Title: Limitations of projection pursuit methods for high dimensional data
Authors: Ana Maria Pires - University of Lisbon (Portugal)
Joao Antonio Branco - CEMAT Instituto Superior Tecnico Universidade de Lisboa (Portugal) [presenting]
Abstract: Any multivariate statistical method which can be defined as ``find a low-dimensional orthogonal projection of the data cloud such that a given statistic of the projected data is optimal'', is a projection pursuit method. Two famous examples are principal components and linear discriminant analysis. The advantage of the formulation as a projection pursuit method is that it offers an easy way to generalize the original method and to lift properties of univariate methods (assuming low = 1) to multivariate methods. For example, using appropriate robust univariate estimators one can easily produce robust principal components or robust linear discriminant functions. For some time it was thought that projection pursuit could bypass the curse of dimensionality. Unfortunately that is not the case. Using some recent results from high-dimensional geometry we will uncover some of the limitations of projection pursuit methods for high dimensional data and discuss possible alleviating solutions.