# Geometric-Unconstrained Progressive Endmember Finding: Orthogonal Projection Analysis

## Abstract

Chapter 8 develops a Causal Iterative Pixel Purity Index (C-IPPI) which can implement IPPI in a causal manner in the sense that each data sample vector is fully processed sample-by-sample one after another for a given fixed set of skewers to produce its own final PPI count. This chapter presents a rather different version of IPPI, referred to as Progressive IPPI (P-IPPI) by interchanging two iterative loops carried out in C-IPPI. In other words, P-IPPI can implement IPPI progressively in the sense that each data sample vector is processed by IPPI with growing sets of skewers skewer by skewer one after another. That is, for the number of skewers, *K*, each data sample vector will be processed by IPPI progressively as the number of skewers grows to from 1 to *K* and its PPI count will also be updated *K* times as every new skewer is processed. As a result, P-IPPI is quite different from C-IPPI from an algorithm design perspective. In particular, comparing C-IPPI, which requires the prior knowledge about the value of *K* and processes each data sample vector for all skewers sample by sample, P-IPPI processes all data sample vectors skewer by skewer with the value of *K* increased by one after each iteration is completed. Consequently, in theory P-IPPI can be implemented skewer by skewer progressively by increasing the value of *K* indefinitely. Nevertheless, for a fixed number of skewers, *K*, both C-IPPI and P-IPPI eventually produce identical results. In analogy with C-IPPI, the same major advantages that can be gained from C-IPPI are applied to P-IPPI. The only advantage provided by P-IPPI that C-IPPI does not have is that there is no need for P-IPPI to determine the value of *K*, while C-IPPI requires prior knowledge about the value of *K*.

## Keywords

Outer Loop Background Pixel Progressive Process Minimum Projection Panel Signature## References

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