Much of previous attention on decision trees focuses on the splitting criteria and optimization of tree sizes. The dilemma between overfitting and achieving maximum accuracy is seldom resolved. We propose a method to construct a decision tree based classifier that maintains highest accuracy on training data and improves on generalization accuracy as it grows in complexity. The classifier consists of multiple trees constructed systematically by pseudorandomly selecting subsets of components of the feature vector, that is, trees constructed in randomly chosen subspaces. The subspace method is compared to single-tree classifiers and other forest construction methods by experiments on publicly available datasets, where the method's superiority is demonstrated. We also discuss independence between trees in a forest and relate that to the combined classification accuracy. keywords: pattern recognition, decision tree, decision forest, stochastic discrimination, decision combination, classif...

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...

We introduce a very large family of binary features for two-dimensional shapes. The salient ones for separating particular shapes are determined by inductive learning during the construction of classi cation trees. There is a feature for every possible geometric arrangement of local topographic codes. The arrangements express coarse constraints on relative angles and distances among the code locations and are nearly invariant to substantial a ne and non-linear deformations. They are also partially ordered, which makes it possible to narrow the search for informative ones at each node of the tree. Di erent trees correspond to di erent aspects of shape. They are statistically weakly dependent due to randomization and are aggregated in a simple way. Adapting the algorithm to a shape family is then fully automatic once training samples are provided. As an illustration, we classify handwritten digits from the NIST database � the error rate is:7%.

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 non-linear 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.

: 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 non-linear 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...

The identification and classification of underwater acoustic signals is an extremely difficult problem because of low SNRs and a high degree of variability in the signals emanated from the same type of sound source. Since different classification techniques have different inductive biases, a single method cannot give the best results for all signal types. Rather, more accurate and robust classification can obtained by combining the outputs (evidences) of multiple classifiers based on neural network and/or statistical pattern recognition techniques. In this paper, five approaches are compared for integrating the decisions made by networks using sigmoidal activation functions exhibiting global responses with those made by localized basis function networks. These methods are compared using realistic oceanic data. The first method uses an entropy-based weighting of individual classifier outputs. The second is based on combination of confidence factors in a manner similar to that used in MY...

In medical decision making (classification, diagnosing, etc.) there are many situations where decision must be made effectively and reliably. Conceptual simple decision making models with the possibility of automatic learning are the most appropriate for performing such tasks. Decision trees are a reliable and effective decision making technique that provide high classification accuracy with a simple representation of gathered knowledge and they have been used in different areas of medical decision making. In the paper we present the basic characteristics of decision trees and the successful alternatives to the traditional induction approach with the emphasis on existing and possible future applications in medicine. Key words: decision trees, classification, decision making, machine learning 1.

Broad classes of statistical classification algorithms have been developed and applied successfully to a wide range of real world domains. In general, ensuring that the particular classification algorithm matches the properties of the data is crucial in providing results that meet the needs of the particular application domain. One way in which the impact of this algorithm/application match can be alleviated is by using ensembles of classifiers, where a variety of classifiers (either different types of classifiers or different instantiations of the same classifier) are pooled before a final classification decision is made. Intuitively, classifier ensembles allow the different needs of a difficult problem to be handled by classifiers suited to those particular needs. Mathematically, classifier ensembles provide an extra degree of freedom in the classical bias/variance tradeoff, allowing solutions that would be difficult (if not impossible) to reach with only a single classifier. Because of these advantages, classifier ensembles have been applied to many difficult real world problems. In this paper, we survey select applications of ensemble methods to problems that have historically been most representative of the difficulties in classification. In particular, we survey applications of ensemble methods to remote sensing, person recognition, one vs. all recognition, and medicine.

Traditional approaches to document object location use a single locator that is expected to locate as many instances of the object class of interest as possible. However, if the class includes subclasses with diverse visual characteristics or is not characterized by easily computable visual features, it is difficult for the single locator to account for wide variation in object characteristics within the class. As a result, increasingly complex models of objects to be located are used. An alternative approach is to combine the decisions of multiple locators, each of which is suitable for certain image conditions. This approach utilizes a collection of simple locators that complement one another, rather than relying on one complex locator. An effective method for combining the location results is vital to the success of this approach. This thesis presents a theory of combining the results of multiple document object locators tuned to different object characteristics. The purpose of the ...