Pattern Dependence Detection using n-TARP Clustering

Consider an experiment involving a potentially small number of subjects. Some random variables are observed on each subject: a high-dimensional one called the "observed" random variable, and a one-dimensional one called the "outcome" random variable. We are interested in the dependencies between the observed random variable and the outcome random variable. We propose a method to quantify and validate the dependencies of the outcome random variable on the various patterns contained in the observed random variable. Different degrees of relationship are explored (linear, quadratic, cubic, ...). This work is motivated by the need to analyze educational data, which often involves high-dimensional data representing a small number of students. Thus our implementation is designed for a small number of subjects; however, it can be easily modified to handle a very large dataset. As an illustration, the proposed method is used to study the influence of certain skills on the course grade of students in a signal processing class. A valid dependency of the grade on the different skill patterns is observed in the data.