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What is Learnable in Valiant's Theory of the Learnable? 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Shape theory via affine transformation: Some generalisations
Jose A. Diaz-Garcia, Francisco J. Caro-Lopera · 2010-12-29 · via math.ST updates on arXiv.org

This work sets the statistical affine shape theory in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical distribution; then the separated published works about real and complex shape distributions can be obtained as corollaries by a suitable selection of the field parameter and univariate integrals involving the generator elliptical function. As a particular case, the complex normal affine density is derived and applied in brain magnetic resonance scans of normal and schizophrenic patients.

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