Supervised Invariant Coordinate Selection

• Activity Number: 39
• Type: Contributed
• Date/Time: Sunday, July 31, 2011 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Eero Liski and Klaus Nordhausen*+ and Hannu Oja
• Companies: University of Tampere and University of Tampere and University of Tampere
• Keywords: Dimension reduction ; Independent component analysis ; Scatter matrix ; Sliced inverse regression

Abstract

Dimension reduction plays an important role in high dimensional data analysis. Principal component analysis (PCA), independent component analysis (ICA), and sliced inversion regression (SIR) are well-known but very different analysis tools for dimension reduction. It appears that these three approaches can all be seen as the comparison of two different scatter matrices. In SIR the second scatter matrix is supervised and therefore the choice of the components is based on the dependence between the observed random vector and a response variable. Based on these notions, we extend the invariant coordinate selection (ICS), allowing the second scatter matrix to be supervised; supervised ICS can then be used in supervised dimension reduction. Several families of supervised scatter matrices are discussed, and their use in supervised dimension reduction is illustrated with an example and simulations. Some useful asymptotical results for statistical inference are also provided.