Learning Riemannian Metrics
This work addresses metric learning for manifolds, with domain-specific applications in text classification, but appears incremental as it builds on existing concepts like TFIDF.
The paper tackles the problem of estimating a Riemannian metric for a differentiable manifold by minimizing the relative volume of a set of points, with results applied to the multinomial simplex for text classification, showing similarity to TFIDF representations.
We propose a solution to the problem of estimating a Riemannian metric associated with a given differentiable manifold. The metric learning problem is based on minimizing the relative volume of a given set of points. We derive the details for a family of metrics on the multinomial simplex. The resulting metric has applications in text classification and bears some similarity to TFIDF representation of text documents.