Projection pursuit-based dimensionality reduction

Dimensionality Reduction (DR) has found many applications in hyperspectral image processing, e.g., data compression, endmember extraction. This paper investigates Projection Pursuit (PP)-based data dimensionality reduction where three approaches are developed. One is to use a Projection Index (PI) to produce projection vectors that can be used to generate Projection Index Components (PICs). It is a common practice that PP generally uses random initial conditions to produce PICs. As a result, when the same PP is performed in different times or different users at the same time, the resulting PICs are generally not the same. In order to resolve this issue, two approaches are proposed. One is referred to as PI-based PRioritized PP (PI-PRPP) which uses a PI as a criterion to prioritize PICs that are produced by any component analysis, for example, Principal Components Analysis (PCA) or Independent Component Analysis. The other approach is called Initialization-Driven PP (ID-PP) which specifies an appropriate set of initial conditions that allows PP to not only produce PICs in the same order but also the same PICs regardless of how many times PP is run or who runs the PP.