Hyperspectral Data Processing: Algorithm Design and Analysis

10.4 Random N-FINDR (RN-FINDR)

The idea of RN-FINDR can also be illustrated by the coin flipping example described in the introduction in the same way as RPPI is interpreted in Section 10.2. In this case, the number of N trials is the total number of data sample vectors. Since the randomness of N-FINDR is caused by its use of p random initial endmembers and not by the number of endmembers, which is fixed at p, the number of the heads turned up in N trials used by the coin flipping experiment, n_H, is then interpreted as the number of times a data sample vector r extracted by N-FINDR as an endmember, denoted as n_N-FINDR(r) where each trial represents one single run and N trials indicates that N-FINDR has run N times. So, a single run is defined by implementing N-FINDR using one random set of p initial endmembers and the set of its final p extracted endmembers is called a realization of N-FINDR resulting from a random set of p initial endmembers. An algorithm implementing N-FINDR in such a manner is RN-FINDR.

Random N-FINDR (RN-FINDR)

1. Initialization

Assume that n_VD is the value estimated by VD and p. Let denote a counter to dictate the number of runs required to implement N-FNDR and E⁽¹⁾ = 0 and for all data sample vectors, r, and let k = 1.

2. At the kth run, apply N-FINDR on ...