N-finder algorithm (N-FINDR) is probably one of most popular and widely used algorithms used for endmember
extraction. Three major obstacles need to be overcome in its practical implementation. One is that the number of
endmembers must be known a priori. A second one is the use of random initial endmembers to initialize N-FINDR,
which results in inconsistent final results of extracted endmembers. A third one is its very expensive computational cost
caused by an exhaustive search. While the first two issues can be resolved by a recently developed concept, virtual
dimensionality (VD) and custom-designed initialization algorithms respectively, the third issue seems to remain
challenging. This paper addresses the latter issue by re-designing N-FINDR which can generate one endmember at a
time sequentially in a successive fashion to ease computational complexity. Such resulting algorithm is called
SeQuential N-FINDR (SQ N-FINDR) as opposed to the original N-FINDR referred to as SiMultaneous N-FINDR (SM
N-FINDR) which generates all endmembers simultaneously at once. Two variants of SQ N-FINDR can be further
derived to reduce computational complexity. Interestingly, experimental results show that SQ N-FINDR can perform as
well as SM-N-FINDR if initial endmembers are appropriately selected.
Endmember extraction has received considerable interest in recent years. Many algorithms have been developed for this
purpose and most of them are designed based on convexity geometry such as vertex or endpoint projection and
maximization of simplex volume. This paper develops statistics-based approaches to endmember extraction in the sense
that different orders of statistics are used as criteria to extract endmembers. The idea behind the proposed statistics-based
endmember extraction algorithms (EEAs) is to assume that a set of endmmembers constitute the most un-correlated
sample pool among all the same number of signatures with correlation measured by statistics which include variance
specified by 2nd order statistics, least squares error (LSE) also specified by 2nd order statistics, skewness 3rd order
statistics, kurtosis 4th order statistics, kth moment and statistical independency specified by infinite order of statistics
measured by mutual information. In order to substantiate proposed statistics-based EEAs, experiments using synthetic
and real images are conducted for demonstration.
Endmember extraction has received considerable interest in recent years. Many algorithms have been developed for this
purpose and most of them are designed based on convexity geometry such as vertex or endpoint projection and
maximization of simplex volume. This paper develops statistics-based approaches to endmember extraction in the sense
that different orders of statistics are used as criteria to extract endmembers. The idea behind the proposed statistics-based
endmember extraction algorithms (EEAs) is to assume that a set of endmmembers constitute the most un-correlated
sample pool among all the same number of signatures with correlation measured by statistics which include variance
specified by 2nd order statistics, least squares error (LSE) also specified by 2nd order statistics (variance), 3rd order
statistics (skewness), 4th order statistics (kurtosis), kth moment, entropy specified by infinite order of statistics and
statistical independency measured by mutual information. Of particular interest are Independent Component Analysis-based
EEAs which use statistics of various orders such as variance, skewness, kurtosis the kth moment and infinite orders
including entropy and divergence. In order to substantiate proposed statistics-based EEAs, experiments using synthetic
and real images are conducted in comparison with several popular and well-known EEAs such as Pixel Purity Index
(PPI), N-finder algorithm (N-FINDR).
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