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Summary.A general method for exploring multivariate data by comparing different estimates of multivariate scatter is presented. The method is based on the eigenvalue-eigenvector decomposition of one scatter matrix relative to another. In particular, it is shown that the eigenvectors can be used to generate an affine invariant co-ordinate system for the multivariate data. Consequently, we view this method as a method for invariant co-ordinate selection. By plotting the data with respect to this new invariant co-ordinate system, various data structures can be revealed. For example, under certain independent components models, it is shown that the invariant coordinates correspond to the independent components. Another example pertains to mixtures of elliptical distributions. In this case, it is shown that a subset of the invariant co-ordinates corresponds to Fisher's linear discriminant subspace, even though the class identifications of the data points are unknown. Some illustrative examples are given.

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The compound-Gaussian (CG) distributions have been successfully used for modelling the non-Gaussian clutter measured by high-resolution radars. Within the CG class, the complex -distribution and the complex -distribution have been used for modelling sea clutter which is often heavy-tailed or spiky in nature. In this paper, a heavy-tailed CG model with an inverse Gaussian texture distribution is proposed and its distributional properties such as closed-form expressions for its probability density function (p.d.f.) as well as its amplitude p.d.f., amplitude cumulative distribution function and its kurtosis parameter are derived. Experimental validation of its usefulness for modelling measured real-world radar lake-clutter is provided where it is shown to yield better fits than its widely used competitors.

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