Application in clustering of density based techniques on boolean spaces

• Grant number: 06/03044-5
• Support Opportunities: Regular Research Grants
• Start date: May 01, 2007
• End date: April 30, 2009
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computer Systems
• Principal Investigator: Carlos Gustavo González
• Grantee: Carlos Gustavo González
• Host Institution: Pró-Reitoria de Pós-Graduação e Pesquisa. Universidade de Sorocaba (UNISO). Sorocaba , SP, Brazil

Abstract

In a previous research, the author considered the use of bit vectors (Boolean vectors) as elements of the metric space of the Boolean algebras, and introduced the use of these spaces in cluster analysis. Thus, the metric takes values in the Boolean algebra (i.e., in the space of bit vectors), and not in a linearly ordered set, such as R ou N. By using these techniques, some new algorithms were proposed, evaluated and compared with another ones in the literature. Given a set of elements of the Boolean spaces, we can formulate a simple notion of density by considering the quotient between the number of elements and the total number of points of the least closer ball (in the topological sense) which includes this set of elements. In clustering, we basically are looking for the regions of greatest density, and thus this research raised the question that density based techniques should be used in a more sophisticated way. For example, some techniques using relative density concepts yield results which are similar to the best ones in the literature. The aim of this project is to propose, evaluate and test new clustering algorithms based upon density techiniques. (AU)