End members, end points and extragrades in numerical soil classification

Soil classification has progressed with the introduction of computers in the mid 20th century to the point where algorithms can be used to organise soil information into clusters that correspond with soil classes. Algorithms such as fuzzy-k means perform well, but can be biased by extreme data. Fuzzy-k means with extragrades was devised to accommodate this problem but estimating the amount of extragrades can be challenging and can lead to dubious classifications. The idea of end members is discussed and it is concluded that end points, observations that represent the most extreme parts of the soil continuum, are useful in the identification of extragrades. We present and discuss a new clustering algorithm, akromeson which identifies extreme points in a given data set and converts them into pseudo clusters, which are then run concurrently with a semi-supervised fuzzy-k means algorithm. We constructed a synthetic data set in order to compare this new method to fuzzy-k means and fuzzy-k means with extragrades. It was able to correctly fix the positions of the centroids, (which was beyond the capacity of fuzzy-k means), and correctly estimated which of the data were genuine extragrades, outperforming fuzzy-k means with extragrades. We then evaluated the performance of akromeson on a data set from the Edgeroi region of New South Wales, Australia. The algorithm identified an extreme cluster on the periphery of the data, and a method was determined on how to use this new method to routinely find clusters. The ability to efficiently cluster data may provide an added advantage to pedologists generally and to stakeholders when they are assessing land use practices, especially in regard to areas which exhibit extreme soil properties that require careful management, which this algorithm is capable of detecting.