A MULTIPLE SEPARATION FUNCTION FOR PATTERN CLASSIFICATION,
Abstract
This paper develops a method for classifying any object which can be represented as a point in n-space into one of m given subsets by constructing a linear function which is derived from the support function in linear topological space, an approach hitherto unexplored in this connection. Greenberg and Konheim (1964) discussed this problem of classification scheme by presenting two possible procedures: one is to use pairwise class separation, and the other is to construct m linear functions which separate one of the sets from all the others. The former requires the construction of m(-1)/2 linear functions, and the latter places more stringent restrictions on the m subsets than the former. The author shows in this report how to construct m instead of m(m-1)/2, linear functions under the more liberal assumptions of the first procedure, thus combining the merits of both procedures. The application of his procedure to a problem in the classification of sequences of student responses on the PLATO teaching system is discussed. In that connection, a possible further development, an even simpler method requiring only one linear function, was explored. The validity of this simpler method could, however, be established only under rather restrictive conditions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1966
- Accession Number
- AD0640541
Entities
People
- Kikumi Tatsuoka
Organizations
- University of Illinois Urbana–Champaign