Hyperspectral Data Processing: Algorithm Design and Analysis

20.3 Representation of Transformed Components for DP

When the data are linearly transformed from the original data space to a new data space, each transformed data sample vector is essentially a linear combination or mixture of data sample vectors in the original space. In order to effectively represent the data in this new linearly transformed data space, it is desirable to find a set of basic constituent elements that can serve as a base for all the transformed data sample vectors. In this case, each basic constituent element represents a one-dimensional transformed component whose information significance can be measured by an information criterion. This section presents one such approach that can be considered as a generalization of PCA and ICA.

20.3.1 Projection Index-Based PP

In Section 6.5, an approach called projection pursuit (PP) is developed to generalize PCA and ICA to a PP-based component analysis transform in which the PP-transformed components are specified by projection vectors derived from a more general concept called projection index (PI). Such a PI-based PP is referred to as PIPP and its generated transformed components can be ranked by an information measure for DP. Although PIPP is already given in Section 6.5.1 of Chapter 6, we recap its details here for reference.

The term “PP”, as first coined by Friedman and Tukey (1974), was used to represent a technique for exploratory analysis of multivariate data. The idea is to project a high-dimensional data set ...