Interactive Principal Components Analysis: A New Technological Resource in the Classroom

Abstract

Principal Components Analysis (PCA) is a mathematical technique widely used in multivariate statistics and pattern recognition. From a statistical point of view, PCA is an optimal linear transformation that eliminates the covariance structure of the data. From a geometrical point of view, it is simply a convenient axes rotation. A successful PCA application depends, at a certain point, on the comprehension of this geometrical concept; however, to visualize these axes rotation can be an important challenge for many students. At the present time, undergraduate students are immersed in a social environment with an increasing amount of collaborative and interactive elements. This situation gives us the opportunity to incorporate new and creative alternatives of knowledge transmission. We present an interactive educational software called Mi-iPCA, that helps students understand geometrical foundations of Principal Components Analysis. Based on the Nintendo’s Wiimote students manipulate axes rotation interactively in order to get a diagonal covariance matrix. The graphical environment shows different projections of the data, as well as several statistics like the percentage of variance explained by each component. Previous applications of this new pedagogical tool suggest that it constitutes an important didactic support in the classroom.