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Clustering, Coding, and the Concept of S...
McCarty, L. Thorne...

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Clustering, Coding, and the Concept of Similarity by McCarty, L. Thorne ( Author )
Lemonjar Open Access
Australian National University
01-09-2023
This paper develops a theory of clustering and coding which combines a geometric model with a probabilistic model in a principled way. The geometric model is a Riemannian manifold with a Riemannian metric, ${g}_{ij}({\bf x})$, which we interpret as a measure of dissimilarity. The probabilistic model consists of a stochastic process with an invariant probability measure which matches the density of the sample input data. The link between the two models is a potential function, $U({\bf x})$, and its gradient, $\nabla U({\bf x})$. We use the gradient to define the dissimilarity metric, which guarantees that our measure of dissimilarity will depend on the probability measure. Finally, we use the dissimilarity metric to define a coordinate system on the embedded Riemannian manifold, which gives us a low-dimensional encoding of our original data.
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Article
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29.34 KB
English
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MYR 0.01
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http://arxiv.org/abs/1401.2411
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