Structure-Preserving Method for Dimension Reduction

• Activity Number: 75
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Ewa Nowakowska*+
• Companies: Polish Academy of Sciences
• Keywords: dimension reduction ; linear discriminant analysis ; principal component analysis ; clustering

Abstract

Linear discriminant analysis (LDA) and principal component analysis (PCA) can be seen as alternative methods for dimension reduction. For k classes, the former returns a k-1 dimensional subspace S* which best discriminates given classes. The latter yields a subspace PC(k-1) spanned by k-1 eigenvectors corresponding to k-1 largest eigenvalues. As such, it grants largest overall variability but takes no partition into account. In general, the two subspaces may differ substantially. This work presents a method of preliminary data transformation which reduces dissimilarity between them without the knowledge of underlying data structure (classes). At the same time, it preserves initial distinctness of the classes' structure to a large extent. In the resulting subspace efficient clustering as well as other analyses of the unknown structure may be performed.