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We introduce a new fuzzy relational clustering technique with Local Scaling Parameter Learning (LSPL). The proposed approach learns the underlying cluster dependent dissimilarity measure while finding compact clusters in the given data set. The learned measure is a Gaussian similarity function defined with respect to each cluster that allows to control the scaling of the clusters and thus, improve the final partition. We minimize one objective function for both the optimal partition and for the cluster dependent scaling parameter. This optimization is done iteratively by dynamically updating the partition and the scaling parameter in each iteration. This makes the proposed algorithm simple and fast. Moreover, as we assume that the data is available in a relational form, the proposed approach is applicable even when only the degree to which pairs of objects in the data are related is available. It is also more practical when similar objects cannot be represented by a single prototype.

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A new hyperspectral endmember detection method that represents endmembers as distributions, autonomously partitions the input data set into several convex regions, and simultaneously determines endmember distributions and proportion values for each convex region is presented. Spectral unmixing methods that treat endmembers as distributions or hyperspectral images as piece-wise convex data sets have not been previously developed. Piece-wise Convex Endmember detection, PCE, can be viewed in two parts, the first, the Endmember Distributions detection (ED) algorithm, estimates a distribution for each endmember rather than estimating a single spectrum. By using endmember distributions, PCE can incorporate an endmember's inherent spectral variation and the variation due to changing environmental conditions. ED uses a new sparsity-promoting polynomial prior while estimating abundance values. The second part of PCE partitions the input hyperspectral data set into convex regions and estimates endmember distributions and proportions for each of these regions. The number of convex regions is determined autonomously using the Dirichlet process. PCE is effective at handling highly-mixed hyperspectral images where all of the pixels in the scene contain mixtures of multiple endmembers. Furthermore, each convex region found by PCE conforms to the Convex Geometry Model for hyperspectral imagery. This model requires that the proportions associated with a pixel be non-negative and sum-to-one. Algorithm results on hyperspectral data indicate that PCE produces endmembers that represent the true ground truth classes of the input data set. The algorithm can also effectively represent endmembers as distributions, thus, incorporating an endmember's spectral variability.

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