Hempel's Raven paradox: a positive approach to cluster analysis

Abstract

A practical conclusion of the Hampel Raven paradox suggests a logical preference for using positive predicates in formulating scientific hypotheses. This led us to outline a new cluster analysis and grouping technique. We define a positive attribute distance (PAD) index that uses a binary representation of the existence or absence of an attribute value in a given object being observed. The resulting binary string representing an entity is then used to calculate distance to other strings using only the ‘1’ bits. This measure, with a matching grouping technique, simplifies clustering and grouping and yields equivalent or better results, as well as more efficient and compact calculations. Scope and purpose Cluster analysis is widely used in many fields of social science. Its basic aim is to assign individuals or objects under study into groups so that they have a high degree of similarity within the group, and that the groups are to be distinct. Various methods have been developed for clustering including regression and other statistical techniques. This paper introduces a new approach for clustering by using a computer representation form – binary 1 and 0 digits. A binary matrix is constructed from the data where rows represent the individuals (entities) and columns are values of attributes measured. The binary content of the matrix indicates which entity has or lacks certain attributes. This representation, simple, compact, and efficient in terms of computer application, allows clustering and grouping calculations that take into account only the positive attributes. Such technique compares favorably with conventional binary representation and has potential for use in cluster analysis.