Learning and Geometry: Computational Approaches

1. Front Matter

   Pages i-xiii

   PDF

2. Learning

   1. Front Matter

      Pages 1-1

      PDF

   2. Learning by MDL

      • J. Rissanen, Bin Yu

      Pages 3-19

   3. Pac Learning, Noise, and Geometry

      • Robert H. Sloan

      Pages 21-41

   4. A Review of Some Extensions to the PAC Learning Model

      • Sanjeev R. Kulkarni

      Pages 43-64

3. Geometry

   1. Front Matter

      Pages 65-65

      PDF

   2. Finite Point Sets and Oriented Matroids Combinatorics in Geometry

      • Jürgen Bokowski

      Pages 67-96

   3. A Survey of Geometric Reasoning Using Algebraic Methods

      • Shang-Ching Chou, Xiao-Shan Gao

      Pages 97-119

   4. Synthetic vs Analytic Geometry for Computers

      • Walter Whiteley

      Pages 121-141

   5. Representing Geometric Configurations

      • Walter Whiteley

      Pages 143-178

   6. Geometry Theorem Proving in Euclidean, Descartesian, Hilbertian and Computerwise Fashion

      • Wu Wen-Tsün

      Pages 179-210

4. Back Matter

   Pages 211-212

   PDF

The field of computational learning theory arose out of the desire to for­ mally understand the process of learning. As potential applications to artificial intelligence became apparent, the new field grew rapidly. The learning of geo­ metric objects became a natural area of study. The possibility of using learning techniques to compensate for unsolvability provided an attraction for individ­ uals with an immediate need to solve such difficult problems. Researchers at the Center for Night Vision were interested in solving the problem of interpreting data produced by a variety of sensors. Current vision techniques, which have a strong geometric component, can be used to extract features. However, these techniques fall short of useful recognition of the sensed objects. One potential solution is to incorporate learning techniques into the geometric manipulation of sensor data. As a first step toward realizing such a solution, the Systems Research Center at the University of Maryland, in conjunction with the Center for Night Vision, hosted a Workshop on Learning and Geometry in January of 1991. Scholars in both fields came together to learn about each others' field and to look for common ground, with the ultimate goal of providing a new model of learning from geometrical examples that would be useful in computer vision. The papers in the volume are a partial record of that meeting.

• algebra
• artificial intelligence
• combinatorics
• computer
• geometry

• Department of Mathematics, University of Maryland, College Park, USA

  David W. Kueker

• Department of Computer Science, University of Maryland, College Park, USA

  Carl H. Smith

Policies and ethics