems. This allows for an easy utilization of inference rules of the well-known inductive learning methodology, which replace the traditional domain-independent operators and make the search task-specific. Moreover, a closer relationship between the underlying task and the processing mechanisms provides a setting for an application of more powerful task-specific heuristics. Initial results obtained with a prototype implementation for the simplest case of single concepts indicate that genetic algorithms can be effectively used to process nigh-level concepts and incorporate task-specific knowledge. The method of abstracting the genetic algorithm to the problem level, described here for the supervised inductive learning, can be also extended to other domains and tasks, since it provides a framework for combining recently popular genetic algorithm methods with traditional problem-solving methodologies. Moreover, in this particular case, it provides a very powerful tool enabling study of the widely accepted but not so well understood inductive learning methodology.

We exhibit a theoretically founded algorithm T2 for agnostic PAC-learning of decision trees of at most 2 levels, whose computation time is almost linear in the size of the training set. We evaluate the performance of this learning algorithm T2 on 15 common "real-world" datasets, and show that for most of these datasets T2 provides simple decision trees with little or no loss in predictive power (compared with C4.5). In fact, for datasets with continuous attributes its error rate tends to be lower than that of C4.5. To the best of our knowledge this is the first time that a PAC-learning algorithm is shown to be applicable to "real-world" classification problems. Since one can prove that T2 is an agnostic PAClearning algorithm, T2 is guaranteed to produce close to optimal 2-level decision trees from sufficiently large training sets for any (!) distribution of data. In this regard T2 differs strongly from all other learning algorithms that are considered in applied machine learning, for w...