Covariance fields

Nikolay H. Balov

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arXiv · 0807.4690

Covariance fields

Nikolay H. Balov

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Abstract

We introduce and study covariance fields of distributions on a Riemannian manifold. At each point on the manifold, covariance is defined to be a symmetric and positive definite (2,0)-tensor. Its product with the metric tensor specifies a linear operator on the respected tangent space. Collectively, these operators form a covariance operator field. We show that, in most circumstances, covariance fields are continuous. We also solve the inverse problem: recovering distribution from a covariance field. Surprisingly, this is not possible on Euclidean spaces. On non-Euclidean manifolds however, covariance fields are true distribution representations.

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Nikolay H. Balov. 2009-01-15. Covariance fields. https://arxiv.org/abs/0807.4690

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