A Nonparametric Recognition Procedure with Storage Constraint,
Abstract
A procedure is described for determining a decision rule for the one-dimensional, two class recognition problem with unknown, nonparametric, class-conditional density functions. A priori class probabilities are known, and the densities are assumed to satisfy Lipschitz conditions with known Lipschitz constant. The procedure is essentially a histogram approach where the partition for the histogram is changed as directed by a performance measure. It is desirable to minimize the difference between the probability of a recognition error when using the decision rule and the minimum attainable probability of recognition error. For a fixed partition conditions are stated that assure achievement of a specified confidence that this difference is below a specified constant. The variable partition procedure operates with limited storage and allows, but does not assure, attainment of the specified confidence. Computer simulated results are given that experimentally illustrate attainment of the desired confidence for the problems considered. A technique is suggested for extending the procedure to multidimensions. This technique converts the multidimensional problem to a one-dimensional problem. It operates by mapping sets in a multidimensional domain one-to-one onto sets in a one-dimensional domain. Computer simulated results are presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1969
- Accession Number
- ADA031727
Entities
People
- E. A. Patrick
- F. K. Bechtel
Organizations
- Purdue University