An algorithm for finding projections with extreme kurtosis

Projection pursuit is a multivariate statistical technique aimed at finding interesting low-dimensional data projections. A projection pursuit index is a function which associates a data projection to a real value measuring its interestingness: the higher the index, the more interesting the projection. Consequently, projection pursuit looks for the data projection which maximizes the projection pursuit index. The absolute value of the fourth standardized cumulant is a prominent projection pursuit index. In the general case, a projection achieving either minimal or maximal kurtosis poses computational difficulties. We address them by an algorithm which converges to the global optimum, whose computational advantages are illustrated with air pollution data.