Department of Computer Science and Electrical Engineering, University of Maryland, Baltimore County, Baltimore, MD 21250, USA.
IEEE Trans Image Process. 2011 Mar;20(3):641-56. doi: 10.1109/TIP.2010.2071310. Epub 2010 Sep 2.
N-finder algorithm (N-FINDR) has been widely used in endmember extraction. When it comes to implementation several issues need to be addressed. One is determination of endmembers, p required for N-FINDR to generate. Another is its computational complexity resulting from an exhaustive search. A third one is its requirement of dimensionality reduction. A fourth and probably the most critical issue is its use of random initial endmembers which results in inconsistent final endmember selection and results are not reproducible. This paper re-invents the wheel by re-designing the N-FINDR in such a way that all the above-mentioned issues can be resolved while making the last issue an advantage. The idea is to implement the N-FINDR as a random algorithm, called random N-FINDR (RN-FINDR) so that a single run using one set of random initial endmembers is considered as one realization. If there is an endmember present in the data, it should appear in any realization regardless of what random set of initial endmembers is used. In this case, the N-FINDR is terminated when the intersection of all realizations produced by two consecutive runs of RN-FINDR remains the same in which case the p is then automatically determined by the intersection set without appealing for any criterion. In order to substantiate the proposed RN-FINDR custom-designed synthetic image experiments with complete knowledge are conducted for validation and real image experiments are also performed to demonstrate its utility in applications.
N-finder 算法（N-FINDR）已被广泛应用于端元提取。在实现时，需要解决几个问题。一个是确定 N-FINDR 生成所需的端元数量 p。另一个是由于穷举搜索而导致的计算复杂性。第三个是其对降维的要求。第四个也是最关键的问题可能是它使用随机初始端元，这导致最终端元选择不一致，结果不可重复。本文通过重新设计 N-FINDR 来解决所有上述问题，同时将最后一个问题转化为优势，从而实现了创新。该想法是将 N-FINDR 实现为一种随机算法，称为随机 N-FINDR（RN-FINDR），以便使用一组随机初始端元进行的单次运行被视为一次实现。如果数据中存在一个端元，那么无论使用哪个随机初始端元集，它都应该在任何实现中出现。在这种情况下，当两次连续运行的 RN-FINDR 产生的所有实现的交集相同时，N-FINDR 就会终止，此时 p 会自动由交集集确定，而无需使用任何标准进行请求。为了验证提出的 RN-FINDR，我们进行了专门设计的、具有完整先验知识的合成图像实验，以验证其有效性，并进行了真实图像实验，以展示其在应用中的实用性。
