In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach. Index Terms: Boolean functions, symbolic manipulation, binary decision diagrams, logic design verification 1.

In the feature subset selection problem, a learning algorithm is faced with the problem of selecting a relevant subset of features upon which to focus its attention, while ignoring the rest. To achieve the best possible performance with a particular learning algorithm on a particular training set, a feature subset selection method should consider how the algorithm and the training set interact. We explore the relation between optimal feature subset selection and relevance. Our wrapper method searches for an optimal feature subset tailored to a particular algorithm and a domain. We study the strengths and weaknesses of the wrapper approach and show a series of improved designs. We compare the wrapper approach to induction without feature subset selection and to Relief, a filter approach to feature subset selection. Significant improvement in accuracy is achieved for some datasets for the two families of induction algorithms used: decision trees and

We address the problem of finding a subset of features that allows a supervised induction algorithm to induce small high-accuracy concepts. We examine notions of relevance and irrelevance, and show that the definitions used in the machine learning literature do not adequately partition the features into useful categories of relevance. We present definitions for irrelevance and for two degrees of relevance. These definitions improve our understanding of the behavior of previous subset selection algorithms, and help define the subset of features that should be sought. The features selected should depend not only on the features and the target concept, but also on the induction algorithm. We describe a method for feature subset selection using cross-validation that is applicable to any induction algorithm, and discuss experiments conducted with ID3 and C4.5 on artificial and real datasets.

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...

This article presents an incremental algorithm for inducing decision trees equivalent to those formed by Quinlan's nonincremental ID3 algorithm, given the same training instances. The new algorithm, named ID5R, lets one apply the ID3 induction process to learning tasks in which training instances are presented serially.

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...

The standard approach to decision tree induction is a top-down, greedy algorithm that makes locally optimal, irrevocable decisions at each node of a tree. In this paper, we study an alternative approach, in which the algorithms use limited lookahead to decide what test to use at a node. We systematically compare, using a very large number of decision trees, the quality of decision trees induced by the greedy approach to that of trees induced using lookahead. The main results of our experiments are: (i) the greedy approach produces trees that are just as accurate as trees produced with the much more expensive lookahead step; and (ii) decision tree induction exhibits pathology, in the sense that lookahead can produce trees that are both larger and less accurate than trees produced without it. 1. Introduction The standard algorithm for constructing decision trees from a set of examples is greedy induction --- a tree is induced top-down with locally optimal choices made at each node, with...

. We investigate the use of oblivious, read-once decision graphs as structures for representing concepts over discrete domains, and present a bottom-up, hill-climbing algorithm for inferring these structures from labelled instances. The algorithm is robust with respect to irrelevant attributes, and experimental results show that it performs well on problems considered difficult for symbolic induction methods, such as the Monk's problems and parity. 1 Introduction Top down induction of decision trees [25, 24, 20] has been one of the principal induction methods for symbolic, supervised learning. The tree structure, which is used for representing the hypothesized target concept, suffers from some wellknown problems, most notably the replication problem and the fragmentation problem [23]. The replication problem forces duplication of subtrees in disjunctive concepts, such as (A B) (C D); the fragmentation problem causes partitioning of the data into fragments, when a high-arity attrib...

Despite the success of many pattern recognition systems in constrained domains, problems that involve noisy input and many classes remain difficult. A promising direction is to use several classifiers simultaneously, such that they can complement each other in correctness. This thesis is concerned with decision combination in a multiple classifier system that is critical to its success. A multiple classifier system consists of a set of classifiers and a decision combination function. It is a preferred solution to a complex recognition problem because it allows simultaneous use of feature descriptors of many types, corresponding measures of similarity, and many classification procedures. It also allows dynamic selection, so that classifiers adapted to inputs of a particular type may be applied only when those inputs are encountered. Decisions by the classifiers are represented as rankings of the class set that are derivable from the results of feature matching. Rank scores contain more ...

this paper, we consider a variety of problems with application to sequencing by hybridization. First, we develop a theory of interactive sequencing by hybridization, based on