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Agnostic Learning of Geometric Patterns
 Journal of Computer and System Sciences
, 1997
"... Goldberg, Goldman, and Scott demonstrated how the problem of recognizing a landmark from a onedimensional visual image can be mapped to that of learning a onedimensional geometric pattern and gave a PAC algorithm to learn that class. In this paper, we present an efficient online agnostic learning ..."
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Goldberg, Goldman, and Scott demonstrated how the problem of recognizing a landmark from a onedimensional visual image can be mapped to that of learning a onedimensional geometric pattern and gave a PAC algorithm to learn that class. In this paper, we present an efficient online agnostic learning algorithm for learning the class of constantdimension geometric patterns. Our algorithm can tolerate both classification and attribute noise. By working in higher dimensional spaces we can represent more features from the visual image in the geometric pattern. Our mapping of the data to a geometric pattern, and our hence our learning algorithm, is applicable to any data representable as a constantdimensional array of values, e.g. sonar data, temporal difference infor...
MultipleInstance Learning of RealValued Geometric Patterns
 Annals of Mathematics and Artificial Intelligence
, 2000
"... Recently, there has been a significant amount of research studying the multipleinstance learning model, yet all of this work has only considered this model when there are boolean labels. However, in many of the application areas for which the multipleinstance model fits, realvalued labels are more ..."
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Recently, there has been a significant amount of research studying the multipleinstance learning model, yet all of this work has only considered this model when there are boolean labels. However, in many of the application areas for which the multipleinstance model fits, realvalued labels are more appropriate than boolean labels. In this paper we define and study a realvalued multipleinstance model in which each multipleinstance example is given a realvalued classification in [0, 1]. The realvalued classification indicates the degree to which the example satisfies the target concept. To provide additional structure to the resulting learning problem, we associate a realvalued label with each point in the multipleinstance example. These values are then combined using a realvalued aggregation operator to obtain the classification for the example. Motivated by the possible application of learning geometric patterns to problems in pattern recognition and scene classification (with...
Geometric Patterns: Algorithms and Applications
 In: Proceedings of the ICML 2000 Workshop on Machine Learning of Spatial Knowledge
"... We review definitions of various concept classes called geometric patterns, which are based on a measure of visual similarity called the Hausdorff metric. These classes generalize multipleinstance learning models, and have possible applications to areas including robot vision, drug activity predict ..."
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Cited by 1 (1 self)
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We review definitions of various concept classes called geometric patterns, which are based on a measure of visual similarity called the Hausdorff metric. These classes generalize multipleinstance learning models, and have possible applications to areas including robot vision, drug activity prediction, and contentbased image retrieval. We also briefly describe algorithms (which have provable guarantees of time complexity and predictive performance) to learn these concept classes. We then summarize ongoing empirical work to evaluate these algorithms on real data.
Exploring Applications of Learning Theory to Pattern Matching and Dynamic Adjustment of TCP Acknowledgment Delays
, 1998
"... Learning theory is a subarea of machine learning that applies results from theoretical computer science, including complexity theory and algorithm design and analysis. In learning theory we rigorously study the efficiency and predictive performance of learning algorithms. While applications of mac ..."
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Learning theory is a subarea of machine learning that applies results from theoretical computer science, including complexity theory and algorithm design and analysis. In learning theory we rigorously study the efficiency and predictive performance of learning algorithms. While applications of machine learning are wellknown, results from learning theory are just beginning to enter the practical arena. The purpose of this dissertation is to develop learning theory algorithms and take initial steps toward modifying them and applying them to practical problems. Here we look at two problems. One is learning geometric patterns, with a preliminary investigation of the learning algorithms' applicability to pattern matching, particularly landmark matching for robot navig...
Agnostic Learning of General Geometric Patterns and MultiInstance Learning in ℜ d
"... The concept class of geometric patterns has been heavily studied and has applications in pattern recognition. Previous work on this concept class has been restricted to one or two dimensions or to finite and discretized domains. We present an algorithm to learn a very flexible generalization of prev ..."
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The concept class of geometric patterns has been heavily studied and has applications in pattern recognition. Previous work on this concept class has been restricted to one or two dimensions or to finite and discretized domains. We present an algorithm to learn a very flexible generalization of previously studied geometric patterns in any constantdimensional real space, making its potential applicability to pattern matching very high since it can operate on any data representable as a constantdimensional array of values. To our knowledge, these classes of patterns are more complex than any class of geometric patterns previously studied. We also give variations of our algorithms to learn the union of constantdimensional geometric objects from multipleinstance examples. 1.
Agnostic Learning of Geometric Patterns (Extended Abstract)
, 1997
"... ) Sally A. Goldman Dept. of Computer Science Washington University St. Louis, MO 63130 sg@cs.wustl.edu Stephen S. Kwek Dept. of Computer Science Washington University St. Louis, MO 63130 kwek@cs.wustl.edu Stephen D. Scott Dept. of Computer Science Washington University St. Louis, MO 63130 ..."
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) Sally A. Goldman Dept. of Computer Science Washington University St. Louis, MO 63130 sg@cs.wustl.edu Stephen S. Kwek Dept. of Computer Science Washington University St. Louis, MO 63130 kwek@cs.wustl.edu Stephen D. Scott Dept. of Computer Science Washington University St. Louis, MO 63130 sds@cs.wustl.edu Abstract Goldberg, Goldman, and Scott demonstrated how the problem of recognizing a landmark from a onedimensional visual image can be mapped to that of learning a onedimensional geometric pattern and gave a PAC algorithm to learn that class. We present an online agnostic learning algorithm for learning the class of onedimensional geometric patterns. Since, when moving from the processed visual image to a onedimensional pattern some key information is lost, we define a class of twodimensional geometric patterns for which the important features from the visual image are incorporated in the geometric pattern, and show how to extend our agnostic learning algorithm to t...