Semi-Definite Programming as a Model for Statistical Data Analysis

In this monograph I present a method to derive a minimum rank covariance matrix for several continuous variables. The minimum rank problem appears in many areas of multivariate analysis as well as in many applications of multivariate analysis such as in biology, medicine, psychology, pharmacology, and machine learning. The method seems to be extremely powerful and enjoys many optimal properties. It is a non-linear distribution-free method that encompases under its umberla major topics such as Factor Analysis, Principal Componens Analysis, MDS, and Multiple Regression. The monograph is composed of two papers, the first of which sets the foundations and the theoratical basis for developing the underlying theory. It also presents several applications of the method. As for the second paper, it includes several examples of a completely different type of applications of the method. In these applications values of interactions are derived from only binary data such as low and high levels of interaction among pairs of objects. The key in all these applications is the low rank property of the covariance matrix which is the criterion for optimality of the method.