Automatic clustering of multi-dimensional data (ACMD) applied to hyperspectral images

ACMD, a new algorithm for Automatic Clustering of Multi-dimensional Data, is a practical method for the automatic segmentation of hyperspectral images into distinct homogenous groupings. The ACMD algorithm employs a top-down approach in which clustered pixels are iteratively split into two sub-clusters. Statistical improvement of homogeneity is tested after each split cycle using a proximity test (PT) and a variance test (VT). PT calculates the ratio of the number of pixels in the sub-cluster that are closer to the mathematical mean of the sub-cluster than they are to the mathematical mean of the original. VT calculates the ratio of the sum of the variance within the two new clusters to variance in the original cluster. ACMD allows a choice of analysis based on prenormalized or non-normalized data sets using angular or Euclidean distance measurements. Splitting is halted when either the PT or VT ratio is greater than predetermined thresholds, unless VT variance in one new segment is ≤ 10 ^-3 of the original cluster. Analysis of synthetic data sets and of real hyperspectral data images is presented.